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                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
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                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
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                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
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                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
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                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
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                "kind": "paper_text",
                "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                "section_id": "sec_0022"
              }
            ],
            "library_release": "1.0.1",
            "library_sha256": "8baa240c279a84a1229eefd5f34e0527291086570378e20500f37bcb9f1f2caa",
            "lifecycle_phase": "unspecified",
            "model_role": "unresolved",
            "model_variant": "OKR-Cell input module",
            "nodes": [
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                "contextual_role": "sample_input",
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                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Measured single-cell expression",
                "node_id": "expression",
                "origin": "source_annotation",
                "representation_type": "expression_values",
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                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Identifiers aligned to expression positions",
                "node_id": "gene_ids",
                "origin": "source_annotation",
                "representation_type": "gene_identifiers",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
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                "axis_semantics": null,
                "contextual_role": "intermediate_representation",
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                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Log1p transformed expression",
                "node_id": "logged",
                "origin": "source_annotation",
                "representation_type": "log_expression",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "intermediate_representation",
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                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "HVG-selected expression",
                "node_id": "selected_values",
                "origin": "source_annotation",
                "representation_type": "selected_expression",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
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                "contextual_role": "intermediate_representation",
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                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Identifiers of the selected genes",
                "node_id": "selected_genes",
                "origin": "source_annotation",
                "representation_type": "selected_gene_identifiers",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
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                "contextual_role": "reference_resource",
                "evidence": [
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                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Gene identifier to vocabulary-index mapping",
                "node_id": "gene_vocabulary",
                "origin": "source_annotation",
                "representation_type": "vocabulary_table",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "intermediate_representation",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Vocabulary identifiers for selected genes",
                "node_id": "gene_indices",
                "origin": "source_annotation",
                "representation_type": "gene_vocabulary_indices",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
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                "evidence": [
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                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Equal-interval nonzero expression bins with zero preserved",
                "node_id": "bin_indices",
                "origin": "source_annotation",
                "representation_type": "expression_bin_indices",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
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                "axis_semantics": null,
                "contextual_role": "model_parameter",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Gene embedding-layer parameters emb_g; trainability unspecified in this section",
                "node_id": "gene_table",
                "origin": "source_annotation",
                "representation_type": "embedding_matrix",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "model_parameter",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Expression embedding-layer parameters emb_x; a separate table",
                "node_id": "bin_table",
                "origin": "source_annotation",
                "representation_type": "embedding_matrix",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "intermediate_representation",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Selected gene embedding vectors",
                "node_id": "gene_vectors",
                "origin": "source_annotation",
                "representation_type": "gene_embeddings",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "intermediate_representation",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Selected expression-bin embedding vectors",
                "node_id": "value_vectors",
                "origin": "source_annotation",
                "representation_type": "expression_embeddings",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "intermediate_representation",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Element-wise sum supplied to Transformer encoder blocks",
                "node_id": "fused",
                "origin": "source_annotation",
                "representation_type": "summed_input_embeddings",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              }
            ],
            "open_questions": [
              "Source title is marked WITHDRAWN in the inventory. This example describes the documented mechanism and changes no eligibility decision.",
              "Missing equations, HVG algorithm, matrix training status, special-token placement and phase-specific masking remain unspecified."
            ],
            "receipt_inputs": [
              {
                "node_id": "fused",
                "port_role": "input embeddings"
              }
            ],
            "recipient_component": "Transformer encoder blocks",
            "record_id": "full_2026-07-06__rec_001277",
            "source_steps": [
              {
                "component": "OKR-Cell input embedding module",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "inputs": [
                  {
                    "node_id": "expression",
                    "port_role": "values"
                  }
                ],
                "operation_type": "log_transform",
                "outputs": [
                  "logged"
                ],
                "step_id": "log",
                "uncertainty": "Section-only reconstruction; missing equations and training details remain unresolved."
              },
              {
                "component": "OKR-Cell input embedding module",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "inputs": [
                  {
                    "node_id": "logged",
                    "port_role": "values"
                  },
                  {
                    "node_id": "gene_ids",
                    "port_role": "values"
                  }
                ],
                "operation_type": "select",
                "outputs": [
                  "selected_values",
                  "selected_genes"
                ],
                "step_id": "hvg",
                "uncertainty": "Section-only reconstruction; missing equations and training details remain unresolved."
              },
              {
                "component": "OKR-Cell input embedding module",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "inputs": [
                  {
                    "node_id": "selected_genes",
                    "port_role": "keys"
                  },
                  {
                    "node_id": "gene_vocabulary",
                    "port_role": "table"
                  }
                ],
                "operation_type": "lookup",
                "outputs": [
                  "gene_indices"
                ],
                "step_id": "gene_token_ids",
                "uncertainty": "Section-only reconstruction; missing equations and training details remain unresolved."
              },
              {
                "component": "OKR-Cell input embedding module",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "inputs": [
                  {
                    "node_id": "selected_values",
                    "port_role": "values"
                  }
                ],
                "operation_type": "bin",
                "outputs": [
                  "bin_indices"
                ],
                "step_id": "bins",
                "uncertainty": "Section-only reconstruction; missing equations and training details remain unresolved."
              },
              {
                "component": "OKR-Cell input embedding module",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "inputs": [
                  {
                    "node_id": "gene_indices",
                    "port_role": "keys"
                  },
                  {
                    "node_id": "gene_table",
                    "port_role": "table"
                  }
                ],
                "operation_type": "lookup",
                "outputs": [
                  "gene_vectors"
                ],
                "step_id": "gene_lookup",
                "uncertainty": "Section-only reconstruction; missing equations and training details remain unresolved."
              },
              {
                "component": "OKR-Cell input embedding module",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "inputs": [
                  {
                    "node_id": "bin_indices",
                    "port_role": "keys"
                  },
                  {
                    "node_id": "bin_table",
                    "port_role": "table"
                  }
                ],
                "operation_type": "lookup",
                "outputs": [
                  "value_vectors"
                ],
                "step_id": "value_lookup",
                "uncertainty": "Section-only reconstruction; missing equations and training details remain unresolved."
              },
              {
                "component": "OKR-Cell input embedding module",
                "evidence": [
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                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "inputs": {
                  "keys": [
                    "selected_genes"
                  ],
                  "table": [
                    "gene_vocabulary"
                  ]
                },
                "operation_id": "lookup",
                "outputs": {
                  "values": [
                    "gene_indices"
                  ]
                },
                "parameters": {
                  "resource_kind": "gene vocabulary"
                },
                "source_step_id": "gene_token_ids",
                "status": "documented_operation",
                "uncertainty": "Section-only reconstruction; missing equations and training details remain unresolved."
              },
              {
                "call_id": "bins",
                "component": "OKR-Cell input embedding module",
                "condition": null,
                "evidence": [
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                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "inputs": {
                  "values": [
                    "selected_values"
                  ]
                },
                "operation_id": "bin",
                "outputs": {
                  "values": [
                    "bin_indices"
                  ]
                },
                "parameters": {
                  "bin_edges": "source-defined; formula not decoded",
                  "scope": "per_cell_nonzero_values",
                  "strategy": "equal_interval",
                  "zero_handling": "retain zero"
                },
                "source_step_id": "bins",
                "status": "documented_operation",
                "uncertainty": "Section-only reconstruction; missing equations and training details remain unresolved."
              },
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                "call_id": "gene_lookup",
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                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "inputs": {
                  "keys": [
                    "gene_indices"
                  ],
                  "table": [
                    "gene_table"
                  ]
                },
                "operation_id": "lookup",
                "outputs": {
                  "values": [
                    "gene_vectors"
                  ]
                },
                "parameters": {
                  "resource_kind": "embedding matrix",
                  "trainability": "unspecified"
                },
                "source_step_id": "gene_lookup",
                "status": "documented_operation",
                "uncertainty": "Section-only reconstruction; missing equations and training details remain unresolved."
              },
              {
                "call_id": "value_lookup",
                "component": "OKR-Cell input embedding module",
                "condition": null,
                "evidence": [
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                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "inputs": {
                  "keys": [
                    "bin_indices"
                  ],
                  "table": [
                    "bin_table"
                  ]
                },
                "operation_id": "lookup",
                "outputs": {
                  "values": [
                    "value_vectors"
                  ]
                },
                "parameters": {
                  "resource_kind": "embedding matrix",
                  "trainability": "unspecified"
                },
                "source_step_id": "value_lookup",
                "status": "documented_operation",
                "uncertainty": "Section-only reconstruction; missing equations and training details remain unresolved."
              },
              {
                "call_id": "fusion",
                "component": "OKR-Cell input embedding module",
                "condition": null,
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "inputs": {
                  "values": [
                    "gene_vectors",
                    "value_vectors"
                  ]
                },
                "operation_id": "add",
                "outputs": {
                  "values": [
                    "fused"
                  ]
                },
                "parameters": {
                  "alignment": "selected gene position and shared embedding feature coordinate"
                },
                "source_step_id": "fusion",
                "status": "documented_operation",
                "uncertainty": "Section-only reconstruction; missing equations and training details remain unresolved."
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                "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                "section_id": "sec_0022"
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            "model_role": "unresolved",
            "model_variant": "OKR-Cell input module",
            "nodes": [
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                "contextual_role": "sample_input",
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                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
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                "information_content": "Measured single-cell expression",
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                "origin": "source_annotation",
                "representation_type": "expression_values",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
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                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Identifiers aligned to expression positions",
                "node_id": "gene_ids",
                "origin": "source_annotation",
                "representation_type": "gene_identifiers",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "intermediate_representation",
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                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Log1p transformed expression",
                "node_id": "logged",
                "origin": "source_annotation",
                "representation_type": "log_expression",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
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                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "HVG-selected expression",
                "node_id": "selected_values",
                "origin": "source_annotation",
                "representation_type": "selected_expression",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "intermediate_representation",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Identifiers of the selected genes",
                "node_id": "selected_genes",
                "origin": "source_annotation",
                "representation_type": "selected_gene_identifiers",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "reference_resource",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Gene identifier to vocabulary-index mapping",
                "node_id": "gene_vocabulary",
                "origin": "source_annotation",
                "representation_type": "vocabulary_table",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "intermediate_representation",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Vocabulary identifiers for selected genes",
                "node_id": "gene_indices",
                "origin": "source_annotation",
                "representation_type": "gene_vocabulary_indices",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "intermediate_representation",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Equal-interval nonzero expression bins with zero preserved",
                "node_id": "bin_indices",
                "origin": "source_annotation",
                "representation_type": "expression_bin_indices",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "model_parameter",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Gene embedding-layer parameters emb_g; trainability unspecified in this section",
                "node_id": "gene_table",
                "origin": "source_annotation",
                "representation_type": "embedding_matrix",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "model_parameter",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Expression embedding-layer parameters emb_x; a separate table",
                "node_id": "bin_table",
                "origin": "source_annotation",
                "representation_type": "embedding_matrix",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "intermediate_representation",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Selected gene embedding vectors",
                "node_id": "gene_vectors",
                "origin": "source_annotation",
                "representation_type": "gene_embeddings",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "intermediate_representation",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Selected expression-bin embedding vectors",
                "node_id": "value_vectors",
                "origin": "source_annotation",
                "representation_type": "expression_embeddings",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "intermediate_representation",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Element-wise sum supplied to Transformer encoder blocks",
                "node_id": "fused",
                "origin": "source_annotation",
                "representation_type": "summed_input_embeddings",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              }
            ],
            "open_questions": [
              "Source title is marked WITHDRAWN in the inventory. This example describes the documented mechanism and changes no eligibility decision.",
              "Missing equations, HVG algorithm, matrix training status, special-token placement and phase-specific masking remain unspecified."
            ],
            "receipt_inputs": [
              {
                "node_id": "fused",
                "port_role": "input embeddings"
              }
            ],
            "recipient_component": "Transformer encoder blocks",
            "record_id": "full_2026-07-06__rec_001277",
            "source_steps": [
              {
                "component": "OKR-Cell input embedding module",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "inputs": [
                  {
                    "node_id": "expression",
                    "port_role": "values"
                  }
                ],
                "operation_type": "log_transform",
                "outputs": [
                  "logged"
                ],
                "step_id": "log",
                "uncertainty": "Section-only reconstruction; missing equations and training details remain unresolved."
              },
              {
                "component": "OKR-Cell input embedding module",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
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                ],
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                    "node_id": "logged",
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                  "selected_values",
                  "selected_genes"
                ],
                "step_id": "hvg",
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              },
              {
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                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
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                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
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                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
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                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
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                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "inputs": {
                  "keys": [
                    "selected_genes"
                  ],
                  "table": [
                    "gene_vocabulary"
                  ]
                },
                "operation_id": "lookup",
                "outputs": {
                  "values": [
                    "gene_indices"
                  ]
                },
                "parameters": {
                  "resource_kind": "gene vocabulary"
                },
                "source_step_id": "gene_token_ids",
                "status": "documented_operation",
                "uncertainty": "Section-only reconstruction; missing equations and training details remain unresolved."
              },
              {
                "call_id": "bins",
                "component": "OKR-Cell input embedding module",
                "condition": null,
                "evidence": [
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                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "inputs": {
                  "values": [
                    "selected_values"
                  ]
                },
                "operation_id": "bin",
                "outputs": {
                  "values": [
                    "bin_indices"
                  ]
                },
                "parameters": {
                  "bin_edges": "source-defined; formula not decoded",
                  "scope": "per_cell_nonzero_values",
                  "strategy": "equal_interval",
                  "zero_handling": "retain zero"
                },
                "source_step_id": "bins",
                "status": "documented_operation",
                "uncertainty": "Section-only reconstruction; missing equations and training details remain unresolved."
              },
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                "call_id": "gene_lookup",
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                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "inputs": {
                  "keys": [
                    "gene_indices"
                  ],
                  "table": [
                    "gene_table"
                  ]
                },
                "operation_id": "lookup",
                "outputs": {
                  "values": [
                    "gene_vectors"
                  ]
                },
                "parameters": {
                  "resource_kind": "embedding matrix",
                  "trainability": "unspecified"
                },
                "source_step_id": "gene_lookup",
                "status": "documented_operation",
                "uncertainty": "Section-only reconstruction; missing equations and training details remain unresolved."
              },
              {
                "call_id": "value_lookup",
                "component": "OKR-Cell input embedding module",
                "condition": null,
                "evidence": [
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                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "inputs": {
                  "keys": [
                    "bin_indices"
                  ],
                  "table": [
                    "bin_table"
                  ]
                },
                "operation_id": "lookup",
                "outputs": {
                  "values": [
                    "value_vectors"
                  ]
                },
                "parameters": {
                  "resource_kind": "embedding matrix",
                  "trainability": "unspecified"
                },
                "source_step_id": "value_lookup",
                "status": "documented_operation",
                "uncertainty": "Section-only reconstruction; missing equations and training details remain unresolved."
              },
              {
                "call_id": "fusion",
                "component": "OKR-Cell input embedding module",
                "condition": null,
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "inputs": {
                  "values": [
                    "gene_vectors",
                    "value_vectors"
                  ]
                },
                "operation_id": "add",
                "outputs": {
                  "values": [
                    "fused"
                  ]
                },
                "parameters": {
                  "alignment": "selected gene position and shared embedding feature coordinate"
                },
                "source_step_id": "fusion",
                "status": "documented_operation",
                "uncertainty": "Section-only reconstruction; missing equations and training details remain unresolved."
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                "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                "section_id": "sec_0022"
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            "model_role": "unresolved",
            "model_variant": "OKR-Cell input module",
            "nodes": [
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                "contextual_role": "sample_input",
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                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
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                "information_content": "Measured single-cell expression",
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                "origin": "source_annotation",
                "representation_type": "expression_values",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
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                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Identifiers aligned to expression positions",
                "node_id": "gene_ids",
                "origin": "source_annotation",
                "representation_type": "gene_identifiers",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "intermediate_representation",
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                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Log1p transformed expression",
                "node_id": "logged",
                "origin": "source_annotation",
                "representation_type": "log_expression",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
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                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "HVG-selected expression",
                "node_id": "selected_values",
                "origin": "source_annotation",
                "representation_type": "selected_expression",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "intermediate_representation",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Identifiers of the selected genes",
                "node_id": "selected_genes",
                "origin": "source_annotation",
                "representation_type": "selected_gene_identifiers",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "reference_resource",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Gene identifier to vocabulary-index mapping",
                "node_id": "gene_vocabulary",
                "origin": "source_annotation",
                "representation_type": "vocabulary_table",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "intermediate_representation",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Vocabulary identifiers for selected genes",
                "node_id": "gene_indices",
                "origin": "source_annotation",
                "representation_type": "gene_vocabulary_indices",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "intermediate_representation",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Equal-interval nonzero expression bins with zero preserved",
                "node_id": "bin_indices",
                "origin": "source_annotation",
                "representation_type": "expression_bin_indices",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "model_parameter",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Gene embedding-layer parameters emb_g; trainability unspecified in this section",
                "node_id": "gene_table",
                "origin": "source_annotation",
                "representation_type": "embedding_matrix",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "model_parameter",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Expression embedding-layer parameters emb_x; a separate table",
                "node_id": "bin_table",
                "origin": "source_annotation",
                "representation_type": "embedding_matrix",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "intermediate_representation",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Selected gene embedding vectors",
                "node_id": "gene_vectors",
                "origin": "source_annotation",
                "representation_type": "gene_embeddings",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "intermediate_representation",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Selected expression-bin embedding vectors",
                "node_id": "value_vectors",
                "origin": "source_annotation",
                "representation_type": "expression_embeddings",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "intermediate_representation",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Element-wise sum supplied to Transformer encoder blocks",
                "node_id": "fused",
                "origin": "source_annotation",
                "representation_type": "summed_input_embeddings",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              }
            ],
            "open_questions": [
              "Source title is marked WITHDRAWN in the inventory. This example describes the documented mechanism and changes no eligibility decision.",
              "Missing equations, HVG algorithm, matrix training status, special-token placement and phase-specific masking remain unspecified."
            ],
            "receipt_inputs": [
              {
                "node_id": "fused",
                "port_role": "input embeddings"
              }
            ],
            "recipient_component": "Transformer encoder blocks",
            "record_id": "full_2026-07-06__rec_001277",
            "source_steps": [
              {
                "component": "OKR-Cell input embedding module",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "inputs": [
                  {
                    "node_id": "expression",
                    "port_role": "values"
                  }
                ],
                "operation_type": "log_transform",
                "outputs": [
                  "logged"
                ],
                "step_id": "log",
                "uncertainty": "Section-only reconstruction; missing equations and training details remain unresolved."
              },
              {
                "component": "OKR-Cell input embedding module",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
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                    "node_id": "logged",
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                  {
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                ],
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                "outputs": [
                  "selected_values",
                  "selected_genes"
                ],
                "step_id": "hvg",
                "uncertainty": "Section-only reconstruction; missing equations and training details remain unresolved."
              },
              {
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                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
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                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
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                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
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                  "keys": [
                    "selected_genes"
                  ],
                  "table": [
                    "gene_vocabulary"
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                },
                "operation_id": "lookup",
                "outputs": {
                  "values": [
                    "gene_indices"
                  ]
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                "parameters": {
                  "resource_kind": "gene vocabulary"
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                "source_step_id": "gene_token_ids",
                "status": "documented_operation",
                "uncertainty": "Section-only reconstruction; missing equations and training details remain unresolved."
              },
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                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "inputs": {
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                    "selected_values"
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                "operation_id": "bin",
                "outputs": {
                  "values": [
                    "bin_indices"
                  ]
                },
                "parameters": {
                  "bin_edges": "source-defined; formula not decoded",
                  "scope": "per_cell_nonzero_values",
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                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
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                "inputs": {
                  "keys": [
                    "gene_indices"
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                  "table": [
                    "gene_table"
                  ]
                },
                "operation_id": "lookup",
                "outputs": {
                  "values": [
                    "gene_vectors"
                  ]
                },
                "parameters": {
                  "resource_kind": "embedding matrix",
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                },
                "source_step_id": "gene_lookup",
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              },
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                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "inputs": {
                  "keys": [
                    "bin_indices"
                  ],
                  "table": [
                    "bin_table"
                  ]
                },
                "operation_id": "lookup",
                "outputs": {
                  "values": [
                    "value_vectors"
                  ]
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                "parameters": {
                  "resource_kind": "embedding matrix",
                  "trainability": "unspecified"
                },
                "source_step_id": "value_lookup",
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                "uncertainty": "Section-only reconstruction; missing equations and training details remain unresolved."
              },
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                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "inputs": {
                  "values": [
                    "gene_vectors",
                    "value_vectors"
                  ]
                },
                "operation_id": "add",
                "outputs": {
                  "values": [
                    "fused"
                  ]
                },
                "parameters": {
                  "alignment": "selected gene position and shared embedding feature coordinate"
                },
                "source_step_id": "fusion",
                "status": "documented_operation",
                "uncertainty": "Section-only reconstruction; missing equations and training details remain unresolved."
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                "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
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                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
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                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
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                ],
                "information_content": "Identifiers aligned to expression positions",
                "node_id": "gene_ids",
                "origin": "source_annotation",
                "representation_type": "gene_identifiers",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
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                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Log1p transformed expression",
                "node_id": "logged",
                "origin": "source_annotation",
                "representation_type": "log_expression",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
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                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
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                ],
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                "node_id": "selected_values",
                "origin": "source_annotation",
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                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
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                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Identifiers of the selected genes",
                "node_id": "selected_genes",
                "origin": "source_annotation",
                "representation_type": "selected_gene_identifiers",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "reference_resource",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Gene identifier to vocabulary-index mapping",
                "node_id": "gene_vocabulary",
                "origin": "source_annotation",
                "representation_type": "vocabulary_table",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "intermediate_representation",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Vocabulary identifiers for selected genes",
                "node_id": "gene_indices",
                "origin": "source_annotation",
                "representation_type": "gene_vocabulary_indices",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "intermediate_representation",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Equal-interval nonzero expression bins with zero preserved",
                "node_id": "bin_indices",
                "origin": "source_annotation",
                "representation_type": "expression_bin_indices",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "model_parameter",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Gene embedding-layer parameters emb_g; trainability unspecified in this section",
                "node_id": "gene_table",
                "origin": "source_annotation",
                "representation_type": "embedding_matrix",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "model_parameter",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Expression embedding-layer parameters emb_x; a separate table",
                "node_id": "bin_table",
                "origin": "source_annotation",
                "representation_type": "embedding_matrix",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "intermediate_representation",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Selected gene embedding vectors",
                "node_id": "gene_vectors",
                "origin": "source_annotation",
                "representation_type": "gene_embeddings",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "intermediate_representation",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Selected expression-bin embedding vectors",
                "node_id": "value_vectors",
                "origin": "source_annotation",
                "representation_type": "expression_embeddings",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "intermediate_representation",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Element-wise sum supplied to Transformer encoder blocks",
                "node_id": "fused",
                "origin": "source_annotation",
                "representation_type": "summed_input_embeddings",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              }
            ],
            "open_questions": [
              "Source title is marked WITHDRAWN in the inventory. This example describes the documented mechanism and changes no eligibility decision.",
              "Missing equations, HVG algorithm, matrix training status, special-token placement and phase-specific masking remain unspecified."
            ],
            "receipt_inputs": [
              {
                "node_id": "fused",
                "port_role": "input embeddings"
              }
            ],
            "recipient_component": "Transformer encoder blocks",
            "record_id": "full_2026-07-06__rec_001277",
            "source_steps": [
              {
                "component": "OKR-Cell input embedding module",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "inputs": [
                  {
                    "node_id": "expression",
                    "port_role": "values"
                  }
                ],
                "operation_type": "log_transform",
                "outputs": [
                  "logged"
                ],
                "step_id": "log",
                "uncertainty": "Section-only reconstruction; missing equations and training details remain unresolved."
              },
              {
                "component": "OKR-Cell input embedding module",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "inputs": [
                  {
                    "node_id": "logged",
                    "port_role": "values"
                  },
                  {
                    "node_id": "gene_ids",
                    "port_role": "values"
                  }
                ],
                "operation_type": "select",
                "outputs": [
                  "selected_values",
                  "selected_genes"
                ],
                "step_id": "hvg",
                "uncertainty": "Section-only reconstruction; missing equations and training details remain unresolved."
              },
              {
                "component": "OKR-Cell input embedding module",
                "evidence": [
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                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
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                    "port_role": "keys"
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                ],
                "operation_type": "lookup",
                "outputs": [
                  "gene_indices"
                ],
                "step_id": "gene_token_ids",
                "uncertainty": "Section-only reconstruction; missing equations and training details remain unresolved."
              },
              {
                "component": "OKR-Cell input embedding module",
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                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
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                "uncertainty": "Section-only reconstruction; missing equations and training details remain unresolved."
              },
              {
                "component": "OKR-Cell input embedding module",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
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                    "port_role": "keys"
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                    "node_id": "gene_table",
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                  }
                ],
                "operation_type": "lookup",
                "outputs": [
                  "gene_vectors"
                ],
                "step_id": "gene_lookup",
                "uncertainty": "Section-only reconstruction; missing equations and training details remain unresolved."
              },
              {
                "component": "OKR-Cell input embedding module",
                "evidence": [
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                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
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                "inputs": [
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                    "node_id": "bin_table",
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                  }
                ],
                "operation_type": "lookup",
                "outputs": [
                  "value_vectors"
                ],
                "step_id": "value_lookup",
                "uncertainty": "Section-only reconstruction; missing equations and training details remain unresolved."
              },
              {
                "component": "OKR-Cell input embedding module",
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                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
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                "inputs": [
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                    "node_id": "gene_vectors",
                    "port_role": "values"
                  },
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                    "node_id": "value_vectors",
                    "port_role": "values"
                  }
                ],
                "operation_type": "add",
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                  "fused"
                ],
                "step_id": "fusion",
                "uncertainty": "Section-only reconstruction; missing equations and training details remain unresolved."
              }
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              "x_control",
              "x_target"
            ]
          },
          "parameters": {
            "criterion": "protein-coding and shared gene selection; aligned sources",
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              "control set",
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              "forced-inclusion perturbation gene",
              "protein-coding feature-selection reference"
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              "x_control",
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            "criterion": "protein-coding and shared gene selection; aligned sources",
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              "x_target"
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          },
          "parameters": {
            "criterion": "protein-coding and shared gene selection; aligned sources",
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              "protein-coding feature-selection reference"
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              "x_target"
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          },
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            "criterion": "protein-coding and shared gene selection; aligned sources",
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              "target_set",
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              "x_control",
              "x_target"
            ]
          },
          "parameters": {
            "criterion": "protein-coding and shared gene selection; aligned sources",
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              "x_control",
              "x_target"
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          },
          "parameters": {
            "criterion": "protein-coding and shared gene selection; aligned sources",
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                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "inputs": {
                  "values": [
                    "expression"
                  ]
                },
                "operation_id": "log_transform",
                "outputs": {
                  "values": [
                    "logged"
                  ]
                },
                "parameters": {
                  "method": "log1p"
                },
                "source_step_id": "log",
                "status": "documented_operation",
                "uncertainty": "Section-only reconstruction; missing equations and training details remain unresolved."
              },
              {
                "call_id": "hvg",
                "component": "OKR-Cell input embedding module",
                "condition": null,
                "evidence": [
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                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "inputs": {
                  "values": [
                    "logged",
                    "gene_ids"
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                },
                "operation_id": "select",
                "outputs": {
                  "values": [
                    "selected_values",
                    "selected_genes"
                  ]
                },
                "parameters": {
                  "criterion": "highly variable genes",
                  "method": "unspecified"
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                "source_step_id": "hvg",
                "status": "documented_operation",
                "uncertainty": "Section-only reconstruction; missing equations and training details remain unresolved."
              },
              {
                "call_id": "gene_token_ids",
                "component": "OKR-Cell input embedding module",
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                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "inputs": {
                  "keys": [
                    "selected_genes"
                  ],
                  "table": [
                    "gene_vocabulary"
                  ]
                },
                "operation_id": "lookup",
                "outputs": {
                  "values": [
                    "gene_indices"
                  ]
                },
                "parameters": {
                  "resource_kind": "gene vocabulary"
                },
                "source_step_id": "gene_token_ids",
                "status": "documented_operation",
                "uncertainty": "Section-only reconstruction; missing equations and training details remain unresolved."
              },
              {
                "call_id": "bins",
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                "evidence": [
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                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "inputs": {
                  "values": [
                    "selected_values"
                  ]
                },
                "operation_id": "bin",
                "outputs": {
                  "values": [
                    "bin_indices"
                  ]
                },
                "parameters": {
                  "bin_edges": "source-defined; formula not decoded",
                  "scope": "per_cell_nonzero_values",
                  "strategy": "equal_interval",
                  "zero_handling": "retain zero"
                },
                "source_step_id": "bins",
                "status": "documented_operation",
                "uncertainty": "Section-only reconstruction; missing equations and training details remain unresolved."
              },
              {
                "call_id": "gene_lookup",
                "component": "OKR-Cell input embedding module",
                "condition": null,
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "inputs": {
                  "keys": [
                    "gene_indices"
                  ],
                  "table": [
                    "gene_table"
                  ]
                },
                "operation_id": "lookup",
                "outputs": {
                  "values": [
                    "gene_vectors"
                  ]
                },
                "parameters": {
                  "resource_kind": "embedding matrix",
                  "trainability": "unspecified"
                },
                "source_step_id": "gene_lookup",
                "status": "documented_operation",
                "uncertainty": "Section-only reconstruction; missing equations and training details remain unresolved."
              },
              {
                "call_id": "value_lookup",
                "component": "OKR-Cell input embedding module",
                "condition": null,
                "evidence": [
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                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "inputs": {
                  "keys": [
                    "bin_indices"
                  ],
                  "table": [
                    "bin_table"
                  ]
                },
                "operation_id": "lookup",
                "outputs": {
                  "values": [
                    "value_vectors"
                  ]
                },
                "parameters": {
                  "resource_kind": "embedding matrix",
                  "trainability": "unspecified"
                },
                "source_step_id": "value_lookup",
                "status": "documented_operation",
                "uncertainty": "Section-only reconstruction; missing equations and training details remain unresolved."
              },
              {
                "call_id": "fusion",
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                "condition": null,
                "evidence": [
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                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "inputs": {
                  "values": [
                    "gene_vectors",
                    "value_vectors"
                  ]
                },
                "operation_id": "add",
                "outputs": {
                  "values": [
                    "fused"
                  ]
                },
                "parameters": {
                  "alignment": "selected gene position and shared embedding feature coordinate"
                },
                "source_step_id": "fusion",
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                "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
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            "nodes": [
              {
                "axis_semantics": null,
                "contextual_role": "sample_input",
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                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
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                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
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                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Identifiers aligned to expression positions",
                "node_id": "gene_ids",
                "origin": "source_annotation",
                "representation_type": "gene_identifiers",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "intermediate_representation",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Log1p transformed expression",
                "node_id": "logged",
                "origin": "source_annotation",
                "representation_type": "log_expression",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "intermediate_representation",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "HVG-selected expression",
                "node_id": "selected_values",
                "origin": "source_annotation",
                "representation_type": "selected_expression",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "intermediate_representation",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Identifiers of the selected genes",
                "node_id": "selected_genes",
                "origin": "source_annotation",
                "representation_type": "selected_gene_identifiers",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "reference_resource",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Gene identifier to vocabulary-index mapping",
                "node_id": "gene_vocabulary",
                "origin": "source_annotation",
                "representation_type": "vocabulary_table",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "intermediate_representation",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Vocabulary identifiers for selected genes",
                "node_id": "gene_indices",
                "origin": "source_annotation",
                "representation_type": "gene_vocabulary_indices",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "intermediate_representation",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Equal-interval nonzero expression bins with zero preserved",
                "node_id": "bin_indices",
                "origin": "source_annotation",
                "representation_type": "expression_bin_indices",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "model_parameter",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Gene embedding-layer parameters emb_g; trainability unspecified in this section",
                "node_id": "gene_table",
                "origin": "source_annotation",
                "representation_type": "embedding_matrix",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "model_parameter",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Expression embedding-layer parameters emb_x; a separate table",
                "node_id": "bin_table",
                "origin": "source_annotation",
                "representation_type": "embedding_matrix",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "intermediate_representation",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Selected gene embedding vectors",
                "node_id": "gene_vectors",
                "origin": "source_annotation",
                "representation_type": "gene_embeddings",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "intermediate_representation",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Selected expression-bin embedding vectors",
                "node_id": "value_vectors",
                "origin": "source_annotation",
                "representation_type": "expression_embeddings",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              },
              {
                "axis_semantics": null,
                "contextual_role": "intermediate_representation",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "information_content": "Element-wise sum supplied to Transformer encoder blocks",
                "node_id": "fused",
                "origin": "source_annotation",
                "representation_type": "summed_input_embeddings",
                "symbolic_shape": null,
                "uncertainty": "Exact tensor layout is not reconstructed in this section-only example."
              }
            ],
            "open_questions": [
              "Source title is marked WITHDRAWN in the inventory. This example describes the documented mechanism and changes no eligibility decision.",
              "Missing equations, HVG algorithm, matrix training status, special-token placement and phase-specific masking remain unspecified."
            ],
            "receipt_inputs": [
              {
                "node_id": "fused",
                "port_role": "input embeddings"
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            ],
            "recipient_component": "Transformer encoder blocks",
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            "source_steps": [
              {
                "component": "OKR-Cell input embedding module",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "inputs": [
                  {
                    "node_id": "expression",
                    "port_role": "values"
                  }
                ],
                "operation_type": "log_transform",
                "outputs": [
                  "logged"
                ],
                "step_id": "log",
                "uncertainty": "Section-only reconstruction; missing equations and training details remain unresolved."
              },
              {
                "component": "OKR-Cell input embedding module",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "inputs": [
                  {
                    "node_id": "logged",
                    "port_role": "values"
                  },
                  {
                    "node_id": "gene_ids",
                    "port_role": "values"
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                ],
                "operation_type": "select",
                "outputs": [
                  "selected_values",
                  "selected_genes"
                ],
                "step_id": "hvg",
                "uncertainty": "Section-only reconstruction; missing equations and training details remain unresolved."
              },
              {
                "component": "OKR-Cell input embedding module",
                "evidence": [
                  {
                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "inputs": [
                  {
                    "node_id": "selected_genes",
                    "port_role": "keys"
                  },
                  {
                    "node_id": "gene_vocabulary",
                    "port_role": "table"
                  }
                ],
                "operation_type": "lookup",
                "outputs": [
                  "gene_indices"
                ],
                "step_id": "gene_token_ids",
                "uncertainty": "Section-only reconstruction; missing equations and training details remain unresolved."
              },
              {
                "component": "OKR-Cell input embedding module",
                "evidence": [
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                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "inputs": [
                  {
                    "node_id": "selected_values",
                    "port_role": "values"
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                "operation_type": "bin",
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                  "bin_indices"
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                "step_id": "bins",
                "uncertainty": "Section-only reconstruction; missing equations and training details remain unresolved."
              },
              {
                "component": "OKR-Cell input embedding module",
                "evidence": [
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                    "kind": "paper_text",
                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
                  }
                ],
                "inputs": [
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                    "node_id": "gene_indices",
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                ],
                "operation_type": "lookup",
                "outputs": [
                  "gene_vectors"
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                "step_id": "gene_lookup",
                "uncertainty": "Section-only reconstruction; missing equations and training details remain unresolved."
              },
              {
                "component": "OKR-Cell input embedding module",
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                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
                    "section_id": "sec_0022"
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                "uncertainty": "Section-only reconstruction; missing equations and training details remain unresolved."
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                    "quote": "#### 4.1.1 Input Embeddings\n\nThe input embedding module transforms single-cell RNA-seq data-structured as a cell-gene matrix X ∈ R N × G , where N denotes the total number of cells, G is the total count of genes, and X i,j represents the raw read count of gene j in cell i ) into a consistent latent representation through three interconnected modules, followed by feature fusion:\n\n1. Gene Tokenization. Each gene is treated as a basic information unit (analogous to a word in NLG) and assigned a unique integer ID id ( g j ). Special tokens (e.g., &lt; cls &gt; for cell representation aggregation, &lt; pad &gt; for input length padding) are included to support cross-study gene set integration. For cell i , the gene token sequence is defined as:\n\nEach gene is treated as a fundamental informational element (analogous to a token in natural language processing) and assigned a unique integer identifier id ( g j ). To support cross-study integration of gene sets, two special tokens are introduced: &lt; cls &gt; for aggregating cell-level representations and &lt; pad &gt; for padding sequences to a uniform length. For cell i , the gene token sequence is defined as:\n\n<!-- formula-not-decoded -->\n\nwhere M (predefined input length) is set to the number of selected highly variable genes (HVGs), a standard practice in single-cell transcriptomic analysis.\n\n2. Gene Expression Binning. To resolve scale inconsistencies across different sequencing batches-a challenge that cannot be fully addressed by TPM normalization or log1p transformation alone, we implement a value binning strategy with standardized parameters:\n2. 1). Preprocessing: Log1p transformation and HVG selection are performed first;\n3. 2). Binning Operation: Non-zero expression values of each cell are partitioned into O equal-interval bins, while zero values are retained as 0. The binned value x ( i ) j is formally defined as:\n\n<!-- formula-not-decoded -->\n\nThe final expression vector for cell i is x ( i ) e = [ x ( i ) 1 , x ( i ) 2 , ..., x ( i ) M ], ensuring consistent semantics of expression levels across batches.\n\n3. Embedding Fusion. Gene tokens and binned expression values are independently projected to D -dimensional vectors via embedding layers ( emb g , emb x ) respectively. The final input embedding for cell i : is obtained by element-wise summation of these two components, integrating both gene identity and expression magnitude information:\n\n<!-- formula-not-decoded -->\n\nwhere h ( i ) ∈ R M × D serves as the input to subsequent Transformer encoder blocks.\n\n",
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      "usage": [
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    },
    {
      "boundaries": "Distribution parameters, prior/posterior origin, reparameterization and temperature remain instance details.",
      "definition": "Produce realized values or selected positions from a documented probability distribution.",
      "inputs": [
        {
          "meaning": "Distribution or its encoded parameters.",
          "name": "distribution",
          "optional": false,
          "variadic": false
        },
        {
          "meaning": "Base random values when explicitly supplied.",
          "name": "noise",
          "optional": true,
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          "meaning": "Other documented sampling operands.",
          "name": "context",
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        }
      ],
      "label": "Sampling",
      "official_reference": "https://docs.pytorch.org/docs/stable/distributions.html",
      "operation_id": "sample",
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