## Heatmap: Category Distribution Across Layers and Heads ### Overview The image consists of four heatmaps arranged horizontally. Each heatmap visualizes the distribution of categories across different layers and heads of a model. The first heatmap, "All Categories," shows the combined distribution of all categories, while the subsequent heatmaps ("Algorithmic," "Knowledge," and "Linguistic") display the distribution of individual categories. The heatmaps share the same axes: "layer" on the x-axis and "head" on the y-axis. A legend is provided next to the "All Categories" heatmap to indicate the color-coding for each category. ### Components/Axes * **X-axis (Layer):** Represents the layer number, ranging from 0 to 35, with tick marks at intervals of 7. * **Y-axis (Head):** Represents the head number, ranging from 0 to 40, with tick marks at intervals of 8. * **Heatmaps:** Each heatmap is a grid of cells, where each cell's color indicates the category or combination of categories present at a specific layer and head. * **Legend (Located to the right of the "All Categories" heatmap):** * **Brown:** "3 categories" * **Purple:** "2 categories" * **Green:** "Linguistic" * **Orange:** "Knowledge" * **Blue:** "Algorithmic" * **Light Gray:** "Unclassified" ### Detailed Analysis **1. All Categories Heatmap:** * This heatmap shows a mix of all categories. * There are regions with single categories, combinations of two categories (purple), and combinations of three categories (brown). * The distribution appears relatively uniform across layers and heads, with some concentrations of specific categories in certain areas. **2. Algorithmic Heatmap:** * This heatmap shows the distribution of the "Algorithmic" category (blue). * The "Algorithmic" category is sparsely distributed across layers and heads. * There are no clear patterns or concentrations of the "Algorithmic" category. **3. Knowledge Heatmap:** * This heatmap shows the distribution of the "Knowledge" category (orange). * The "Knowledge" category is more concentrated in the middle layers (around layer 16 to 32) and heads (around head 8 to 24). * There are fewer instances of the "Knowledge" category in the earlier and later layers. **4. Linguistic Heatmap:** * This heatmap shows the distribution of the "Linguistic" category (green). * The "Linguistic" category is distributed across layers and heads, with some concentrations in the earlier layers (around layer 0 to 16). * There are fewer instances of the "Linguistic" category in the later layers. ### Key Observations * The "All Categories" heatmap provides an overview of the combined distribution of all categories. * The "Algorithmic" category is sparsely distributed. * The "Knowledge" category is concentrated in the middle layers and heads. * The "Linguistic" category is concentrated in the earlier layers. * The "Unclassified" category is not explicitly shown in its own heatmap, but its presence can be inferred from the "All Categories" heatmap in areas where no other categories are present. ### Interpretation The heatmaps visualize the distribution of different categories across the layers and heads of a model. The distribution patterns suggest that different layers and heads may be specialized for processing different types of information. For example, the concentration of the "Knowledge" category in the middle layers and heads may indicate that these layers are responsible for processing knowledge-related information. Similarly, the concentration of the "Linguistic" category in the earlier layers may indicate that these layers are responsible for processing linguistic information. The sparse distribution of the "Algorithmic" category may suggest that this category is less important for the model's overall performance. The presence of combinations of categories in the "All Categories" heatmap indicates that some layers and heads may be involved in processing multiple types of information.

\n ## Scatter Plots: Category Distribution Across Layers and Heads ### Overview The image presents four scatter plots, each visualizing the distribution of different categories across 'layer' and 'head' dimensions. The first plot shows the distribution of "All Categories", while the subsequent three plots focus on "Algorithmic", "Knowledge", and "Linguistic" categories respectively. Each plot uses a scatter plot to represent the density of data points for each category. ### Components/Axes Each of the four plots shares the same axes: * **X-axis:** "layer", ranging from approximately 0 to 35. * **Y-axis:** "head", ranging from approximately 0 to 40. * **Categories/Colors:** * "Unclassified" (Teal/Green) * "Algorithmic" (Blue) * "Knowledge" (Orange) * "Linguistic" (Green) * The first plot ("All Categories") also indicates the number of categories present in a given region (2 categories, 3 categories). ### Detailed Analysis or Content Details **1. All Categories Plot:** * The plot shows a mix of all four categories. * The teal/green ("Unclassified") category is prevalent in the lower-left region (low layer, low head). * The blue ("Algorithmic") category is concentrated in the right side (high layer) and middle head values. * The orange ("Knowledge") category is concentrated in the middle-right region (high layer, middle head). * The green ("Linguistic") category is concentrated in the left side (low layer) and middle head values. * The region around layer 28-35 and head 0-8 shows "3 categories" present. * The region around layer 0-7 and head 16-24 shows "2 categories" present. **2. Algorithmic Plot:** * The blue ("Algorithmic") category is the only one present. * The points are scattered across the layer range (0-35), but are more densely populated between layers 7 and 28. * The points are scattered across the head range (0-40), with a slight concentration between heads 0 and 16. **3. Knowledge Plot:** * The orange ("Knowledge") category is the only one present. * The points are concentrated in the middle-right region, with layers ranging from approximately 14 to 35 and heads ranging from approximately 8 to 32. * There is a noticeable gap in the data between layers 0 and 14. **4. Linguistic Plot:** * The green ("Linguistic") category is the only one present. * The points are concentrated in the left side, with layers ranging from approximately 0 to 28 and heads ranging from approximately 8 to 32. * There is a noticeable gap in the data between layers 28 and 35. ### Key Observations * The "All Categories" plot demonstrates a clear separation of categories based on layer and head values. * The "Algorithmic" category appears to be more prevalent in higher layers. * The "Knowledge" category appears to be more prevalent in middle to higher layers. * The "Linguistic" category appears to be more prevalent in lower to middle layers. * The individual category plots show that each category occupies a distinct region of the layer/head space. ### Interpretation The data suggests that different categories of information are processed at different layers and heads within a neural network or similar system. The "Algorithmic" category is associated with higher layers, potentially indicating that it emerges from more complex processing. The "Knowledge" category also appears in higher layers, suggesting it builds upon the algorithmic processing. The "Linguistic" category is more prominent in lower layers, potentially indicating that it is involved in initial feature extraction. The "Unclassified" category being prevalent in the lower-left suggests that initial processing is often ambiguous or requires further refinement. The separation of these categories across the layer/head space suggests a modular organization of information processing within the system. The gaps in the "Knowledge" and "Linguistic" plots could indicate specific layers or heads that are not involved in processing those types of information.

\n ## Heatmap Series: Classification Distribution Across Model Layers and Attention Heads ### Overview The image displays a series of four horizontally arranged heatmaps. The leftmost panel, titled "All Categories," is a composite visualization showing the classification of attention heads across a neural network model. The three subsequent panels to its right decompose this composite view, showing the distribution for each individual category: "Algorithmic," "Knowledge," and "Linguistic." A shared legend is positioned to the immediate right of the "All Categories" panel. The visualization maps classifications onto a 2D grid defined by model "layer" (x-axis) and attention "head" (y-axis). ### Components/Axes * **Titles:** Four panel titles are present at the top: "All Categories", "Algorithmic", "Knowledge", "Linguistic". * **Axes:** * **X-axis (all panels):** Labeled "layer". The scale runs from 0 to 35, with major tick marks at 0, 7, 14, 21, 28, and 35. * **Y-axis (all panels):** Labeled "head". The scale runs from 0 to 40, with major tick marks at 0, 8, 16, 24, 32, and 40. * **Legend:** Located between the "All Categories" and "Algorithmic" panels. It defines six classification categories with associated colors: * **Brown:** "3 categories" * **Purple:** "2 categories" * **Green:** "Linguistic" * **Orange:** "Knowledge" * **Blue:** "Algorithmic" * **Light Gray:** "Unclassified" (This is the background color of all cells not marked with another color). * **Data Representation:** Each cell in the 36x41 grid (layers 0-35, heads 0-40) represents a specific attention head. The cell's color indicates its classification according to the legend. ### Detailed Analysis **Panel 1: "All Categories" (Composite View)** * **Spatial Distribution:** Colored cells (classified heads) are scattered across the entire grid, with no single region completely devoid of classifications. There is a visible concentration of colored cells in the central region, roughly between layers 14-28 and heads 8-32. * **Category Breakdown (Visual Estimate):** * **Unclassified (Light Gray):** The majority of cells. Visually, it appears that less than 25% of the total heads are classified into any category. * **Algorithmic (Blue):** Scattered individual cells and small clusters. A slight density increase is visible in the lower-left quadrant (layers 0-14, heads 24-40). * **Knowledge (Orange):** Forms more distinct clusters and short horizontal streaks, particularly prominent in the central band (layers ~14-28, heads ~16-32). * **Linguistic (Green):** Appears as widely dispersed individual cells and small groups, with a subtle presence across the entire grid. * **2 categories (Purple):** Relatively rare, appearing as isolated cells, often adjacent to or within clusters of single-category heads. * **3 categories (Brown):** Very rare, only a few isolated cells are visible (e.g., near layer 21, head 8). **Panel 2: "Algorithmic" (Blue)** * **Trend:** The blue cells show a scattered distribution with a mild concentration in the lower layers (0-14) and lower heads (24-40). There is no strong, continuous pattern; classifications appear as isolated points or very small, tight clusters. **Panel 3: "Knowledge" (Orange)** * **Trend:** This category shows the most structured distribution. Orange cells form clear horizontal bands and clusters, primarily concentrated in the middle layers (approximately 14 to 28). The density is highest in the head range of 16 to 32. There are very few orange cells in the earliest (0-7) or latest (28-35) layers. **Panel 4: "Linguistic" (Green)** * **Trend:** Green cells are the most uniformly dispersed across the entire layer-head space. While present everywhere, there is a slight visual increase in density in the upper half of the head axis (heads 0-20) compared to the lower half. ### Key Observations 1. **Functional Specialization:** The "Knowledge" category exhibits the strongest spatial specialization, being heavily concentrated in the model's middle layers. This suggests these layers/heads are primarily engaged in processing factual or world knowledge. 2. **Ubiquity of Linguistic Processing:** The "Linguistic" category is found throughout the model, indicating that syntactic and basic language processing functions are distributed across many layers and heads, not confined to a specific module. 3. **Sparsity of Classification:** A large majority of attention heads remain "Unclassified" by the criteria used in this analysis, suggesting either the classification method is highly selective or many heads perform functions not captured by these three categories. 4. **Multi-Category Heads:** The presence of heads classified under "2 categories" and "3 categories" (purple and brown) indicates that some attention heads perform hybrid functions, integrating algorithmic, knowledge-based, and linguistic processing. ### Interpretation This visualization provides a functional map of a large language model's attention mechanism. The data suggests a **hierarchical and distributed processing architecture**: * **Early Layers (0-14):** Show a mix of all categories but with a slight bias towards "Algorithmic" and "Linguistic" functions. This aligns with the hypothesis that lower layers handle more fundamental syntactic and structural processing. * **Middle Layers (14-28):** Are the clear hub for **"Knowledge" retrieval and application**. The dense clustering here implies these layers are critical for accessing and manipulating the model's parametric knowledge base. * **Late Layers (28-35):** See a reduction in "Knowledge" activity and a return to a more mixed, sparse distribution, potentially involved in task-specific formatting or output generation. * **Overall Principle:** The model does not have a single "knowledge center" or "language center." Instead, capabilities are **distributed across the network**, with certain regions showing strong functional biases. The "Linguistic" function's ubiquity acts as a substrate upon which more specialized "Algorithmic" and "Knowledge" processes are built. The existence of multi-category heads highlights the integrated, non-modular nature of neural computation, where single components can simultaneously participate in multiple types of processing. This map is crucial for understanding model interpretability, guiding pruning or editing efforts, and diagnosing failure modes.

## Heatmap: Category Distribution Across Layers and Heads ### Overview The image presents four heatmaps visualizing the distribution of linguistic, knowledge, and algorithmic categories across neural network layers (x-axis: 0-35) and heads (y-axis: 0-40). The "All Categories" heatmap shows overlapping distributions, while the subsequent panels isolate specific categories. Colors correspond to predefined categories (see legend). ### Components/Axes - **X-axis (layer)**: 0 to 35, representing neural network layers. - **Y-axis (head)**: 0 to 40, representing attention heads. - **Legend**: - Brown: 3 categories - Purple: 2 categories - Green: Linguistic - Orange: Knowledge - Blue: Algorithmic - Gray: Unclassified ### Detailed Analysis #### All Categories - **Distribution**: - Green (Linguistic) and orange (Knowledge) dominate, with green concentrated in layers 14-28 and orange peaking at layer 21. - Blue (Algorithmic) is sparse but present across all layers. - Brown (3 categories) and purple (2 categories) are rare, appearing sporadically in layers 14-35. - Gray (Unclassified) fills gaps between colored points. #### Algorithmic - **Distribution**: - Blue squares are uniformly distributed but denser in layers 14-21. - No clear trend; density remains low compared to other categories. #### Knowledge - **Distribution**: - Orange squares cluster strongly in layers 14-28, with a peak at layer 21. - Density decreases sharply in layers 0-7 and 28-35. #### Linguistic - **Distribution**: - Green squares are evenly spread across all layers but densest in layers 14-28. - Layer 21 shows the highest concentration. ### Key Observations 1. **Layer 21 Dominance**: All three primary categories (Linguistic, Knowledge, Algorithmic) show elevated activity in layer 21. 2. **Knowledge Concentration**: Knowledge (orange) is most tightly clustered around layer 21, suggesting a focal point for this category. 3. **Algorithmic Sparsity**: Algorithmic (blue) points are dispersed but lack the density of other categories. 4. **Unclassified Prevalence**: Gray areas (Unclassified) are most prominent in layers 0-7 and 32-40. ### Interpretation The data suggests that **layer 21** acts as a critical hub for integrating linguistic, knowledge, and algorithmic processing. The tight clustering of Knowledge in this layer implies specialized functionality, while the broader spread of Linguistic points indicates distributed processing. Algorithmic elements appear less localized, possibly reflecting general-purpose operations. The scarcity of 2- and 3-category points (brown/purple) suggests these represent edge cases or transitional states. The dominance of Unclassified regions in peripheral layers (0-7, 32-40) may indicate incomplete categorization or noise in those areas. This pattern aligns with hierarchical processing models, where middle layers specialize in complex feature integration.