## Heatmap: Category Distribution Across Layers and Heads ### Overview The image presents four heatmaps displaying the distribution of different categories across layers and heads of a model. The first heatmap shows "All Categories," while the subsequent heatmaps focus on "Algorithmic," "Knowledge," and "Linguistic" categories individually. The heatmaps use color to indicate the presence of a category at a specific layer and head combination. ### Components/Axes * **Titles:** "All Categories," "Algorithmic," "Knowledge," "Linguistic" * **Y-axis:** "head" with tick marks at 0, 6, 12, 18, 24, and 30. * **X-axis:** "layer" with tick marks at 0, 6, 12, 18, 24, and 30. * **Legend (located to the right of the "All Categories" heatmap):** * Brown: "3 categories" * Purple: "2 categories" * Green: "Linguistic" * Orange: "Knowledge" * Blue: "Algorithmic" * Gray: "Unclassified" (This is the background color of the heatmaps) ### Detailed Analysis **1. All Categories Heatmap:** This heatmap shows a mix of all categories. * Brown squares (3 categories) are sparsely distributed. * Purple squares (2 categories) are also sparsely distributed. * Green squares (Linguistic) are scattered throughout the heatmap. * Orange squares (Knowledge) are scattered throughout the heatmap. * Blue squares (Algorithmic) are scattered throughout the heatmap. **2. Algorithmic Heatmap:** This heatmap shows the distribution of the "Algorithmic" category (blue squares). * Blue squares are present across all layers and heads, but are not densely packed. * There appears to be a slightly higher concentration of blue squares in the lower layers (layer 18-30). **3. Knowledge Heatmap:** This heatmap shows the distribution of the "Knowledge" category (orange squares). * Orange squares are present across all layers and heads, but are not densely packed. * There appears to be a slightly higher concentration of orange squares in the middle layers (layer 6-18). **4. Linguistic Heatmap:** This heatmap shows the distribution of the "Linguistic" category (green squares). * Green squares are present across all layers and heads, but are not densely packed. * The distribution appears relatively uniform across layers and heads. ### Key Observations * The "All Categories" heatmap confirms that the other three categories ("Algorithmic," "Knowledge," and "Linguistic") are present in the combined view. * The individual heatmaps show the specific distribution of each category. * The heatmaps are sparse, indicating that most layer/head combinations are not strongly associated with a single category. ### Interpretation The heatmaps visualize the distribution of different categories across the layers and heads of a model. The sparsity of the heatmaps suggests that individual layer/head combinations are not strongly specialized for a single category. The "All Categories" heatmap provides a combined view, while the individual heatmaps allow for a more detailed analysis of each category's distribution. The slight variations in concentration across layers for "Algorithmic" and "Knowledge" might indicate some degree of specialization at different depths of the model. The presence of "2 categories" and "3 categories" indicates overlap between the categories.

\n ## Scatter Plots: Category Activation by Layer and Head ### Overview The image presents four scatter plots, each visualizing the activation of different categories across layers and heads. The plots show the distribution of activations, likely representing the strength of a particular category's response within a neural network model. Each plot focuses on a specific category (All Categories, Algorithmic, Knowledge, Linguistic) and displays activation levels against layer and head indices. ### Components/Axes Each plot shares the following components: * **X-axis:** "layer", ranging from approximately 0 to 32, with markers at 0, 6, 12, 18, 24, and 30. * **Y-axis:** "head", ranging from approximately 0 to 32, with markers at 0, 6, 12, 18, 24, and 30. * **Color:** Represents the number of categories activated. The colorbar on the "All Categories" plot indicates: * Green: 3 categories * Yellow/Orange: 2 categories * Blue: 1 category * **Plot Titles:** Each plot is labeled with the category it represents: "All Categories", "Algorithmic", "Knowledge", "Linguistic". ### Detailed Analysis or Content Details **1. All Categories Plot:** * The plot displays a dense scattering of points, with a gradient of colors indicating the number of categories activated. * The highest concentration of points (green, 3 categories) is located in the lower-left quadrant (low layer, low head) and extends diagonally upwards and to the right. * There's a noticeable transition from green to yellow/orange and then to blue as the layer and head indices increase. * The points are relatively evenly distributed across the layer and head dimensions. **2. Algorithmic Plot:** * This plot shows a sparse scattering of blue points (1 category). * The points are concentrated in the lower layer range (0-18) and lower head range (0-12). * There is a slight upward trend in head index as the layer index increases. * No points are visible in the upper-right quadrant (high layer, high head). **3. Knowledge Plot:** * This plot displays orange/yellow points (2 categories) and some blue points (1 category). * The points are primarily concentrated in the higher layer range (12-30) and mid-range head indices (6-24). * There's a clear clustering of points around layer 24 and head 12. * The distribution appears more concentrated than the "Algorithmic" plot. **4. Linguistic Plot:** * This plot shows a dense scattering of green points (3 categories) and some yellow/orange points (2 categories). * The points are concentrated in the higher layer range (18-30) and higher head range (12-30). * The distribution is relatively uniform across the upper-right quadrant. * There is a clear concentration of points in the upper-right corner. ### Key Observations * The "All Categories" plot shows a broad activation pattern, while the individual category plots reveal more specific activation regions. * "Algorithmic" activations are primarily in the lower layers and heads. * "Knowledge" activations are concentrated in the higher layers and mid-range heads. * "Linguistic" activations are dominant in the higher layers and heads. * The number of activated categories varies significantly across the different plots. ### Interpretation The data suggests that different categories are processed at different layers and heads within the neural network. "Algorithmic" information appears to be processed earlier in the network (lower layers), while "Knowledge" and "Linguistic" information are processed later (higher layers). The varying density of points and the number of activated categories indicate that some categories are more strongly represented or require more complex processing than others. The concentration of "Knowledge" activations around layer 24 and head 12 might indicate a specific module or component responsible for processing knowledge-related information. The "All Categories" plot provides a holistic view, showing how these individual category activations contribute to the overall network activity. The plots demonstrate a hierarchical processing structure, where lower layers extract basic features and higher layers combine these features to represent more complex concepts. The differences in activation patterns across categories suggest that the network has learned to specialize different parts of its architecture for different types of information.

\n ## Heatmap Set: Categorical Distribution Across Layers and Heads ### Overview The image displays four horizontally arranged heatmaps, each plotting categorical data points on a grid defined by "layer" (x-axis) and "head" (y-axis). The leftmost heatmap, titled "All Categories," includes a legend and shows a composite view of all data. The subsequent three heatmaps isolate individual categories: "Algorithmic," "Knowledge," and "Linguistic." The visualization appears to map the presence or activation of specific functional categories within the layers and attention heads of a neural network model (likely a transformer). ### Components/Axes * **Chart Type:** Four separate heatmaps (scatter plots on a grid). * **Titles:** * Leftmost: "All Categories" * Second from left: "Algorithmic" * Third from left: "Knowledge" * Rightmost: "Linguistic" * **Axes (Identical for all four charts):** * **X-axis:** Label: "layer". Scale: 0 to 30, with major tick marks at 0, 6, 12, 18, 24, 30. * **Y-axis:** Label: "head". Scale: 0 to 30, with major tick marks at 0, 6, 12, 18, 24, 30. The axis is inverted, with 0 at the top and 30 at the bottom. * **Legend (Located on the left side of the "All Categories" heatmap):** * **Brown square:** "3 categories" * **Purple square:** "2 categories" * **Green square:** "Linguistic" * **Orange square:** "Knowledge" * **Blue square:** "Algorithmic" * **Light Gray square:** "Unclassified" (This corresponds to the background grid color). ### Detailed Analysis **1. "All Categories" Heatmap (Leftmost):** * **Content:** Displays a dense, mixed scatter of colored squares (blue, orange, green, purple, brown) across the entire grid. The background is light gray ("Unclassified"). * **Spatial Distribution:** Data points are scattered without a single dominant cluster, though there is a slight visual concentration in the central region (layers ~12-24, heads ~6-24). Brown ("3 categories") and purple ("2 categories") points are interspersed among the single-category points, indicating locations where multiple categories co-occur. **2. "Algorithmic" Heatmap (Second from left):** * **Content:** Shows only blue squares ("Algorithmic") on the light gray background. * **Trend/Distribution:** The blue points are distributed across the grid but appear somewhat sparse. There is no strong, singular cluster, but a loose grouping is visible in the lower-left quadrant (layers ~0-18, heads ~12-30). **3. "Knowledge" Heatmap (Third from left):** * **Content:** Shows only orange squares ("Knowledge") on the light gray background. * **Trend/Distribution:** The orange points show a more defined clustering pattern compared to the Algorithmic category. A notable concentration exists in the central to upper-right region (layers ~12-30, heads ~0-18). There are fewer points in the lower layers (0-12). **4. "Linguistic" Heatmap (Rightmost):** * **Content:** Shows only green squares ("Linguistic") on the light gray background. * **Trend/Distribution:** The green points are widely scattered but show a visible density in the central and right portions of the grid (layers ~12-30). There is a relative sparsity in the very low layers (0-6) and the top rows (heads 0-6). ### Key Observations 1. **Category Co-occurrence:** The "All Categories" map reveals that specific layer-head positions (marked in brown and purple) are associated with two or three categories simultaneously, suggesting multifunctional components. 2. **Spatial Specialization:** While there is overlap, the individual category maps suggest a degree of spatial specialization: * **Knowledge** points lean towards mid-to-high layers and mid-to-low heads. * **Linguistic** points are prevalent in mid-to-high layers. * **Algorithmic** points are more diffuse but have a presence in lower layers and heads. 3. **Coverage:** No single category uniformly covers the entire layer-head space. Significant portions of the grid remain "Unclassified" (light gray) in each individual category plot. ### Interpretation This visualization likely analyzes the functional specialization within a large neural network, such as a transformer-based language model. Each "head" probably refers to an attention head within a specific "layer." * **What the data suggests:** The model's processing is not monolithic. Different computational functions ("Algorithmic," "Knowledge," "Linguistic") are distributed across its architecture. The clustering patterns imply that certain regions of the network are more dedicated to specific types of processing. For instance, knowledge retrieval or storage might be concentrated in later layers, while linguistic syntactic processing could be more widespread. * **Relationships:** The "All Categories" map is the union of the other three. The presence of multi-category (brown, purple) points is critical—it highlights components that serve integrated functions, bridging, for example, linguistic structure with factual knowledge. * **Anomalies/Notable Trends:** The relative absence of points in the very first layers (0-6) and very last heads (24-30) across all categories is notable. This could indicate that the earliest and latest parts of the network perform more – - ## Textual Information Extraction The image contains the following text, transcribed exactly as it appears: **Titles:** * All Categories * Algorithmic * Knowledge * Linguistic **Axis Labels:** * head (Y-axis label for all charts) * layer (X-axis label for all charts) **Axis Markers:** * Y-axis: 0, 6, 12, 18, 24, 30 * X-axis: 0, 6, 12, 18, 24, 30 **Legend Text (from top to bottom):** * 3 categories * 2 categories * Linguistic * Knowledge * Algorithmic * Unclassified

## Heatmaps: Category Distribution Across Layers and Heads ### Overview The image displays four heatmaps visualizing the distribution of linguistic, knowledge-based, and algorithmic categories across neural network layers and attention heads. The "All Categories" heatmap combines all classifications, while the subsequent panels isolate specific categories. Spatial patterns reveal how different cognitive functions are localized within the model architecture. ### Components/Axes - **X-axis**: Layer index (0-30), representing neural network depth - **Y-axis**: Head index (0-30), representing attention mechanism components - **Legend**: - Brown: 3 categories - Purple: 2 categories - Green: Linguistic - Orange: Knowledge - Blue: Algorithmic - Gray: Unclassified - **Heatmap Titles**: - All Categories (combined) - Algorithmic (blue) - Knowledge (orange) - Linguistic (green) ### Detailed Analysis 1. **All Categories Heatmap**: - Mixed distribution of brown (3 categories), purple (2 categories), green, orange, and blue squares - Gray squares (unclassified) appear sparsely in upper layers (24-30) - Highest density of colored squares in layers 12-24 2. **Algorithmic Heatmap**: - Exclusively blue squares (algorithmic category) - Concentrated in layers 12-24, heads 6-18 - Notable cluster at layer 18, head 12 3. **Knowledge Heatmap**: - Orange squares dominate layers 6-24 - Strong presence in heads 12-24 - Notable cluster at layer 24, head 24 4. **Linguistic Heatmap**: - Green squares prevalent in layers 0-24 - Dense distribution in heads 0-18 - Notable cluster at layer 6, head 6 ### Key Observations - **Spatial Segregation**: Categories show distinct spatial patterns, with minimal overlap between heatmaps - **Layer Depth Correlation**: Algorithmic and Knowledge categories concentrate in deeper layers (12-24) - **Head Specialization**: Linguistic category dominates early heads (0-18), while Knowledge/Algorithmic occupy mid-to-late heads - **Unclassified Presence**: Gray squares in "All Categories" suggest 8-12% of layer-head combinations remain unclassified ### Interpretation The data demonstrates clear functional specialization within the neural architecture: 1. **Linguistic Processing**: Early layers (0-12) and heads (0-18) specialize in language-related tasks, suggesting foundational language understanding occurs in shallower network regions 2. **Knowledge Integration**: Mid-layers (12-24) show strong Knowledge category presence, indicating hierarchical knowledge representation building upon linguistic foundations 3. **Algorithmic Operations**: Deeper layers (18-30) contain algorithmic processing, possibly handling complex pattern recognition and decision-making 4. **Unclassified Regions**: The presence of gray squares in upper layers suggests either model uncertainty or emergent properties not captured by current categorization This spatial distribution pattern aligns with theories of neural network modularity, where different cognitive functions are localized in specific architectural regions. The clear separation between categories implies effective feature disentanglement, while the unclassified regions warrant further investigation into potential model ambiguities or novel processing mechanisms.