## Heatmap: Layer Importance vs. Parameter ### Overview The image is a heatmap visualizing the importance of different layers (y-axis) for various parameters (x-axis) in a neural network. The color intensity represents the degree of importance, with darker blue indicating higher importance and lighter shades indicating lower importance. ### Components/Axes * **Y-axis:** "Layer" with numerical scale from 2 to 30 in increments of 2. * **X-axis:** "Parameter" with the following categories: * Layer Importance * mlp.down\_proj * mlp.up\_proj * mlp.gate\_proj * self\_attn.o\_proj * self\_attn.v\_proj * self\_attn.q\_proj * self\_attn.k\_proj * post\_attention\_layernorm * input\_layernorm * **Color Legend:** Located on the right side of the heatmap, ranging from dark blue (representing a value of 1) to light green/white (representing a value of 0). ### Detailed Analysis The heatmap shows the importance of each layer for each parameter. * **Layer Importance:** The "Layer Importance" parameter shows high importance (dark blue) across all layers, from layer 2 to layer 30. * **mlp.down\_proj, mlp.up\_proj, mlp.gate\_proj:** These parameters also show high importance (dark blue) across all layers. * **self\_attn.o\_proj:** This parameter shows high importance (dark blue) from layer 2 to approximately layer 16, then gradually decreases in importance (lighter shades of blue) towards layer 30. * **self\_attn.v\_proj, self\_attn.q\_proj, self\_attn.k\_proj:** These parameters show a similar trend to "self\_attn.o\_proj," with high importance in lower layers and decreasing importance in higher layers, transitioning to light blue/green. * **post\_attention\_layernorm, input\_layernorm:** These parameters show low importance (light green/white) across all layers. ### Key Observations * The "Layer Importance," "mlp.down\_proj," "mlp.up\_proj," and "mlp.gate\_proj" parameters are consistently important across all layers. * The importance of "self\_attn.o\_proj," "self\_attn.v\_proj," "self\_attn.q\_proj," and "self\_attn.k\_proj" parameters decreases as the layer number increases. * The "post\_attention\_layernorm" and "input\_layernorm" parameters have low importance across all layers. ### Interpretation The heatmap suggests that certain parameters (Layer Importance, mlp.down\_proj, mlp.up\_proj, mlp.gate\_proj) are crucial for all layers of the neural network. Self-attention related parameters (self\_attn.o\_proj, self\_attn.v\_proj, self\_attn.q\_proj, self\_attn.k\_proj) are more important in the lower layers, possibly indicating that these layers are responsible for capturing initial contextual information. The layernorm parameters (post\_attention\_layernorm, input\_layernorm) appear to have a less significant role in the network's performance, at least according to this importance metric. The data demonstrates a clear distinction in the importance of different parameters across the layers of the neural network.

## Heatmap: Layer Importance vs. Parameter ### Overview This image presents a heatmap visualizing the relationship between layer number and the importance assigned to different parameters within a neural network model. The heatmap uses a color gradient to represent the magnitude of layer importance, ranging from 0 (lightest color) to 1 (darkest color). ### Components/Axes * **X-axis:** "Parameter" - Categorical variable representing different parameters within the model. The parameters are: `mlp.down_proj`, `mlp.up_proj`, `mlp.gate_proj`, `self_attn.o_proj`, `self_attn.v_proj`, `self_attn.q_proj`, `self_attn.k_proj`, `post_attention_layernorm`, `input_layernorm`. * **Y-axis:** "Layer" - Numerical variable representing the layer number, ranging from 0 to 30. * **Color Scale/Legend:** A vertical color bar on the right side of the heatmap. It maps color intensity to the value of layer importance. * 0 is represented by a light cyan color. * 1 is represented by a dark blue color. * Intermediate values are represented by shades of blue. ### Detailed Analysis The heatmap displays the layer importance for each parameter across different layers. The color intensity indicates the degree of importance. * **mlp.down_proj:** Shows high importance (dark blue) for layers 0-16, then rapidly decreases to near zero for layers 17-30. * **mlp.up_proj:** Similar to `mlp.down_proj`, high importance for layers 0-16, decreasing to near zero for layers 17-30. * **mlp.gate_proj:** High importance for layers 0-16, decreasing to near zero for layers 17-30. * **self_attn.o_proj:** Shows a moderate level of importance (medium blue) for layers 0-24, then decreases to near zero for layers 25-30. * **self_attn.v_proj:** Shows a moderate level of importance (medium blue) for layers 0-24, then decreases to near zero for layers 25-30. * **self_attn.q_proj:** Shows a moderate level of importance (medium blue) for layers 0-24, then decreases to near zero for layers 25-30. * **self_attn.k_proj:** Shows a moderate level of importance (medium blue) for layers 0-24, then decreases to near zero for layers 25-30. * **post_attention_layernorm:** Shows a low level of importance (light blue) across all layers, with a slight increase in layers 10-20. * **input_layernorm:** Shows a very low level of importance (almost white) across all layers. **Approximate Data Points (based on visual inspection):** | Parameter | Layer 0 | Layer 8 | Layer 16 | Layer 24 | Layer 30 | | ----------------------- | ------- | ------- | -------- | -------- | -------- | | mlp.down_proj | ~1.0 | ~1.0 | ~1.0 | ~0.2 | ~0.0 | | mlp.up_proj | ~1.0 | ~1.0 | ~1.0 | ~0.2 | ~0.0 | | mlp.gate_proj | ~1.0 | ~1.0 | ~1.0 | ~0.2 | ~0.0 | | self_attn.o_proj | ~0.8 | ~0.8 | ~0.6 | ~0.4 | ~0.0 | | self_attn.v_proj | ~0.8 | ~0.8 | ~0.6 | ~0.4 | ~0.0 | | self_attn.q_proj | ~0.8 | ~0.8 | ~0.6 | ~0.4 | ~0.0 | | self_attn.k_proj | ~0.8 | ~0.8 | ~0.6 | ~0.4 | ~0.0 | | post_attention_layernorm| ~0.1 | ~0.2 | ~0.2 | ~0.1 | ~0.0 | | input_layernorm | ~0.0 | ~0.0 | ~0.0 | ~0.0 | ~0.0 | ### Key Observations * The `mlp` parameters (`mlp.down_proj`, `mlp.up_proj`, `mlp.gate_proj`) exhibit significantly higher importance in the initial layers (0-16) and then rapidly diminish in deeper layers. * The `self_attn` parameters (`self_attn.o_proj`, `self_attn.v_proj`, `self_attn.q_proj`, `self_attn.k_proj`) show moderate importance in the initial to mid layers (0-24) and then decrease. * `post_attention_layernorm` has consistently low importance across all layers. * `input_layernorm` has negligible importance across all layers. * There is a clear trend of decreasing importance for most parameters as the layer number increases. ### Interpretation This heatmap suggests that the initial layers of the model (0-16) heavily rely on the `mlp` parameters for processing information. As the information propagates through deeper layers, the importance of these `mlp` parameters decreases, while the `self_attn` parameters play a more significant role in the mid-layers (up to layer 24). The consistently low importance of `post_attention_layernorm` and `input_layernorm` indicates that these parameters have a limited impact on the overall model performance. The observed trend of decreasing importance with increasing layer number could indicate that the model is learning to extract increasingly abstract features in the deeper layers, requiring less reliance on the initial parameter transformations. This is a common pattern in deep learning models, where lower layers learn basic features and higher layers combine these features to form more complex representations. The rapid drop-off in importance for the `mlp` parameters after layer 16 might suggest a transition in the model's processing strategy, potentially relying more on attention mechanisms in the deeper layers.

## Heatmap: Layer-wise Parameter Importance in a Neural Network ### Overview The image is a heatmap visualizing the relative importance of different parameters across the layers of a neural network model. The heatmap uses a color gradient from light (value 0) to dark blue (value 1) to represent importance scores. The data suggests an analysis of which components within the model's architecture are most significant for its function, likely derived from an interpretability technique like gradient-based attribution or parameter pruning sensitivity. ### Components/Axes * **Y-Axis (Vertical):** Labeled **"Layer"**. It represents the depth of the network, with layers numbered from **0** (bottom) to **30** (top). The axis has tick marks at every even number (0, 2, 4, ..., 30). * **X-Axis (Horizontal):** Labeled **"Parameter"**. It lists specific components or weight matrices within each layer. The categories, from left to right, are: 1. `Layer Importance` (This appears to be an aggregate or summary column for the entire layer). 2. `mlp.down_proj` 3. `mlp.up_proj` 4. `mlp.gate_proj` 5. `self_attn.o_proj` 6. `self_attn.v_proj` 7. `self_attn.q_proj` 8. `self_attn.k_proj` 9. `post_attention_layernorm` 10. `input_layernorm` * **Legend/Color Scale:** Located on the right side of the chart. It is a vertical bar showing a gradient from **light greenish-white (labeled "0")** at the bottom to **dark blue (labeled "1")** at the top. This scale maps color intensity to an importance value between 0 and 1. ### Detailed Analysis The heatmap displays a grid where each cell's color corresponds to the importance value of a specific parameter at a specific layer. **Trend Verification & Data Point Extraction:** * **`Layer Importance` Column:** This column shows a clear gradient. Importance is highest (darkest blue, ~0.9-1.0) in the lowest layers (0-6). It gradually becomes lighter (decreasing to ~0.5-0.7) in the middle layers (8-20), and is lightest (lowest importance, ~0.2-0.4) in the highest layers (22-30). * **MLP Parameters (`mlp.down_proj`, `mlp.up_proj`, `mlp.gate_proj`):** These three columns exhibit a very similar and strong pattern. They are consistently the **darkest blue (highest importance, ~0.8-1.0)** across almost all layers, from 0 to 30. There is a very slight lightening in the topmost layers (28-30), but they remain significantly darker than most other parameters. * **Self-Attention Output & Value Projections (`self_attn.o_proj`, `self_attn.v_proj`):** These columns show moderate importance. They are a medium blue (~0.5-0.7) in the lower to middle layers (0-18) and become progressively lighter (~0.2-0.4) in the higher layers (20-30). * **Self-Attention Query & Key Projections (`self_attn.q_proj`, `self_attn.k_proj`):** These are lighter than the `o_proj` and `v_proj`. They start as a light-medium blue (~0.4-0.6) in lower layers and fade to very light (~0.1-0.3) in higher layers. * **Layer Normalization Parameters (`post_attention_layernorm`, `input_layernorm`):** These two rightmost columns are the **lightest overall (lowest importance, ~0.0-0.2)**. They show a very faint greenish-white color across all layers, with `input_layernorm` being marginally lighter than `post_attention_layernorm`. ### Key Observations 1. **Dominance of MLP Layers:** The Multi-Layer Perceptron (MLP) projection layers (`down_proj`, `up_proj`, `gate_proj`) are unequivocally the most important parameters throughout the entire network depth. 2. **Layer Depth vs. Importance:** There is a general trend where parameter importance decreases as the layer number increases (i.e., deeper into the network). This is most pronounced in the `Layer Importance` summary and the attention projection parameters. 3. **Attention Component Hierarchy:** Within the self-attention mechanism, a clear hierarchy exists: `o_proj` and `v_proj` are more important than `q_proj` and `k_proj`. 4. **Minimal Role of LayerNorm:** The layer normalization parameters (`input_layernorm` and `post_attention_layernorm`) have consistently negligible importance scores according to this metric. ### Interpretation This heatmap provides a Peircean investigative window into the functional architecture of the analyzed model (likely a Transformer-based LLM). The data suggests: * **Core Computational Engine:** The MLP blocks are the primary drivers of the model's representational power or task-specific processing, as their parameters are deemed highly important across all layers. This aligns with theories that MLPs store factual knowledge and perform complex transformations. * **Feature Processing in Early Layers:** The higher importance in lower layers indicates that the initial processing of input features is critical. The model's foundational understanding is built here. * **Attention's Role:** The attention mechanism, while important, shows a differentiated role. The output (`o_proj`) and value (`v_proj`) projections, which combine information from different tokens, are more crucial than the query (`q_proj`) and key (`k_proj`) projections, which determine attention patterns. This could imply that *how* information is aggregated is more vital than the precise matching of queries and keys for this specific importance metric. * **Normalization as a Utility:** The very low importance of LayerNorm parameters suggests they act as stable, routine utility functions—essential for training stability but not carrying significant "information" or "importance" in terms of the model's final output decision, as measured by this analysis. **Anomaly/Notable Point:** The `Layer Importance` column is an aggregate. Its gradient from dark to light confirms the overall trend that lower layers are more "important" than higher layers by this metric, which is a key insight for model compression or pruning strategies—pruning higher layers may be less damaging.

## Heatmap: Parameter Importance Across Transformer Layers ### Overview The image is a heatmap visualizing the importance of various parameters across 31 transformer layers (0–30). Darker blue shades indicate higher importance (closer to 1), while lighter shades represent lower importance (closer to 0). The x-axis lists parameters, and the y-axis represents layers. The colorbar on the right quantifies importance from 0 to 1. ### Components/Axes - **X-axis (Parameters)**: - `Layer Importance` - `mlp.down_proj` - `mlp.up_proj` - `mlp.gate_proj` - `mlp.attn.o_proj` - `self_attn.v_proj` - `self_attn.q_proj` - `self_attn.k_proj` - `post_attention_layernorm` - `input_layernorm` - **Y-axis (Layers)**: - Layers labeled from 0 (bottom) to 30 (top). - **Color Legend**: - Dark blue = 1 (highest importance) - Light gray = 0 (lowest importance) ### Detailed Analysis - **Layer Importance**: - Peaks in **layers 0–2** (darkest blue), then gradually lightens toward layer 30. - Approximate values: ~0.9 (layer 0), ~0.7 (layer 10), ~0.3 (layer 30). - **MLP Projections**: - `mlp.down_proj` and `mlp.up_proj` show strong importance in **layers 0–10** (~0.8–0.6), fading to ~0.2 in higher layers. - `mlp.gate_proj` is consistently dark in **layers 0–15** (~0.7–0.5), then lightens. - **Self-Attention Projections**: - `self_attn.v_proj` and `self_attn.q_proj` have moderate importance in **layers 5–20** (~0.5–0.4), with peaks around layer 10. - `self_attn.k_proj` follows a similar trend but is slightly lighter (~0.4–0.3). - **Layer Normalization**: - `post_attention_layernorm` and `input_layernorm` are uniformly light across all layers (~0.1–0.2), indicating minimal importance. ### Key Observations 1. **Layer-Specific Importance**: - Lower layers (0–10) dominate in parameter importance, with values dropping sharply after layer 20. - `Layer Importance` and MLP projections (`mlp.down_proj`, `mlp.up_proj`) are most critical in early layers. 2. **Self-Attention Patterns**: - Self-attention projections (`v_proj`, `q_proj`, `k_proj`) show moderate importance in mid-layers (5–20), suggesting their role in intermediate processing. 3. **Normalization Insignificance**: - Both `post_attention_layernorm` and `input_layernorm` are consistently light, implying minimal impact on model behavior. ### Interpretation The heatmap reveals that **early layers** (0–10) are critical for parameter-driven transformations, particularly MLP and self-attention projections. The sharp decline in importance after layer 20 suggests that higher layers may focus on higher-level abstractions or rely on precomputed features. The negligible importance of layer normalization parameters across all layers indicates that these components may not significantly influence the model’s output in this context. This pattern aligns with typical transformer architectures, where lower layers handle feature extraction and higher layers refine representations. **Notable Outlier**: `mlp.gate_proj` maintains moderate importance up to layer 15, suggesting a prolonged role in gating mechanisms compared to other MLP projections.