## Heatmap: Layer-Token Value Distribution ### Overview The image displays a heatmap visualizing the distribution of values across 31 layers (y-axis) and 11 token categories (x-axis). Values range from 0.5 (lightest blue) to 1.0 (darkest blue), with a prominent dark blue rectangular block dominating the center of the visualization. ### Components/Axes - **X-axis (Token)**: - Categories: `last_q`, `first_answer`, `second_answer`, `exact_answer_before_first`, `exact_answer_first`, `exact_answer_last`, `exact_answer_after_last`, `-8`, `-7`, `-6`, `-5`, `-4`, `-3`, `-2`, `-1` - **Y-axis (Layer)**: - Numerical scale from 0 to 30 (inclusive) - **Legend**: - Color bar on the right with gradient from light blue (0.5) to dark blue (1.0) - **Key Feature**: - Dark blue rectangular block spanning layers 10–20 and tokens `exact_answer_first` to `exact_answer_last` ### Detailed Analysis - **Dark Blue Block**: - Positioned centrally (layers 10–20, tokens `exact_answer_first` to `exact_answer_last`) - Values approximate **0.9–1.0** (darkest blue) - **Surrounding Gradient**: - Layers 0–9 and 21–30 show lighter blue shades (values ~0.6–0.8) - Tokens `-8` to `-1` exhibit moderate values (~0.7–0.8) in layers 10–20 - **Edge Cases**: - `last_q` and `first_answer` tokens show minimal intensity (<0.6) across all layers - Tokens `-8` to `-1` have sparse dark blue patches in layers 5–15 ### Key Observations 1. **Central Cluster Dominance**: The dark blue block occupies ~40% of the heatmap, indicating a strong concentration of high values in specific layers and tokens. 2. **Layer-Specific Patterns**: Layers 10–20 consistently show higher values for `exact_answer_*` tokens compared to other layers. 3. **Negative Token Behavior**: Tokens `-8` to `-1` display intermediate values, suggesting partial correlation with the central cluster. ### Interpretation The heatmap reveals that layers 10–20 are critical for processing `exact_answer_*` tokens, with values peaking near 1.0. This suggests these layers may specialize in precise answer extraction or validation. The gradient around the central block implies diminishing importance of these tokens in other layers. The sparse dark blue patches in negative tokens (-8 to -1) hint at potential secondary processing roles, though their values remain significantly lower than the central cluster. The minimal activity in `last_q` and `first_answer` tokens across all layers indicates these may serve distinct, less value-intensive functions in the system.