## Heatmap: Token-Layer Interaction Intensity ### Overview The image is a heatmap visualizing the interaction intensity between tokens and transformer layers in a neural network. Darker blue shades represent higher interaction values (closer to 1.0), while lighter shades indicate lower values (closer to 0.5). The x-axis lists token types and their instances, while the y-axis shows layer numbers (0-30). The color scale on the right quantifies interaction strength. ### 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` - Sub-categories: Numeric suffixes (e.g., `first_answer_1`, `first_answer_2`, ..., `first_answer_30`) - **Y-axis (Layer)**: Layer numbers 0 to 30 (bottom to top) - **Legend**: Color scale from 0.5 (light gray) to 1.0 (dark blue), positioned on the right ### Detailed Analysis - **Token-Layer Distribution**: - **`last_q`**: High intensity (dark blue) in layers 0-10, decreasing to light gray in layers 20-30. - **`first_answer`**: Peaks in layers 10-20 (dark blue at layer 15), fading in layers 0-5 and 25-30. - **`second_answer`**: Similar to `first_answer` but slightly lower intensity overall. - **`exact_answer_before_first`**: High intensity in layers 10-20, with a sharp drop after layer 20. - **`exact_answer_first`**: Concentrated in layers 10-20, with moderate intensity. - **`exact_answer_last`**: Low intensity (<0.6) across all layers, with slight peaks in layers 5-10. - **`exact_answer_after_last`**: Uniformly low intensity (<0.55) across all layers. ### Key Observations 1. **Layer-Specific Token Dominance**: - Early layers (0-10) prioritize `last_q` and `first_answer`. - Middle layers (10-20) show strong activity for `first_answer`, `second_answer`, and `exact_answer_before_first`. - Late layers (20-30) exhibit minimal interaction with most tokens, except faint traces of `exact_answer_last`. 2. **Token Hierarchy**: - `last_q` dominates early layers, suggesting it anchors initial processing. - Answer-related tokens (`first_answer`, `exact_answer_*`) cluster in middle layers, indicating layered refinement. - `exact_answer_after_last` shows negligible interaction, possibly indicating redundancy or post-processing roles. 3. **Color Consistency**: - Dark blue regions align with the legend’s 0.9-1.0 range, confirming high interaction. - Light gray areas (<0.6) match the legend’s lower end, validating weak/no interaction. ### Interpretation The heatmap reveals a hierarchical token processing pipeline: - **Layer 0-10**: Focus on input (`last_q`) and initial answer generation (`first_answer`). - **Layer 10-20**: Refinement of answers (`exact_answer_before_first`, `exact_answer_first`), with `second_answer` acting as a secondary refinement step. - **Layer 20-30**: Minimal token interaction, suggesting these layers may handle higher-level tasks (e.g., context integration) or have sparse relevance to these tokens. Notably, `exact_answer_after_last`’s uniform low intensity implies it may not be actively processed in this architecture, or its role is abstracted into other mechanisms. The sharp drop in `exact_answer_before_first` after layer 20 suggests a cutoff in answer refinement stages.