## Heatmap: Layer vs. Token ### Overview The image is a heatmap visualizing the relationship between "Layer" and "Token". The color intensity represents a value, with darker blue indicating higher values and lighter blue indicating lower values. The heatmap shows how different tokens are represented across different layers of a model. ### Components/Axes * **Y-axis (Layer):** Represents the layer number, ranging from 0 to 30 in increments of 2. * **X-axis (Token):** Represents different tokens, including "last\_q", "exact\_answer\_first", "exact\_answer\_last", "exact\_answer\_after\_last", and numerical tokens from -8 to -1. * **Color Scale:** A color bar on the right side of the heatmap indicates the value range, from 0.5 (lightest blue) to 1.0 (darkest blue). ### Detailed Analysis The heatmap displays the intensity of a certain metric (unspecified) for each combination of layer and token. * **"last\_q", "exact\_answer\_first", "exact\_answer\_last", "exact\_answer\_after\_last" Tokens:** These tokens show high values (dark blue) in the lower layers (approximately layers 14 to 30). The values are lower (lighter blue) in the upper layers (approximately layers 0 to 12). * **Numerical Tokens (-8 to -1):** These tokens generally show lower values (lighter blue) compared to the "last\_q" and "exact\_answer" tokens. There are some variations across layers, with some layers showing slightly higher values than others. The values appear to increase slightly for tokens closer to -1. * **Layer 0-12:** The values for all tokens are generally lower (lighter blue) in these layers compared to the lower layers. ### Key Observations * The "last\_q" and "exact\_answer" tokens have significantly higher values in the lower layers (14-30) compared to the upper layers (0-12). * The numerical tokens (-8 to -1) have generally lower values across all layers compared to the "last\_q" and "exact\_answer" tokens. * There is some variation in values across different layers for the numerical tokens. ### Interpretation The heatmap suggests that the "last\_q" and "exact\_answer" tokens are more strongly represented in the lower layers of the model, while the numerical tokens have a weaker representation overall. The variations across layers for the numerical tokens may indicate that these tokens are processed differently at different stages of the model. The lower values in the upper layers (0-12) for all tokens may indicate that these layers are less sensitive to the specific tokens being analyzed. The data suggests that the model may be focusing on "last\_q" and "exact\_answer" related tokens in the later processing stages.