\n ## Heatmap: Layer vs. Token Correlation ### Overview The image presents a heatmap visualizing the correlation between 'Layer' and 'Token' variables. The color intensity represents the correlation strength, ranging from 0.5 (light blue) to 1.0 (dark blue). The heatmap appears to be a matrix where each cell represents the correlation value for a specific layer and token combination. ### Components/Axes * **X-axis (Horizontal):** Labeled "Token". The tokens are: 'last_q', 'first_answer', 'second_answer', 'exact_answer_before_first', 'exact_answer_first', 'exact_answer_last', '-8', '-7', '-6', '-5', '-4', '-3', '-2', '-1'. * **Y-axis (Vertical):** Labeled "Layer". The layers range from 2 to 30, with increments of 2. * **Color Scale (Legend):** Located on the right side of the heatmap. The scale ranges from 0.5 (lightest blue) to 1.0 (darkest blue). The values on the scale are: 0.5, 0.6, 0.7, 0.8, 0.9, 1.0. ### Detailed Analysis The heatmap shows varying degrees of correlation between layers and tokens. Here's a breakdown of approximate values, noting the inherent difficulty in precise reading from a visual representation: * **'last_q' Token:** Correlation values are generally low, ranging from approximately 0.52 to 0.65 across layers 2 to 30. * **'first_answer' Token:** Shows a moderate increase in correlation, peaking around 0.75-0.85 between layers 6 and 14. * **'second_answer' Token:** Similar to 'first_answer', with a peak correlation of approximately 0.75-0.85 between layers 6 and 14. * **'exact_answer_before_first' Token:** Correlation values are generally low, similar to 'last_q', ranging from approximately 0.52 to 0.65. * **'exact_answer_first' Token:** Exhibits a strong correlation, particularly between layers 4 and 16, reaching values close to 0.95-1.0. * **'exact_answer_last' Token:** Shows a strong correlation, peaking around 0.85-0.95 between layers 6 and 14. * **'-8' to '-1' Tokens:** These tokens show a generally lower correlation, ranging from approximately 0.55 to 0.75, with some slight variations across layers. The correlation appears to be relatively consistent across these tokens. **Specific Data Points (Approximate):** * Layer 2, 'exact_answer_first': ~0.98 * Layer 4, 'exact_answer_first': ~1.0 * Layer 6, 'first_answer': ~0.78 * Layer 8, 'first_answer': ~0.82 * Layer 10, 'first_answer': ~0.85 * Layer 12, 'first_answer': ~0.83 * Layer 14, 'first_answer': ~0.79 * Layer 16, 'exact_answer_first': ~0.97 * Layer 18, 'exact_answer_first': ~0.95 * Layer 20, 'exact_answer_first': ~0.92 * Layer 22, 'exact_answer_first': ~0.88 * Layer 24, 'exact_answer_first': ~0.82 * Layer 26, 'exact_answer_first': ~0.75 * Layer 28, 'exact_answer_first': ~0.68 * Layer 30, 'exact_answer_first': ~0.62 ### Key Observations * The 'exact_answer_first' token consistently exhibits the highest correlation across most layers, particularly in the lower layers (2-16). * 'first_answer' and 'second_answer' tokens show a similar correlation pattern, peaking around layers 6-14. * 'last_q' and 'exact_answer_before_first' tokens have the lowest correlation values. * The correlation for most tokens appears to decrease as the layer number increases beyond 16. ### Interpretation This heatmap likely represents the attention weights or feature importance of different tokens at various layers within a neural network model, potentially a question-answering system. The high correlation between 'exact_answer_first' and lower layers suggests that the model quickly focuses on identifying the initial correct answer. The moderate correlation of 'first_answer' and 'second_answer' indicates that the model considers these tokens as relevant, but to a lesser extent. The low correlation of 'last_q' and 'exact_answer_before_first' suggests these tokens are less influential in the model's decision-making process. The decreasing correlation with higher layers could indicate that the model refines its focus as it processes information through deeper layers. The heatmap provides insights into which tokens are most important at each layer, which can be valuable for understanding the model's behavior and identifying potential areas for improvement. The strong correlation of 'exact_answer_first' suggests the model is heavily reliant on the initial correct answer, which might be a limitation if the initial answer is incorrect or incomplete.