## Heatmap: Layer vs. Token ### Overview The image is a heatmap displaying the relationship between "Layer" (y-axis) and "Token" (x-axis). The color intensity represents a value, with darker blue indicating higher values and lighter blue indicating lower values. The heatmap provides a visual representation of how different tokens are represented across different layers. ### 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):** * Scale: 0 to 30, incrementing by 2 (0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30) * **Color Scale (Right side of the heatmap):** * 1. 0 (Darkest Blue) * 0.9 * 0.8 * 0.7 * 0.6 * 0.5 (Lightest Blue) ### Detailed Analysis The heatmap shows varying intensities of blue, indicating different values for each layer-token combination. * **last\_q:** The values are relatively high (darker blue) from layer 0 to layer 30, with some variation. * **first\_answer:** The values are relatively high (darker blue) from layer 0 to layer 30, with some variation. * **second\_answer:** The values are relatively high (darker blue) from layer 0 to layer 30, with some variation. * **exact\_answer\_before\_first:** The values are relatively high (darker blue) from layer 0 to layer 30, with some variation. There is a notably darker blue region around layers 14-18. * **exact\_answer\_first:** The values are relatively high (darker blue) from layer 0 to layer 30, with some variation. * **exact\_answer\_last:** The values are relatively high (darker blue) from layer 0 to layer 30, with some variation. * **exact\_answer\_after\_last:** The values are relatively high (darker blue) from layer 0 to layer 30, with some variation. * **-8 to -1:** The values are generally lower (lighter blue) compared to the other tokens, with some variation across layers. ### Key Observations * The tokens "last\_q", "first\_answer", "second\_answer", "exact\_answer\_before\_first", "exact\_answer\_first", "exact\_answer\_last", and "exact\_answer\_after\_last" generally have higher values across all layers compared to the tokens "-8" to "-1". * There is a noticeable darker blue region for "exact\_answer\_before\_first" around layers 14-18, indicating a higher value in this specific layer range. * The tokens "-8" to "-1" show a trend of lower values, suggesting they might be less relevant or have a different representation across the layers. ### Interpretation The heatmap visualizes the relationship between different tokens and layers, likely in a neural network or similar model. The color intensity could represent activation strength, attention weights, or some other measure of importance. The higher values for "last\_q", "first\_answer", "second\_answer", "exact\_answer\_before\_first", "exact\_answer\_first", "exact\_answer\_last", and "exact\_answer\_after\_last" suggest that these tokens are more significant or receive more attention across all layers. The lower values for "-8" to "-1" indicate that these tokens might be less relevant or have a different role in the model. The darker blue region for "exact\_answer\_before\_first" around layers 14-18 could indicate that this token is particularly important in those specific layers.

\n ## Heatmap: Layer vs. Token Correlation ### Overview The image presents a heatmap visualizing the correlation between 'Layer' and 'Token' variables. The heatmap uses a color gradient from light blue (low correlation) to dark blue (high correlation), with values ranging from approximately 0.5 to 1.0. The heatmap appears to represent a matrix where each cell's color indicates the strength of the relationship between a specific layer and a specific token. ### 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 are numbered from 0 to 30, with each number representing a distinct layer. * **Color Scale (Legend):** Located on the right side of the heatmap. The scale ranges from 0.5 (light blue) to 1.0 (dark blue). The scale is linear. * **Data Cells:** Each cell represents the correlation value between a specific layer and a specific token. ### Detailed Analysis The heatmap shows varying degrees of correlation between layers and tokens. Here's a breakdown of observed trends and approximate values: * **'last_q' Token:** Shows consistently low correlation (around 0.5 - 0.6) across all layers. * **'first_answer' Token:** Correlation starts low at layer 0 (approximately 0.55) and increases to a peak around layer 10-12 (approximately 0.85-0.9), then decreases again. * **'second_answer' Token:** Similar trend to 'first_answer', with a peak correlation around layers 8-14 (approximately 0.8-0.9). * **'exact_answer_before_first' Token:** Shows a moderate correlation (around 0.65-0.75) across most layers, with a slight increase towards the middle layers. * **'exact_answer_first' Token:** Exhibits a strong correlation (around 0.8-0.9) across layers 6-18, with a peak around layer 10-12. * **'exact_answer_last' Token:** Shows a moderate correlation (around 0.7-0.8) across layers 6-20. * **'-8' to '-1' Tokens:** These tokens show a generally increasing correlation with increasing layer number, peaking around layers 16-24. The correlation values range from approximately 0.6 to 0.9. Specifically: * '-8': Correlation increases from ~0.6 at layer 0 to ~0.85 at layer 24. * '-7': Correlation increases from ~0.6 at layer 0 to ~0.9 at layer 20. * '-6': Correlation increases from ~0.6 at layer 0 to ~0.9 at layer 22. * '-5': Correlation increases from ~0.6 at layer 0 to ~0.9 at layer 24. * '-4': Correlation increases from ~0.6 at layer 0 to ~0.9 at layer 26. * '-3': Correlation increases from ~0.6 at layer 0 to ~0.9 at layer 28. * '-2': Correlation increases from ~0.6 at layer 0 to ~0.9 at layer 30. * '-1': Correlation increases from ~0.6 at layer 0 to ~0.9 at layer 30. ### Key Observations * The 'first_answer' and 'exact_answer_first' tokens exhibit the highest correlations, particularly in the middle layers (6-18). * The 'last_q' token consistently shows the lowest correlation across all layers. * The negative numbered tokens show a clear positive correlation with layer number, suggesting their influence increases as the model progresses through layers. * There is a noticeable diagonal pattern in the heatmap, indicating a relationship between layer number and token influence. ### Interpretation This heatmap likely represents the attention weights or activation patterns within a neural network model, possibly a language model. The 'tokens' likely represent different parts of the input or output sequence, and the 'layers' represent different stages of processing within the model. The high correlation between 'first_answer' and 'exact_answer_first' in the middle layers suggests that these tokens are strongly related during the model's reasoning process. The low correlation of 'last_q' might indicate that the initial question has less influence on the model's final answer. The increasing correlation of the negative numbered tokens with layer number suggests that these tokens become more important as the model processes information and refines its understanding. This could indicate that these tokens represent features or concepts that are gradually learned or refined throughout the model's layers. The heatmap provides insights into how the model attends to different parts of the input and how this attention changes across different layers. This information can be valuable for understanding the model's behavior, identifying potential biases, and improving its performance.

## Heatmap: Layer-wise Token Activation/Attention Intensity ### Overview The image is a heatmap visualization, likely representing the intensity of attention weights, activation values, or another saliency metric across different layers of a neural network model for specific tokens in a sequence. The chart shows how the importance or activation of certain tokens varies as information propagates through the model's layers. ### Components/Axes * **Chart Type:** Heatmap. * **Y-Axis (Vertical):** Labeled **"Layer"**. It represents the depth within the neural network, with values ranging from **0** at the top to **30** at the bottom, in increments of 2 (0, 2, 4, ..., 30). * **X-Axis (Horizontal):** Labeled **"Token"**. It lists specific tokens or positions in an input sequence. The labels, from left to right, are: 1. `last_q` 2. `first_answer` 3. `second_answer` 4. `exact_answer_before_first` 5. `exact_answer_first` 6. `exact_answer_last` 7. `exact_answer_after_last` 8. `-8` 9. `-7` 10. `-6` 11. `-5` 12. `-4` 13. `-3` 14. `-2` 15. `-1` * **Color Scale/Legend:** Positioned on the **right side** of the chart. It is a vertical color bar indicating the value mapped to each cell's color. The scale ranges from **0.5** (lightest blue/white) at the bottom to **1.0** (darkest blue) at the top. The gradient moves from white/light blue (low value) through medium blue to dark navy blue (high value). ### Detailed Analysis The heatmap is a grid where each cell's color corresponds to a value between 0.5 and 1.0 for a specific (Layer, Token) pair. **Spatial & Color Analysis:** * **High-Value Clusters (Dark Blue):** The most intense, dark blue cells (values approaching 1.0) are concentrated in two primary columns: * **`exact_answer_first` (Column 5):** Shows consistently high values (dark blue) from approximately **Layer 10 down to Layer 30**. The intensity appears strongest around **Layers 14-22**. * **`exact_answer_last` (Column 6):** Also exhibits very high values, particularly from **Layer 12 to Layer 30**, with a peak intensity similar to `exact_answer_first`. * **Moderate-Value Regions (Medium Blue):** * The columns for `exact_answer_before_first` (Column 4) and `exact_answer_after_last` (Column 7) show medium blue shades, indicating moderate values (approx. 0.7-0.85), especially in the middle to lower layers (10-30). * The column for `last_q` (Column 1) displays a patchy pattern of medium blue, with some higher values in the very early layers (0-6) and again in the mid-layers. * **Low-Value Regions (Light Blue/White):** * The columns labeled with negative numbers (`-8` to `-1`, Columns 8-15) are predominantly light blue or white, indicating values closer to the lower end of the scale (0.5-0.65). This suggests these positional tokens have relatively low saliency/activation across all layers. * The tokens `first_answer` (Column 2) and `second_answer` (Column 3) also show generally low to moderate values, lighter than the "exact_answer" columns. **Trend Verification:** * **Vertical Trend (Across Layers):** For the high-value tokens (`exact_answer_first`, `exact_answer_last`), the trend is not linear. Values start low in the initial layers (0-8), increase sharply in the middle layers (10-20), and remain high through the final layers (22-30). This suggests these tokens become critically important in the model's intermediate processing stages. * **Horizontal Trend (Across Tokens):** There is a clear hierarchy of token importance. The "exact answer" boundary tokens (`first`, `last`) are the most salient, followed by their immediate context (`before_first`, `after_last`), then the question token (`last_q`), and finally the generic answer tokens and positional indices, which are the least salient. ### Key Observations 1. **Token Specificity Matters:** The model pays dramatically more attention to tokens explicitly marking the boundaries of the "exact answer" (`exact_answer_first`, `exact_answer_last`) compared to generic answer tokens (`first_answer`, `second_answer`) or positional indices. 2. **Mid-Layer Focus:** The peak activation for critical tokens occurs in the middle to late layers (10-30), not in the earliest embedding layers. This aligns with the understanding that deeper layers in transformers often handle more abstract, task-specific reasoning. 3. **Positional Token Noise:** The low, uniform values for the numbered positional tokens (`-8` to `-1`) suggest they serve as background or structural elements without carrying significant task-specific information in this context. 4. **Symmetry around Answer:** The columns `exact_answer_before_first` and `exact_answer_after_last` show similar, moderate intensity patterns, indicating the model attends to the context immediately surrounding the answer span. ### Interpretation This heatmap provides a technical window into the internal mechanics of a language model, likely during a question-answering task. The data suggests the model has learned to **precisely localize the answer span** by assigning high importance to the tokens that demarcate its start (`exact_answer_first`) and end (`exact_answer_last`). This focus intensifies as the signal propagates through the network's layers, peaking in the mid-to-deep layers where complex feature integration occurs. The stark contrast between the high-value "exact answer" columns and the low-value positional columns indicates the model is not merely relying on token position but is performing **content-based attention**. It successfully identifies and prioritizes the semantically crucial tokens for the task. The moderate attention to the immediate context (`before_first`, `after_last`) may reflect the model verifying the answer's coherence with its surrounding text. **Notable Anomaly:** The token `last_q` (presumably the last token of the question) shows some early-layer activation, which is logical as the question is processed first. However, its importance does not peak as dramatically as the answer-boundary tokens in deeper layers, suggesting the model's focus shifts decisively from question understanding to answer extraction as processing depth increases. In summary, this visualization demonstrates a model that has developed an efficient internal strategy: it uses specific, learned boundary markers to isolate the answer span, dedicating its computational resources (attention/activation) most heavily to these critical points during deep processing.

## Heatmap: Layer-Token Activation Intensity ### Overview The image is a heatmap visualizing the intensity of activation or attention values across different layers and tokens in a neural network. The x-axis represents tokens (ranging from -1 to 30), and the y-axis represents layers (labeled with terms like "last_q", "first_answer", "second_answer", etc.). The color intensity corresponds to activation values, with darker blue indicating higher values (closer to 1.0) and lighter blue indicating lower values (closer to 0.5). ### Components/Axes - **X-axis (Token)**: Labeled with integers from -1 to 30, representing token positions. - **Y-axis (Layer)**: Labeled with terms such as: - "last_q" - "first_answer" - "second_answer" - "exact_answer_before_first" - "exact_answer_first" - "exact_answer_last" - "exact_answer_after_last" - Numerical layers 1–30 (e.g., "1", "2", ..., "30"). - **Legend**: Positioned on the right, showing a gradient from light blue (0.5) to dark blue (1.0). No explicit legend labels are present, but the colorbar implies a continuous scale. ### Detailed Analysis - **Token Ranges**: - **Tokens -1, 0, 1**: Lightest blue (values ~0.5–0.6), indicating low activation. - **Tokens 2–10**: Gradual increase in intensity, peaking at ~0.7–0.8. - **Tokens 11–17**: Moderate activation (~0.7–0.9). - **Tokens 18–20**: Darkest blue (values ~0.9–1.0), suggesting peak activation. - **Tokens 21–30**: Decreasing intensity, returning to ~0.6–0.7. - **Layer Ranges**: - **Layers 1–10**: Light to moderate blue (~0.5–0.7), with sporadic darker patches. - **Layers 11–14**: Darkest blue (~0.9–1.0), indicating highest activation. - **Layers 15–20**: Moderate activation (~0.7–0.9), with some variability. - **Layers 21–30**: Light blue (~0.5–0.6), showing minimal activation. ### Key Observations 1. **Peak Activation**: The highest values (darkest blue) are concentrated in **layers 12–14** and **tokens 18–20**, suggesting these regions are critical for processing. 2. **Edge Effects**: The lowest activation values (~0.5) occur at the edges of the heatmap (layers 28–30 and tokens -1, 0, 1). 3. **Gradient Pattern**: Activation intensity increases toward the center (layers 12–14, tokens 18–20) and decreases toward the edges, forming a "peak" structure. ### Interpretation The heatmap likely represents attention weights or activation magnitudes in a transformer-based model. The central layers (12–14) and tokens (18–20) exhibit the strongest activation, implying they play a pivotal role in encoding or decoding information. The gradual decline in activation toward the edges suggests diminishing relevance of peripheral tokens or layers. This pattern aligns with typical attention mechanisms, where central tokens (e.g., key words in a sentence) dominate processing, while peripheral tokens (e.g., punctuation or filler words) have weaker influence. The absence of extreme outliers indicates a relatively balanced distribution of activation across the model.