## 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 spans layers 0 to 30 and various tokens, including "last_q", "first_answer", "second_answer", "exact_answer_before_first", "exact_answer_first", "exact_answer_last", "exact_answer_after_last", and numerical tokens from -8 to -1. ### Components/Axes * **X-axis (Token):** Categorical, listing tokens: "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, ranging from 0 to 30 in increments of 2. * **Color Scale:** A gradient from light blue (approximately 0.5) to dark blue (1.0), indicating the value associated with each cell in the heatmap. ### Detailed Analysis The heatmap displays varying intensities of blue, indicating different values for each layer-token combination. * **"last\_q", "first\_answer", "second\_answer":** These tokens show relatively high values (darker blue) across most layers, especially from layer 0 to approximately layer 20. The values seem to decrease slightly in the higher layers (20-30). * **"exact\_answer\_before\_first", "exact\_answer\_first", "exact\_answer\_last", "exact\_answer\_after\_last":** These tokens exhibit a band of high values (darker blue) concentrated between approximately layers 8 and 18. Outside this band, the values are generally lower (lighter blue). * **Numerical Tokens (-8 to -1):** These tokens generally show lower values (lighter blue) across all layers compared to the other tokens. There are some localized areas of slightly higher values, but overall, the intensity is less. ### Key Observations * The tokens related to "exact\_answer" exhibit a distinct band of high values in the middle layers (8-18). * The initial tokens ("last\_q", "first\_answer", "second\_answer") have higher values in the lower layers, gradually decreasing as the layer number increases. * The numerical tokens (-8 to -1) generally have the lowest values across all layers. ### Interpretation The heatmap likely represents the activation or importance of different tokens across various layers of a neural network model, possibly a transformer model used for question answering. * The high values for "last\_q", "first\_answer", and "second\_answer" in the lower layers suggest that these tokens are important for initial processing and understanding of the question. * The concentration of high values for "exact\_answer" tokens in the middle layers indicates that these layers are crucial for identifying and processing the exact answer within the context. * The lower values for numerical tokens might indicate that these tokens are less relevant for the specific task or model being analyzed. The distinct patterns observed in the heatmap suggest that different layers of the model specialize in processing different types of tokens, contributing to the overall question-answering process. The black box highlights the "exact_answer" tokens, emphasizing their importance in the middle layers.

\n ## Heatmap: Layer vs. Token Correlation ### Overview The image presents a heatmap visualizing the correlation between different layers of a model and various tokens. The heatmap uses a color gradient to represent correlation values, ranging from 0.5 (light blue) to 1.0 (dark blue). The x-axis represents tokens, and the y-axis represents layers. ### Components/Axes * **X-axis (Horizontal):** "Token" with the following categories: "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):** "Layer" ranging from 0 to 30, with increments of 2. * **Color Scale (Right):** Represents correlation values. * 0.5: Light Blue * 0.6: Light-Medium Blue * 0.7: Medium Blue * 0.8: Medium-Dark Blue * 0.9: Dark Blue * 1.0: Very Dark Blue * **Legend Position:** Top-right corner. ### Detailed Analysis The heatmap shows varying degrees of correlation between layers and tokens. Here's a breakdown of observed values, noting approximate values due to the visual nature of the data: * **Layer 0-4:** High correlation (approximately 0.9-1.0) with "first\_answer" and "second\_answer". Correlation decreases as we move towards "exact\_answer\_last" and the negative tokens. * **Layer 6-8:** Maintains high correlation (approximately 0.8-0.9) with "first\_answer" and "second\_answer". A slight increase in correlation with "exact\_answer\_before\_first" and "exact\_answer\_first" is observed. * **Layer 10-12:** Correlation with "first\_answer" and "second\_answer" remains high (approximately 0.8-0.9). Correlation with "exact\_answer\_first" and "exact\_answer\_last" increases to around 0.7-0.8. * **Layer 14-16:** A peak in correlation (approximately 0.9-1.0) is observed with "exact\_answer\_first". Correlation with "first\_answer" and "second\_answer" decreases slightly to around 0.7-0.8. * **Layer 18-20:** Correlation with "exact\_answer\_first" remains high (approximately 0.8-0.9). Correlation with the negative tokens (-8 to -1) begins to increase, reaching around 0.6-0.7. * **Layer 22-24:** Correlation with "exact\_answer\_first" decreases to around 0.7-0.8. Correlation with the negative tokens continues to increase, reaching around 0.7-0.8 for -4 and -3. * **Layer 26-28:** Correlation with "exact\_answer\_first" is around 0.6-0.7. Correlation with the negative tokens is relatively stable, around 0.6-0.7. * **Layer 30:** Low correlation (approximately 0.5-0.6) across all tokens. **Specific Data Points (Approximate):** * Layer 0, "first\_answer": ~0.95 * Layer 0, "exact\_answer\_last": ~0.55 * Layer 14, "exact\_answer\_first": ~1.0 * Layer 18, "-4": ~0.65 * Layer 30, "last\_q": ~0.55 * Layer 30, "exact\_answer\_first": ~0.6 ### Key Observations * The highest correlations are generally observed between layers 0-16 and the "first\_answer" and "second\_answer" tokens. * Correlation with "exact\_answer\_first" peaks around layer 14-16. * Correlation with negative tokens (-8 to -1) increases with layer depth, peaking around layers 18-24. * Layer 30 exhibits the lowest overall correlation with all tokens. * The "last\_q" token consistently shows lower correlation values compared to the answer tokens. ### Interpretation This heatmap likely represents the attention weights or activation patterns within a neural network model, specifically related to question answering. The strong correlation between early layers (0-16) and "first\_answer" and "second\_answer" suggests that these layers are crucial for initial answer generation. The peak in correlation with "exact\_answer\_first" around layer 14-16 indicates that this layer is particularly important for refining the answer towards a precise match. The increasing correlation with negative tokens as the layer depth increases could indicate that later layers are involved in identifying and suppressing incorrect or irrelevant information. The low correlation in layer 30 suggests that this layer might be involved in a more global processing step or a final decision-making stage. The relatively low correlation of "last\_q" across all layers might suggest that the model doesn't heavily rely on the initial question representation in later stages of processing, or that the question information is effectively integrated into the hidden states. The heatmap provides valuable insights into how the model processes information at different layers and how different tokens contribute to the final answer. This information can be used to diagnose potential issues, optimize model architecture, and improve performance.

## Heatmap: Layer vs. Token Activation/Attention ### Overview The image displays a heatmap visualizing a numerical value (likely attention weight, activation strength, or correlation) across two dimensions: **Layer** (vertical axis) and **Token** (horizontal axis). The data is represented by a color gradient from light blue (low value) to dark blue (high value). A prominent black rectangular outline highlights a specific region of interest within the heatmap. ### Components/Axes * **Y-Axis (Vertical):** Labeled **"Layer"**. The scale runs from **0** at the top to **30** at the bottom, with major tick marks at every even number (0, 2, 4, ..., 30). This likely represents layers in a neural network model. * **X-Axis (Horizontal):** Labeled **"Token"**. It contains a series of categorical and numerical labels. From left to right, the labels are: * `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` * **Color Scale/Legend:** Positioned on the right side of the chart. It is a vertical color bar labeled with numerical values. The scale ranges from **0.5** (lightest blue/white at the bottom) to **1.0** (darkest blue at the top), with intermediate markers at **0.6, 0.7, 0.8, and 0.9**. * **Highlighted Region:** A thick black rectangle is drawn around a vertical block of cells. This region spans horizontally from the token `exact_answer_before_first` to `exact_answer_after_last` (covering four token columns) and vertically across all layers (0 to 30). ### Detailed Analysis The heatmap shows a grid of colored cells, where each cell's color corresponds to a value between approximately 0.5 and 1.0. * **General Pattern:** The left side of the heatmap (tokens `last_q` through `exact_answer_after_last`) generally exhibits higher values (darker blue shades) compared to the right side (numerical tokens `-8` to `-1`), which are predominantly lighter. * **Within the Highlighted Region:** The four columns within the black rectangle (`exact_answer_before_first`, `exact_answer_first`, `exact_answer_last`, `exact_answer_after_last`) show the highest concentration of dark blue cells, indicating values consistently in the upper range of the scale (0.7 to 1.0). The intensity appears particularly strong in the middle layers (approximately layers 8 through 20). * **Layer Trends:** For the highlighted tokens, values seem to peak in the middle layers and are slightly lower in the very top (0-4) and bottom (26-30) layers. For the numerical tokens on the right, values are uniformly low across all layers, with only faint blue shading. * **Token Trends:** Moving from left to right across the x-axis, there is a clear gradient of decreasing value intensity. The `exact_answer_*` tokens have the highest values, followed by `second_answer` and `first_answer`, then `last_q`. The numerical tokens (`-8` to `-1`) have the lowest values. ### Key Observations 1. **Strongest Signal:** The model's layers show the strongest response (highest values) to tokens related to the "exact answer" (`exact_answer_before_first`, `exact_answer_first`, `exact_answer_last`, `exact_answer_after_last`). 2. **Spatial Focus:** The black rectangle explicitly draws attention to this "exact answer" token group, suggesting it is the primary subject of analysis. 3. **Clear Dichotomy:** There is a stark contrast between the high-value region on the left (semantic/answer tokens) and the low-value region on the right (numerical position tokens). 4. **Mid-Layer Peak:** Within the high-value region, the signal is not uniform across layers; it appears most intense in the network's middle layers. ### Interpretation This heatmap likely visualizes **attention weights** or **activation patterns** in a transformer-based language model during a question-answering task. The data suggests the following: * **Model Focus:** The model allocates significantly more "attention" or computational resources to tokens directly surrounding and comprising the exact answer compared to other parts of the input (like the question token `last_q` or positional markers `-8` to `-1`). * **Information Processing:** The concentration of high values in the middle layers aligns with common findings in neural network interpretability, where mid-level layers often process task-specific, semantic information. * **Functional Implication:** The pattern indicates the model has learned to identify and prioritize the span of text that constitutes the precise answer. The tokens `exact_answer_before_first` and `exact_answer_after_last` likely act as boundary markers, helping the model isolate the answer span. The low values for numerical tokens suggest they serve a minor, possibly structural, role that does not require strong activation. * **Anomaly/Outlier:** There are no major outliers; the gradient from high to low values across token types is smooth and consistent, indicating a robust and focused pattern of model behavior for this task. The black rectangle is an annotation, not a data feature, used to emphasize the key finding.

## Heatmap: Attention Weights Across Transformer Layers and Tokens ### Overview The image is a heatmap visualizing attention weights across 31 transformer layers (0–30) and 11 token categories. Attention values range from 0.5 (light blue) to 1.0 (dark blue), with a highlighted region (black rectangle) emphasizing specific layers and tokens. The heatmap suggests a focus on token relationships and layer-specific processing patterns. ### Components/Axes - **X-axis (Tokens)**: `last_q`, `first_answer`, `second_answer`, `exact_answer_before_last`, `exact_answer_last`, `exact_answer_after_last` (Token categories related to question/answer positions in a sequence) - **Y-axis (Layers)**: Layers 0–30 (representing transformer decoder layers in a model) - **Color Scale**: Vertical bar on the right, ranging from 0.5 (lightest blue) to 1.0 (darkest blue), indicating attention weight magnitude. - **Highlighted Region**: Black rectangle spanning layers 10–20 and tokens `exact_answer_last` to `exact_answer_after_last`. ### Detailed Analysis - **Token Categories**: - `last_q`: Appears in all layers, with moderate attention (0.6–0.8). - `first_answer`, `second_answer`: Lower attention (0.5–0.7) in early layers, increasing slightly in later layers. - `exact_answer_before_last`, `exact_answer_last`, `exact_answer_after_last`: High attention (0.8–1.0) in layers 10–20, with `exact_answer_last` showing the strongest focus (darkest blue). - **Layer Trends**: - Early layers (0–10): Lower overall attention weights (0.5–0.7), with gradual increases toward `exact_answer_last`. - Middle layers (10–20): Peak attention for `exact_answer_last` and `exact_answer_after_last` (0.9–1.0). - Later layers (20–30): Attention weights decline slightly (0.7–0.9), with `exact_answer_last` remaining dominant. - **Color Consistency**: Darker blues in the highlighted region align with the legend’s 0.9–1.0 range, confirming high attention in this subregion. ### Key Observations 1. **Concentration of Attention**: The highlighted region (`exact_answer_last`/`exact_answer_after_last` in layers 10–20) shows the highest attention weights, suggesting these tokens are critical for the model’s decision-making. 2. **Layer-Specific Processing**: Early layers focus on general context (`last_q`), while middle layers specialize in precise answer tokens. Later layers refine these relationships but show reduced intensity. 3. **Uniformity in Later Layers**: Layers 20–30 exhibit more uniform attention across tokens, possibly indicating stabilized representations. ### Interpretation This heatmap likely represents attention weights in a transformer-based model (e.g., for question answering). The highlighted region indicates that layers 10–20 prioritize tokens directly related to the exact answer, suggesting these layers are pivotal for extracting precise information. The decline in attention weights in later layers may reflect the model’s consolidation of information rather than active processing. The trend implies that earlier layers handle contextual understanding, while middle layers focus on answer extraction, and later layers refine outputs. The uniformity in later layers could indicate over-smoothing or reduced discriminative power in deeper layers.