## Heatmap: Layer vs. Token ### Overview The image is a heatmap visualizing 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 color scale ranges from 0.5 to 1.0. ### Components/Axes * **Y-axis:** "Layer" with numerical labels from 0 to 30, incrementing by 2. * **X-axis:** "Token" with categorical labels: "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:** Ranges from 0.5 (lightest blue) to 1.0 (darkest blue), with intermediate values of 0.6, 0.7, 0.8, and 0.9. The color scale is positioned on the right side of the heatmap. ### Detailed Analysis The heatmap shows the values for each combination of layer and token. * **Tokens "last\_q", "first\_answer", "second\_answer", "exact\_answer\_before\_first", "exact\_answer\_first", "exact\_answer\_last", "exact\_answer\_after\_last":** * Layers 0-16: Generally have higher values (darker blue), mostly between 0.8 and 1.0. * Layers 18-30: Values tend to decrease (lighter blue), ranging from 0.6 to 0.8. * **Tokens "-8" to "-1":** * Values are generally lower (lighter blue) compared to the other tokens, mostly between 0.5 and 0.7. * There are some exceptions, such as layer 26 for token "-8", which has a slightly higher value (around 0.7-0.8). ### Key Observations * The first seven tokens ("last\_q" to "exact\_answer\_after\_last") show a similar pattern: higher values in the lower layers (0-16) and decreasing values in the higher layers (18-30). * The last eight tokens ("-8" to "-1") have consistently lower values across all layers. * There is a clear distinction in the heatmap between the first group of tokens and the second group of tokens. ### Interpretation The heatmap suggests that the initial layers (0-16) of the model are more sensitive to the first seven tokens ("last\_q" to "exact\_answer\_after\_last"), while the later layers (18-30) are less sensitive. The tokens "-8" to "-1" appear to have a consistently lower impact across all layers. This could indicate that the first set of tokens are more important for the model's initial processing, while the second set of tokens might represent less relevant or more nuanced information that is processed differently across the layers. The data suggests a hierarchical processing of information within the model, where different layers focus on different aspects of the input.

\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.

## Heatmap: Layer vs. Token Activation/Attention Pattern ### Overview The image is a heatmap visualization, likely representing activation strengths, attention weights, or some form of normalized score (ranging from 0.5 to 1.0) across different layers of a neural network model and specific token positions. The chart shows how a particular metric varies for different tokens at each layer depth. ### Components/Axes * **Chart Type:** Heatmap. * **Y-Axis (Vertical):** Labeled **"Layer"**. It represents the depth within a model, with tick marks and labels at intervals of 2, starting from **0** at the top and descending to **30** at the bottom. * **X-Axis (Horizontal):** Labeled **"Token"**. It lists specific token identifiers or positions. The labels are rotated 90 degrees for readability. From left to right, the tokens 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 Bar/Legend:** Positioned on the **right side** of the chart. It is a vertical gradient bar mapping color intensity to numerical values. * **Scale:** Linear, from **0.5** (lightest blue/white) at the bottom to **1.0** (darkest blue) at the top. * **Labels:** Major ticks are labeled at **0.5, 0.6, 0.7, 0.8, 0.9, and 1.0**. ### Detailed Analysis The heatmap displays a grid where each cell's color corresponds to a value between 0.5 and 1.0 for a specific Layer-Token pair. **General Trend Verification:** * **Vertical Trend (Per Token):** For most tokens, the value (color intensity) is not constant across layers. There is significant variation from top (Layer 0) to bottom (Layer 30). * **Horizontal Trend (Per Layer):** Within a single layer row, the value varies considerably across different tokens. No single layer shows a uniform color across all tokens. **Specific Observations by Token Group:** 1. **Named Tokens (Left 7 columns):** * `last_q`, `first_answer`, `second_answer`: Show moderate to high values (medium to dark blue) in the early-to-mid layers (approx. Layers 0-16). The intensity often peaks around Layers 4-12. * `exact_answer_before_first`, `exact_answer_first`, `exact_answer_last`: These three tokens exhibit a very strong, consistent pattern. They display the **highest values (darkest blue, ~0.9-1.0)** across a broad range of layers, particularly from Layer 4 down to approximately Layer 20. This forms a prominent dark vertical band in the center-left of the heatmap. * `exact_answer_after_last`: Shows a more moderate pattern, with higher values in early layers that fade in deeper layers. 2. **Numerical Tokens (Right 8 columns, `-8` to `-1`):** * These tokens generally show **lower values (lighter blue, ~0.5-0.7)** compared to the named "exact_answer" tokens. * There is a subtle gradient: tokens `-8` and `-7` tend to have slightly higher values in the very early layers (0-6) compared to tokens `-1` and `-2`. * The region for these tokens becomes very light (values near 0.5) in the middle layers (approx. Layers 10-22), indicating minimal activation or attention. **Spatial Grounding & Key Data Points:** * **Highest Values (~1.0):** Concentrated in the columns for `exact_answer_before_first`, `exact_answer_first`, and `exact_answer_last`, primarily between **Layers 8 and 16**. * **Lowest Values (~0.5):** Found in the columns for the numerical tokens (`-5` to `-1`) in the **middle layer range (Layers 12-20)**. * **Notable Anomaly:** The column for `exact_answer_after_last` shows a pocket of higher value (darker blue) around **Layer 26-28**, which is an outlier compared to its surrounding layers and the general trend of the numerical tokens to its right. ### Key Observations 1. **Strong Selective Activation:** The model's internal representations (as measured by this metric) are highly selective. Tokens related to the "exact answer" (especially `before_first`, `first`, and `last`) elicit a much stronger response across many layers than the question token (`last_q`) or other answer tokens. 2. **Layer-Specific Processing:** The processing focus shifts with depth. Early layers (0-10) show broad activation across many named tokens. Mid-layers (10-20) show extreme specialization for the core "exact answer" tokens. Deeper layers (20-30) show a more diffuse and generally weaker pattern. 3. **Positional Encoding for Numerical Tokens:** The numerical tokens (`-8` to `-1`), which likely represent relative positions (e.g., tokens before the answer), show a weak and fading signal, suggesting they are less critical for the measured metric in deeper processing stages. ### Interpretation This heatmap likely visualizes **attention weights** or **activation norms** from a transformer-based model during a question-answering task. The data suggests the model has learned to strongly focus on and process the tokens that constitute the "exact answer" throughout a significant portion of its network depth (Layers 4-20). This indicates these tokens are information-rich and central to the model's reasoning or output generation process. The weaker signal for the question token (`last_q`) and other answer tokens implies they may serve more as context, while the core answer tokens are the primary carriers of the required information. The fading signal for positional numerical tokens in mid-layers suggests that precise positional information becomes less important as the model integrates semantic meaning in deeper layers. The outlier high-value spot for `exact_answer_after_last` in deep layers could indicate a late-stage verification or formatting step related to the answer's boundary. In essence, the chart provides a "brain scan" of the model, revealing which parts of the input it deems most important and at what stage of processing. The clear, strong pattern for the exact answer tokens is a sign of a model that has successfully learned to identify and prioritize the key information for its task.

## 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.