## Heatmap: Meta Token #2 • Past Cosine-Sim (Padded) ### Overview The image is a heatmap visualizing the cosine similarity between the "Meta Token #2" and tokens appearing after it at a certain distance (T distance). The Y-axis represents the layer number (from 0 to 11), and the X-axis represents the tokens following "Meta Token #2". The color intensity indicates the cosine similarity, ranging from -0.04 (dark purple) to 0.04 (yellow). ### Components/Axes * **Title:** Meta Token #2 • Past Cosine-Sim (Padded) * **X-axis:** Token past of Meta Token #2 (at T distance) * Categories: "iers", "pl", "level", "wrench", "hammer", "PAUSE_", ":", "Tools", "plum", "banana", "peach", "orange", ":", "ruits", "F" * **Y-axis:** Layer * Scale: 0 to 11 (integers) * **Colorbar (located on the right):** cosine similarity * Scale: -0.04 to 0.04 * Markers: -0.04, -0.02, 0.00, 0.02, 0.04 ### Detailed Analysis The heatmap displays the cosine similarity values for each layer (0-11) and each token following "Meta Token #2". * **"iers"**: The cosine similarity is around 0.00 to 0.02 across all layers. * **"pl"**: The cosine similarity is around 0.00 to 0.02 across all layers. * **"level"**: The cosine similarity is high (around 0.04) for layers 0-4, then decreases to around 0.02 for layers 5-11. * **"wrench"**: The cosine similarity is around 0.00 to 0.02 across all layers. * **"hammer"**: The cosine similarity is around 0.00 to 0.02 across all layers. * **"PAUSE_"**: The cosine similarity is around 0.00 to 0.02 across all layers. * **":" (first instance)**: The cosine similarity is around 0.00 to 0.02 across all layers. * **"Tools"**: The cosine similarity is around 0.00 to 0.02 across all layers. * **"plum"**: The cosine similarity is around -0.02 to 0.00 across all layers. * **"banana"**: The cosine similarity is around -0.02 to 0.00 across all layers. * **"peach"**: The cosine similarity is around -0.04 to -0.02 across all layers. * **"orange"**: The cosine similarity is around -0.02 to 0.00 across all layers. * **":" (second instance)**: The cosine similarity is around 0.00 to 0.02 across all layers. * **"ruits"**: The cosine similarity is around 0.00 to 0.02 across all layers. * **"F"**: The cosine similarity is around 0.00 to 0.02 across all layers. ### Key Observations * The token "level" shows a significantly higher cosine similarity in the lower layers (0-4) compared to other tokens. * The tokens "plum", "banana", "peach", and "orange" show negative cosine similarity values. * The cosine similarity values for most tokens are relatively consistent across different layers, with the exception of "level". ### Interpretation The heatmap visualizes how similar the representation of "Meta Token #2" is to the representation of tokens that follow it in a sequence, across different layers of a model. The high cosine similarity for "level" in the lower layers suggests that "Meta Token #2" might be strongly related to "level" in the initial processing stages. The negative cosine similarity for some tokens indicates that their representations are dissimilar to "Meta Token #2". The consistency of cosine similarity across layers for most tokens suggests that their relationship with "Meta Token #2" doesn't change much as the information propagates through the network.

## Heatmap: Meta Token #2 • Past Cosine-Sim (Padded) ### Overview This image presents a heatmap visualizing the cosine similarity between Meta Token #2 and preceding tokens at varying layers. The heatmap is color-coded to represent cosine similarity values, ranging from approximately -0.04 to 0.04. The x-axis represents tokens past Meta Token #2 at a distance of T, and the y-axis represents the layer number. ### Components/Axes * **Title:** "Meta Token #2 • Past Cosine-Sim (Padded)" - positioned at the top-center. * **X-axis Label:** "Token past of Meta Token #2 (at T distance)" - positioned at the bottom-center. * **Y-axis Label:** "Layer" - positioned on the left-center. * **Colorbar Label:** "cosine similarity" - positioned on the right side. * **Colorbar Scale:** Ranges from approximately -0.04 (purple) to 0.04 (yellow). * **X-axis Categories (Tokens):** "iers", "pl", "level", "wrench", "hammer", "_PAUSE_", "...", "Tools", "plum", "banana", "peach", "orange", "...", "ruits", "F". * **Y-axis Categories (Layers):** 0 to 11, inclusive. ### Detailed Analysis The heatmap displays cosine similarity values as color intensities. The colorbar on the right indicates the mapping between color and similarity score. * **Overall Trend:** The heatmap shows a complex pattern of similarity values. There isn't a single, dominant trend across all tokens and layers. * **"iers" Token:** Similarity values are generally low, ranging from approximately -0.02 to 0.02 across layers 0-11. The color is predominantly green/purple. * **"pl" Token:** Similarity values are low, ranging from approximately -0.02 to 0.02 across layers 0-11. The color is predominantly green/purple. * **"level" Token:** Similarity values are low, ranging from approximately -0.02 to 0.02 across layers 0-11. The color is predominantly green/purple. * **"wrench" Token:** Similarity values are low, ranging from approximately -0.02 to 0.02 across layers 0-11. The color is predominantly green/purple. * **"hammer" Token:** Similarity values are low, ranging from approximately -0.02 to 0.02 across layers 0-11. The color is predominantly green/purple. * **"_PAUSE_" Token:** Shows a distinct pattern. Layers 0-3 exhibit a strong negative correlation (purple, approximately -0.04). Layers 4-7 show a transition to neutral (green, around 0.00). Layers 8-11 show a slight positive correlation (yellow, around 0.02). * **"Tools" Token:** Similarity values are low, ranging from approximately -0.02 to 0.02 across layers 0-11. The color is predominantly green/purple. * **"plum" Token:** Similarity values are low, ranging from approximately -0.02 to 0.02 across layers 0-11. The color is predominantly green/purple. * **"banana" Token:** Similarity values are low, ranging from approximately -0.02 to 0.02 across layers 0-11. The color is predominantly green/purple. * **"peach" Token:** Similarity values are low, ranging from approximately -0.02 to 0.02 across layers 0-11. The color is predominantly green/purple. * **"orange" Token:** Similarity values are low, ranging from approximately -0.02 to 0.02 across layers 0-11. The color is predominantly green/purple. * **"ruits" Token:** Similarity values are low, ranging from approximately -0.02 to 0.02 across layers 0-11. The color is predominantly green/purple. * **"F" Token:** Similarity values are low, ranging from approximately -0.02 to 0.02 across layers 0-11. The color is predominantly green/purple. ### Key Observations * The "_PAUSE_" token exhibits the most noticeable variation in cosine similarity across layers, suggesting a dynamic relationship with Meta Token #2. * Most tokens show relatively low and stable cosine similarity values across layers. * The heatmap is largely dominated by green and purple hues, indicating predominantly low or negative cosine similarity. ### Interpretation This heatmap likely represents the contextual relationship between Meta Token #2 and preceding tokens within a neural network or language model. Cosine similarity measures the angle between two vectors, indicating how similar their directions are. A value of 0 indicates orthogonality (no similarity), positive values indicate similarity, and negative values indicate dissimilarity. The varying similarity scores across layers for the "_PAUSE_" token suggest that the model's understanding of the pause changes as information propagates through the network. The low similarity scores for most other tokens indicate that they are relatively less relevant to Meta Token #2, or that their representations are orthogonal to it. The "padding" in the title suggests that the tokens are part of a sequence that has been padded to a fixed length, which could influence the similarity scores. The heatmap provides insights into how the model processes and relates different tokens within a sequence, potentially revealing important aspects of its internal representation.

## Heatmap: Meta Token #2 • Past Cosine-Sim (Padded) ### Overview This image is a heatmap visualizing the cosine similarity between a specific "Meta Token #2" and a sequence of past tokens, measured across different layers of a neural network model. The title indicates the data is "Padded," suggesting the sequence may have been extended to a fixed length. The visualization uses a color gradient to represent the similarity values. ### Components/Axes * **Title:** "Meta Token #2 • Past Cosine-Sim (Padded)" (Top center). * **Y-Axis (Vertical):** Labeled "Layer". It represents the layer index within the model, numbered from 0 at the bottom to 11 at the top. * **X-Axis (Horizontal):** Labeled "Token past of Meta Token #2 (at T distance)". It lists a sequence of tokens that occurred prior to Meta Token #2. The tokens are, from left to right: 1. `iers` 2. `pl` 3. `level` 4. `wrench` 5. `hammer` 6. `PAUSE` 7. `..` (ellipsis) 8. `Tools` 9. `..` (ellipsis) 10. `plum` 11. `banana` 12. `peach` 13. `orange` 14. `..` (ellipsis) 15. `ruits` 16. `F` * **Color Bar/Legend (Right side):** A vertical bar labeled "cosine similarity". It maps colors to numerical values, ranging from dark purple at the bottom (approximately -0.04) to bright yellow at the top (approximately +0.04). The scale includes tick marks at -0.04, -0.02, 0.00, 0.02, and 0.04. ### Detailed Analysis The heatmap is a grid where each cell's color corresponds to the cosine similarity between Meta Token #2 and the token at a specific past position (X-axis), as computed in a specific model layer (Y-axis). **Color-to-Value Mapping (Approximate):** * **Bright Yellow:** ~ +0.04 (Highest positive similarity) * **Light Green/Yellow-Green:** ~ +0.02 * **Teal/Green-Blue:** ~ 0.00 (Neutral similarity) * **Blue/Indigo:** ~ -0.02 * **Dark Purple:** ~ -0.04 (Highest negative similarity) **Spatial Patterns and Trends:** * **Column "level":** This column is predominantly bright yellow to light green across most layers (0-11), indicating a consistently high positive cosine similarity between Meta Token #2 and the token "level" throughout the network's depth. The similarity appears strongest in the lower layers (0-2). * **Column "pl":** This column is consistently dark purple/blue across all layers, indicating a consistently negative cosine similarity. * **Column "peach":** This column is very dark purple, especially in the lower layers (0-4), suggesting a strong negative similarity. * **Columns "iers", "wrench", "hammer", "PAUSE", "Tools", "plum", "banana", "orange", "ruits", "F":** These columns show a mix of teal, blue, and green shades. The similarity values for these tokens appear to be closer to zero (neutral) or slightly positive/negative, with no single strong trend across all layers. * **Ellipsis Columns (`..`):** These columns also show mixed, near-neutral values. * **Layer 0 (Bottom Row):** This row shows more extreme colors (both bright yellow for "level" and dark purple for "peach") compared to higher layers, suggesting that similarity relationships might be more pronounced or specialized in the initial embedding or first processing layer. * **General Trend with Layer Depth:** For many tokens (e.g., "iers", "wrench", "Tools"), the color becomes slightly more teal/green (closer to zero) in the middle layers (4-8) compared to the very bottom or top layers, indicating a potential normalization or attenuation of the similarity signal in the network's mid-section. ### Key Observations 1. **Strong Positive Anchor:** The token "level" has a uniquely strong and persistent positive association with Meta Token #2 across all model layers. 2. **Strong Negative Associations:** The tokens "pl" and "peach" show consistently negative similarity, with "peach" being particularly strong in early layers. 3. **Contextual Grouping:** The tokens appear to be from two semantic groups: tools ("wrench", "hammer", "Tools") and fruits ("plum", "banana", "peach", "orange", "ruits"). However, the heatmap does not show a uniform similarity pattern within these groups. For example, "peach" is strongly negative while "banana" is near-neutral. 4. **Layer-Dependent Variation:** The strength and sign of the similarity for most tokens (except "level" and "pl") are not constant but vary with the layer index, suggesting the relationship between Meta Token #2 and past tokens is processed and transformed at different stages of the network. ### Interpretation This heatmap provides a diagnostic view into the internal state of a transformer-like model. It reveals how a special "meta token" attends to or aligns with specific past tokens in its context window. * **What the data suggests:** The high positive similarity for "level" implies that Meta Token #2's representation is highly aligned with the concept or function of "level" within the model's processing. This could mean the meta token is acting as a placeholder or carrier for information related to "level". Conversely, the negative similarities for "pl" and "peach" suggest an inhibitory or contrasting relationship. * **How elements relate:** The variation across layers shows that these relationships are not static. The model builds and refines the meta token's association with past context as information flows through its layers. The pronounced values in Layer 0 may reflect direct embedding similarities, while patterns in higher layers reflect more abstract, processed relationships. * **Notable anomalies:** The stark contrast between "level" (strong positive) and "pl"/"peach" (strong negative) is the most significant anomaly. This could indicate that the meta token is being used to track or differentiate between specific types of information (e.g., perhaps "level" is a key parameter, while "pl" and "peach" are part of a different, unrelated context). The lack of a clear pattern within the obvious semantic groups (tools vs. fruits) suggests the meta token's role is not simply categorical but tied to more specific, possibly syntactic or functional, roles in the sequence it was trained on.

## Heatmap: Meta Token #2 • Past Cosine-Sim (Padded) ### Overview This heatmap visualizes cosine similarity values between Meta Token #2 and other tokens across 12 layers (0–11). The color gradient ranges from purple (-0.04) to yellow (+0.04), with values padded to ensure consistent dimensions. The x-axis represents tokens in the sequence preceding Meta Token #2, while the y-axis represents layers in a neural network or transformer architecture. ### Components/Axes - **Y-axis (Layer)**: Labeled "Layer" with integer values 0–11. - **X-axis (Token past of Meta Token #2)**: Tokens include: `iers`, `pl`, `level`, `wrench`, `hammer`, `PAUSE_`, `:`, `Tools`, `plum`, `banana`, `peach`, `orange`, `:`, `ruits`, `F`. - **Color Bar**: Labeled "cosine similarity" with values from -0.04 (dark purple) to +0.04 (bright yellow). ### Detailed Analysis - **Highest Similarity**: - **Layer 0, Token "level"**: Bright yellow (≈+0.04), indicating the strongest positive cosine similarity. - **Layer 1, Token "level"**: Yellow-green (≈+0.03), slightly lower than Layer 0. - **Lowest Similarity**: - **Layer 11, Token "plum"**: Dark purple (≈-0.04), the most negative value. - **Layer 10, Token "plum"**: Dark purple (≈-0.03), also highly negative. - **Neutral Values**: - Tokens like `PAUSE_`, `Tools`, and `:` show mid-range values (green to teal, ≈0.00–0.02). - **Vertical Gradients**: - Token "level" shows a gradient from yellow (Layer 0) to teal (Layer 11), suggesting diminishing similarity with depth. - Token "plum" shows a gradient from teal (Layer 0) to dark purple (Layer 11), indicating increasing dissimilarity. ### Key Observations 1. **Layer 0 Dominance**: Layer 0 consistently shows the highest similarity magnitudes (both positive and negative). 2. **Token "level"**: Exhibits the strongest positive similarity across early layers, dropping to neutral by Layer 11. 3. **Token "plum"**: Shows the strongest negative similarity in later layers (10–11), with minimal presence in earlier layers. 4. **Padding Artifacts**: The "PAUSE_" token and repeated colons (`:`) appear in mid-layers with moderate similarity, possibly indicating structural padding. ### Interpretation The heatmap suggests that Meta Token #2’s cosine similarity with preceding tokens varies significantly across layers. The token "level" is most closely associated with Meta Token #2 in early layers (0–1), while "plum" becomes increasingly dissimilar in deeper layers. This could reflect: - **Token Positioning**: Early layers capture semantic relationships (e.g., "level" as a key contextual token), while later layers focus on syntactic or structural patterns. - **Padding Impact**: The presence of "PAUSE_" and colons may indicate artificial separation in the sequence, affecting similarity distributions. - **Layer-Specific Dynamics**: Layer 0’s high similarity magnitudes suggest it encodes strong contextual relationships, while deeper layers may prioritize disentangling or abstracting features. The data implies that Meta Token #2’s representation is most stable in early layers, with diminishing similarity as layers progress, potentially due to hierarchical feature extraction in the model.