## Heatmap: Token Attribution
### Overview
The image is a heatmap visualizing token attribution. The x-axis represents different mathematical expressions, and the y-axis represents various tokens. The color intensity represents the attribution score, ranging from negative (red) to positive (green).
### Components/Axes
* **X-axis (Top)**: Mathematical expressions: "8 x 48 = 384", "3 x 4 = 12", "6 - 4 = 2", "50(10x5)", "$35 ($85 - $50)"
* **Y-axis (Left)**: Tokens: "-", "1", "6", ",", "0", "0", "0", "_x", "-", "0", ".", "8", "_="
* **Colorbar (Right)**: "Token Attribution" with a scale from -1.0 (red) to 1.0 (green). The colorbar has tick marks at -1.0, -0.5, 0.0, 0.5, and 1.0.
### Detailed Analysis
The heatmap consists of a 13x5 grid of values. Each cell's color corresponds to the "Token Attribution" value.
Here's a breakdown of the values in the heatmap:
| Token | 8 x 48 = 384 | 3 x 4 = 12 | 6 - 4 = 2 | 50(10x5) | $35 ($85 - $50) |
|---|---|---|---|---|---|
| - | 0.3452 | 0.2580 | 0.5823 | 0.0161 | -0.0472 |
| 1 | 0.0811 | -0.0066 | -0.0037 | 0.3934 | -0.0356 |
| 6 | 0.0234 | 0.0145 | 0.0512 | 0.0243 | 0.0135 |
| , | 0.0049 | -0.0019 | -0.0196 | -0.0211 | -0.0011 |
| 0 | -0.0009 | 0.0008 | -0.0015 | -0.0010 | -0.0000 |
| 0 | 0.0000 | 0.0000 | -0.0000 | 0.0000 | -0.0001 |
| 0 | 0.0001 | 0.0002 | 0.0002 | -0.0001 | -0.0002 |
| \_x | 1.3714 | 0.6865 | 0.1771 | 0.6837 | -0.3675 |
| - | 0.0089 | 0.0134 | 0.0232 | -0.0061 | -0.0099 |
| 0 | -0.0054 | 0.0008 | 0.0012 | 0.0025 | 0.0016 |
| . | 0.0020 | 0.0022 | 0.0026 | 0.0026 | -0.0011 |
| 8 | -0.0007 | 0.0015 | 0.0007 | -0.0036 | 0.0009 |
| \_= | 0.0081 | 0.0104 | 0.0097 | -0.0127 | 0.0004 |
### Key Observations
* The token "_x" has the highest positive attribution for "8 x 48 = 384" (1.3714), indicating it is a significant factor in the model's understanding or processing of this expression.
* The token "_x" also has a high positive attribution for "3 x 4 = 12" (0.6865) and "50(10x5)" (0.6837).
* The token "_x" has a negative attribution for "$35 ($85 - $50)" (-0.3675).
* Most other tokens have relatively low attribution scores, close to zero.
### Interpretation
The heatmap suggests that the token "_x" plays a crucial role in the model's processing of mathematical expressions involving multiplication. The high positive attribution scores for "_x" in expressions like "8 x 48 = 384", "3 x 4 = 12", and "50(10x5)" indicate that the model strongly associates this token with the concept of multiplication. The negative attribution for "_x" in "$35 ($85 - $50)" might indicate that the model considers it irrelevant or even detrimental in the context of subtraction or financial calculations. The other tokens have minimal impact on the model's understanding of these expressions.
