## Heatmap: Token Attribution
### Overview
The image is a heatmap displaying token attribution scores for different mathematical expressions. The rows represent individual tokens, and the columns represent different mathematical equations. The color intensity indicates the magnitude and direction (positive or negative) of the attribution score. A color bar on the right provides a visual key for the attribution scores.
### Components/Axes
* **Rows (Tokens):** The rows are labeled with the following tokens: '\_$', '1', '6', ',', '0', '0', '0', '/', '-', '0', '.', '8', '='.
* **Columns (Mathematical Expressions):** The columns are labeled with the following mathematical expressions: '9 + 3 = 12', '7 x 5 = 35', '4900 / 100 = 49', '9 - 3 = 6', '6 - 6 = 0'.
* **Color Bar (Token Attribution):** A vertical color bar on the right side of the heatmap indicates the range of token attribution scores. The color bar ranges from approximately -1.5 (red) to 1.5 (dark green), with 0 (light yellow) in the middle.
* **Values:** Each cell contains a numerical value representing the token attribution score for the corresponding token and mathematical expression.
### Detailed Analysis or Content Details
Here's a breakdown of the values in the heatmap:
* **Row '\_$':**
* '9 + 3 = 12': -0.0756
* '7 x 5 = 35': 0.0216
* '4900 / 100 = 49': 0.0065
* '9 - 3 = 6': 0.1044
* '6 - 6 = 0': -0.0691
* **Row '1':**
* '9 + 3 = 12': 0.0198
* '7 x 5 = 35': -0.0041
* '4900 / 100 = 49': -0.0987
* '9 - 3 = 6': 0.0141
* '6 - 6 = 0': -0.0096
* **Row '6':**
* '9 + 3 = 12': 0.0001
* '7 x 5 = 35': 0.0000
* '4900 / 100 = 49': -0.0004
* '9 - 3 = 6': 0.0000
* '6 - 6 = 0': -0.0000
* **Row ',':**
* '9 + 3 = 12': 0.0017
* '7 x 5 = 35': -0.0041
* '4900 / 100 = 49': -0.0351
* '9 - 3 = 6': -0.0060
* '6 - 6 = 0': -0.0070
* **Row '0':**
* '9 + 3 = 12': 0.0005
* '7 x 5 = 35': 0.0006
* '4900 / 100 = 49': -0.0048
* '9 - 3 = 6': -0.0003
* '6 - 6 = 0': -0.0002
* **Row '0':**
* '9 + 3 = 12': 0.0000
* '7 x 5 = 35': -0.0000
* '4900 / 100 = 49': -0.0001
* '9 - 3 = 6': 0.0000
* '6 - 6 = 0': 0.0000
* **Row '0':**
* '9 + 3 = 12': 0.0003
* '7 x 5 = 35': 0.0005
* '4900 / 100 = 49': -0.0004
* '9 - 3 = 6': 0.0000
* '6 - 6 = 0': 0.0001
* **Row '/':**
* '9 + 3 = 12': 0.3820
* '7 x 5 = 35': 0.0909
* '4900 / 100 = 49': 1.9074
* '9 - 3 = 6': 0.6336
* '6 - 6 = 0': 0.6902
* **Row '-':**
* '9 + 3 = 12': 0.0458
* '7 x 5 = 35': 0.0362
* '4900 / 100 = 49': 0.0022
* '9 - 3 = 6': 0.0116
* '6 - 6 = 0': 0.0091
* **Row '0':**
* '9 + 3 = 12': 0.0005
* '7 x 5 = 35': 0.0006
* '4900 / 100 = 49': 0.0000
* '9 - 3 = 6': 0.0002
* '6 - 6 = 0': 0.0002
* **Row '.':**
* '9 + 3 = 12': 0.0014
* '7 x 5 = 35': 0.0003
* '4900 / 100 = 49': 0.0012
* '9 - 3 = 6': 0.0001
* '6 - 6 = 0': -0.0002
* **Row '8':**
* '9 + 3 = 12': 0.0005
* '7 x 5 = 35': 0.0003
* '4900 / 100 = 49': 0.0002
* '9 - 3 = 6': 0.0001
* '6 - 6 = 0': 0.0002
* **Row '=':**
* '9 + 3 = 12': 0.0017
* '7 x 5 = 35': 0.0026
* '4900 / 100 = 49': 0.0024
* '9 - 3 = 6': 0.0007
* '6 - 6 = 0': 0.0021
### Key Observations
* The token '/' in the '4900 / 100 = 49' expression has a significantly high attribution score (1.9074) compared to other tokens and expressions.
* The token '/' also has relatively high attribution scores in the '9 + 3 = 12', '9 - 3 = 6', and '6 - 6 = 0' expressions.
* Most other tokens have relatively low attribution scores, close to zero.
### Interpretation
The heatmap suggests that the division operator '/' is a key factor in determining the outcome of the mathematical expressions, particularly in the '4900 / 100 = 49' expression. This could indicate that the model places a high importance on the division operation when evaluating the correctness or meaning of these expressions. The other tokens have relatively little impact on the model's assessment, as indicated by their low attribution scores. The negative attribution scores suggest that those tokens might be slightly detrimental to the model's understanding in certain contexts.
