## Scatter Plot: Projection of activations on tG and tP
### Overview
The image contains two scatter plots, side-by-side, displaying the projection of activations on *tG* and *tP*. The left plot represents "Affirmative Statements," and the right plot represents "Negated Statements." Each plot shows data points colored red or blue, corresponding to "False" and "True" respectively. The x-axis represents *a_ij^T t_G*, and the y-axis represents *a_ij^T t_P*.
### Components/Axes
**Overall Title:** Projection of activations on *tG* and *tP*
**Left Plot (Affirmative Statements):**
* **Title:** Affirmative Statements
* **X-axis:** *a_ij^T t_G* (values ranging from 0.0 to 1.0 x 10^6)
* **Y-axis:** *a_ij^T t_P* (values ranging from -2.75 x 10^6 to -1.00 x 10^6)
**Right Plot (Negated Statements):**
* **Title:** Negated Statements
* **X-axis:** Values ranging from 0 to 800000
* **Y-axis:** *a_ij^T t_P* (values ranging from -2.8 x 10^6 to -1.4 x 10^6)
**Legend (Located in the bottom-right of the image, within the Negated Statements plot):**
* Red: False
* Blue: True
### Detailed Analysis
**Left Plot (Affirmative Statements):**
* **False (Red):** The red data points are primarily clustered in the lower-left quadrant. The x-values range approximately from 0 to 0.4 x 10^6, and the y-values range approximately from -2.75 x 10^6 to -1.75 x 10^6.
* **True (Blue):** The blue data points are clustered in two main regions. One cluster is in the top-left, with x-values around 0.1 to 0.2 x 10^6 and y-values around -1.3 x 10^6 to -1.2 x 10^6. The second cluster is in the top-right, with x-values around 0.6 to 0.9 x 10^6 and y-values around -1.8 x 10^6 to -1.6 x 10^6.
**Right Plot (Negated Statements):**
* **False (Red):** The red data points are clustered in the upper-left quadrant. The x-values range approximately from 0 to 400000, and the y-values range approximately from -2.0 x 10^6 to -1.6 x 10^6.
* **True (Blue):** The blue data points are clustered in the lower-right quadrant. The x-values range approximately from 500000 to 800000, and the y-values range approximately from -2.4 x 10^6 to -2.0 x 10^6.
### Key Observations
* In the "Affirmative Statements" plot, the "True" data points are separated into two distinct clusters, while the "False" data points form a single cluster.
* In the "Negated Statements" plot, the "True" and "False" data points are more clearly separated into two distinct clusters.
* The range of y-values (*a_ij^T t_P*) is similar for both plots, but the range of x-values (*a_ij^T t_G*) differs.
### Interpretation
The scatter plots visualize the projection of activations onto *tG* and *tP* for affirmative and negated statements, differentiating between true and false statements. The clustering patterns suggest that the model processes affirmative and negated statements differently. The separation of "True" and "False" data points in the "Negated Statements" plot indicates a clearer distinction in the model's representation for these types of statements compared to "Affirmative Statements." The two clusters of "True" data points in the "Affirmative Statements" plot might indicate two different ways the model represents true affirmative statements. The x and y axes represent different aspects of the model's internal representation, and the plots show how these aspects vary depending on the type and truth value of the statement.
