## Heatmaps: Layer 2, Head 8 ### Overview Two side-by-side heatmaps are presented, both labeled "Layer 2, Head 8." The left heatmap is titled "1/14 x³," and the right is titled "Softmax." Both share identical axes (0–175 in increments of 25) and color scales, but differ in patterns and value ranges. ### Components/Axes - **Axes**: - X-axis: 0 to 175 (increments of 25). - Y-axis: 0 to 175 (increments of 25). - **Color Scales**: - Left heatmap: Ranges from **-0.06 (dark blue)** to **0.02 (yellow)**. - Right heatmap: Ranges from **-0.06 (dark blue)** to **0.10 (yellow)**. - **Legends**: - Positioned on the right of each heatmap. - Left: Gradient from blue (negative values) to yellow (positive values). - Right: Same gradient but with a higher upper bound (0.10 vs. 0.02). ### Detailed Analysis #### Left Heatmap ("1/14 x³") - **Pattern**: Diagonal stripes with alternating green, blue, and yellow bands. - **Trend**: - Values increase linearly along the diagonal (from bottom-left to top-right). - Color intensity shifts from dark blue (negative) to yellow (positive) as values approach 0.02. - **Notable Features**: - Diagonal line at ~y = x (slope = 1). - No significant outliers; values are evenly distributed along the diagonal. #### Right Heatmap ("Softmax") - **Pattern**: Checkerboard-like grid with a prominent diagonal line. - **Trend**: - Diagonal line (y = x) shows higher values (green/yellow), while off-diagonal regions are darker (blue). - Checkerboard pattern suggests alternating high/low values in a structured manner. - **Notable Features**: - Diagonal line peaks at ~0.10 (yellow) near the top-right corner. - Off-diagonal regions cluster around -0.06 (dark blue). ### Key Observations 1. **Left Heatmap**: - Represents a cubic function scaled by 1/14, showing a linear gradient along the diagonal. - Values are tightly clustered between -0.06 and 0.02. 2. **Right Heatmap**: - Softmax output exhibits a bimodal distribution: high values along the diagonal and low values elsewhere. - Checkerboard pattern may indicate alternating activation states or interactions between variables. ### Interpretation - **Left Heatmap**: - The "1/14 x³" label suggests a mathematical transformation applied to input data. The linear diagonal trend implies a direct proportionality between input (x-axis) and output (y-axis), scaled by the cubic term. - **Right Heatmap**: - The "Softmax" label indicates a normalization process, likely converting raw scores into probabilities. The diagonal dominance suggests that the model assigns higher confidence to matching inputs (e.g., in a classification task). - **Comparison**: - The left heatmap’s smaller value range (-0.06 to 0.02) contrasts with the right’s broader range (-0.06 to 0.10), indicating different scales of activation or transformation. - The checkerboard pattern in the softmax heatmap may reflect sparse or structured interactions, while the left heatmap’s stripes suggest a smoother, continuous relationship. ### Spatial Grounding - **Legend Position**: Right-aligned for both heatmaps. - **Color Matching**: - Dark blue consistently represents negative values in both heatmaps. - Yellow denotes the maximum positive values (0.02 for the left, 0.10 for the right). ### Trend Verification - **Left Heatmap**: Diagonal line slopes upward (slope ≈ 1), confirming linear growth. - **Right Heatmap**: Diagonal line peaks at the top-right, with checkerboard patterns reinforcing structured variability. ### Component Isolation - **Header**: Titles ("1/14 x³" and "Softmax") clarify the mathematical context. - **Main Chart**: Axes and color scales dominate, with distinct patterns for each heatmap. - **Footer**: No additional text or annotations. ### Final Notes - The left heatmap likely visualizes a pre-softmax activation (e.g., raw logits), while the right shows post-softmax probabilities. - The diagonal dominance in both suggests alignment between input and output dimensions, critical for tasks like attention mechanisms or classification. - The checkerboard pattern in the softmax heatmap may indicate localized interactions or constraints in the model’s architecture.