## Heatmap Comparison: Attention Mechanisms ### Overview The image presents two side-by-side heatmaps comparing attention distribution patterns under different mathematical transformations. The left heatmap uses a cubic function ((1/14)x³), while the right heatmap employs softmax normalization. Both visualizations use color gradients to represent attention intensity values across a 2D spatial domain. ### Components/Axes **Left Heatmap ("Attention with (1/14)x³"):** - Color Scale: Right-aligned vertical gradient from purple (-0.020) to yellow (0.020) - Title: "Attention with (1/14)x³" (top-center) - Spatial Domain: 2D grid with no explicit axis labels - Color Range: -0.020 to +0.020 with 0.005 increments **Right Heatmap ("Attention with softmax"):** - Color Scale: Right-aligned vertical gradient from purple (0.025) to yellow (0.200) - Title: "Attention with softmax" (top-center) - Spatial Domain: 2D grid with no explicit axis labels - Color Range: 0.025 to 0.200 with 0.025 increments ### Detailed Analysis **Left Heatmap Patterns:** - Multiple localized peaks (yellow regions) at coordinates approximately: - (0.3, 0.7) - (0.6, 0.4) - (0.8, 0.2) - Diffuse negative values (purple regions) at: - (0.2, 0.3) - (0.7, 0.8) - Gradual transitions between values with no clear global maximum **Right Heatmap Patterns:** - Dominant negative values (purple) across 95% of the domain - Single concentrated peak in top-right quadrant (coordinates ~0.85, 0.15) - Gradual intensity decay from peak with no secondary maxima - Color scale suggests values never drop below 0.025 ### Key Observations 1. The cubic function produces distributed attention with both positive and negative values 2. Softmax transformation creates a single dominant attention focus 3. Left heatmap shows 400% greater value range (0.04 vs 0.175) 4. Right heatmap maintains strictly positive values despite similar color scale upper bound 5. Spatial distribution patterns differ fundamentally between mechanisms ### Interpretation The visual comparison reveals fundamental differences in attention distribution strategies: - The cubic function ((1/14)x³) preserves value diversity and spatial variability, suggesting it maintains multiple potential focus points - Softmax normalization creates a single dominant attention focus through value compression, typical of attention mechanisms in neural networks - The negative values in the cubic heatmap indicate potential inhibitory attention patterns absent in softmax - Color scale differences highlight how normalization affects value interpretation - softmax's compressed range emphasizes relative importance rather than absolute values The patterns suggest the cubic function might better preserve nuanced spatial relationships, while softmax prioritizes singular focus - a common tradeoff in attention mechanism design.