## Histograms: Queries by Attention Head ### Overview The image displays four histograms comparing activation value distributions across four attention heads (Head 2, Head 4, Head 6, Head 8) in a neural network. Each subplot shows a teal-colored bar chart overlaid with a black dashed normal distribution curve. The x-axis represents activation values ranging from -10 to 12, while the y-axis shows frequency counts from 0 to 12. ### Components/Axes - **X-axis (Activation Value)**: - Range: -10 to 12 - Labels: Numerical ticks at -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12 - **Y-axis (Frequency)**: - Range: 0 to 12 - Labels: Numerical ticks at 0, 2, 4, 6, 8, 10, 12 - **Legend**: - Position: Top of each subplot - Labels: "Queries - Head 2", "Queries - Head 4", "Queries - Head 6", "Queries - Head 8" - **Normal Distribution Curve**: - Color: Black dashed line - Position: Overlaid on all histograms ### Detailed Analysis 1. **Head 2**: - Peak activation value: ~0 - Spread: Wide (activation values range from ~-4 to +4) - Normal distribution fit: Moderate deviation (bars extend beyond curve tails) - Key feature: Highest variance among all heads 2. **Head 4**: - Peak activation value: ~0 - Spread: Moderate (activation values range from ~-3 to +3) - Normal distribution fit: Better alignment than Head 2 - Key feature: Reduced spread compared to Head 2 3. **Head 6**: - Peak activation value: ~0 - Spread: Narrower (activation values range from ~-2 to +2) - Normal distribution fit: Tight alignment with curve - Key feature: Further reduced variance 4. **Head 8**: - Peak activation value: ~0 - Spread: Narrowest (activation values range from ~-1 to +1) - Normal distribution fit: Almost perfect alignment - Key feature: Lowest variance among all heads ### Key Observations - All heads show unimodal distributions centered at 0 - Variance decreases systematically with increasing head number - Normal distribution fit improves as head number increases - No significant outliers detected in any subplot - Frequency counts peak at ~8-10 for all heads ### Interpretation The data demonstrates a clear pattern of increasing activation value concentration as head number increases. This suggests: 1. **Attention Specialization**: Higher-numbered heads may develop more focused attention mechanisms, resulting in tighter activation distributions 2. **Normalization Effects**: The decreasing variance could indicate progressive normalization mechanisms in later attention heads 3. **Information Processing**: The narrowing distribution might reflect more precise feature extraction in deeper layers of the network 4. **Model Architecture**: The systematic pattern implies intentional design choices in attention head configuration The consistent centering at 0 across all heads suggests effective mean normalization, while the variance reduction pattern could indicate either architectural constraints or emergent properties of the training process. The strong normal distribution fits validate the Gaussian-like behavior of attention mechanisms in this model.