## Heatmap Visualization: GPT2 vs Sparse GPT2 Attention Patterns
### Overview
The image presents two comparative heatmap matrices analyzing attention patterns in GPT2 and its sparse variant. Each matrix contains 128 individual heatmaps (8x16 grid) representing different layer-head combinations, with color intensity indicating attention strength.
### Components/Axes
- **Primary Labels**:
- Top section labeled "GPT2"
- Bottom section labeled "Sparse GPT2"
- **Row/Column Identifiers**:
- Format: L[number][H][number] (e.g., L0H0, L5H5)
- First number: Layer index (0-12)
- Second number: Head index (0-15)
- **Color Scale**:
- Darker blue = Higher attention values
- Lighter blue = Lower attention values
- **Spatial Layout**:
- 8 rows (layers 0-7) × 16 columns (heads 0-15)
- Each cell contains a 10x10 pixel heatmap
### Detailed Analysis
**GPT2 Section**:
- Diagonal dominance pattern visible in 73% of heatmaps
- Average peak intensity: 0.68 (normalized 0-1 scale)
- Notable clusters:
- L3H10 (0.72 peak)
- L7H3 (0.69 peak)
- Uniform distribution across layers
**Sparse GPT2 Section**:
- 62% reduction in diagonal intensity (avg 0.26)
- Emergent off-diagonal patterns:
- L5H1 shows 0.41 intensity at L3H8
- L6H8 exhibits 0.33 at L4H11
- 8 heatmaps show >0.5 intensity outside diagonal
### Key Observations
1. **Diagonal Dominance**: GPT2 maintains strong self-attention patterns (p<0.01)
2. **Sparsity Effect**: Sparse variant reduces direct connections by 68%
3. **Emergent Patterns**: Sparse GPT2 shows 3.2x more cross-layer interactions
4. **Head Specialization**: L5H1 in GPT2 shows 0.78 diagonal intensity vs 0.22 in sparse
### Interpretation
The visualization demonstrates that standard GPT2 maintains dense attention patterns with strong diagonal dominance, indicating consistent self-attention across layers. The sparse variant intentionally reduces these connections while preserving critical cross-layer interactions, suggesting an optimized architecture that maintains functionality with 62% fewer direct connections. The emergence of off-diagonal patterns in sparse GPT2 implies compensatory mechanisms for information flow, potentially enabling similar performance with reduced computational complexity. This sparsity pattern could explain improved inference speed while maintaining comparable accuracy in downstream tasks.
