## Heatmap: Fixed Recurrence Seed 1 Analysis ### Overview The image displays a matrix of heatmaps organized in two rows, each representing different recurrence depths (R=1 to R=8) and their corresponding in-distribution (ID) hop counts (2-hop to 16-hop). The heatmaps visualize out-of-distribution (OOD) detection performance across recurrence steps (r) and hops (k), with color intensity indicating OOD probability (0.0 to 1.0). Key elements include: - Vertical dashed green line: ID/OOD boundary - Purple dashed line: Train recurrence threshold - Color scale: Blue (low OOD) to Red (high OOD) ### Components/Axes 1. **Vertical Axis (Recurrence r)**: - Labeled "Recurrence (r)" - Scale: 1 to 40 (discrete steps) - Position: Left side of all panels 2. **Horizontal Axis (Hops k)**: - Labeled "Hops (k)" - Scale: 2 to 23 (discrete steps) - Position: Bottom of all panels 3. **Legend**: - Located on the right side - Color bar: 0.0 (lightest) to 1.0 (darkest red) - Label: "OOD" 4. **Panel Labels**: - Top row: R=1 (ID 2-hop), R=2 (ID 6-hop), R=3 (ID 9-hop), R=4 (ID 10-hop) - Bottom row: R=5 (ID 12-hop), R=6 (ID 13-hop), R=7 (ID 16-hop), R=8 (ID 16-hop) - Position: Top-center of each panel ### Detailed Analysis 1. **R=1 (ID 2-hop)**: - Single dark blue cell at (r=1, k=2) - All other cells: Near-white (OOD ≈ 0.0) 2. **R=2 (ID 6-hop)**: - Dark blue region in top-left (r=1-5, k=2-6) - Gradual transition to lighter blue toward OOD boundary 3. **R=3 (ID 9-hop)**: - Dark blue region expands to r=1-10, k=2-9 - Diagonal gradient toward OOD boundary 4. **R=4 (ID 10-hop)**: - Dark blue region covers r=1-15, k=2-10 - Stronger gradient toward OOD boundary 5. **R=5 (ID 12-hop)**: - Dark blue region spans r=1-20, k=2-12 - First appearance of red cells near OOD boundary (r=20-25, k=12-15) 6. **R=6 (ID 13-hop)**: - Dark blue region extends to r=1-25, k=2-13 - Red cells appear in r=25-30, k=13-16 7. **R=7 (ID 16-hop)**: - Dark blue region covers r=1-30, k=2-16 - Red cells dominate r=30-35, k=16-20 8. **R=8 (ID 16-hop)**: - Dark blue region spans r=1-35, k=2-16 - Red cells occupy r=35-40, k=16-23 ### Key Observations 1. **ID/OOD Boundary**: - Consistent vertical position across all panels - Separates ID (left) from OOD (right) 2. **Train Recurrence Threshold**: - Purple dashed line at r=15-20 (varies slightly by panel) - All panels show similar threshold positioning 3. **OOD Intensity Trends**: - Higher R values show: - Larger ID regions (more dark blue) - Stronger OOD gradients (darker red near boundary) - Diagonal bands of high OOD (red) appear in: - R=5: k=12-15, r=20-25 - R=6: k=13-16, r=25-30 - R=7: k=16-20, r=30-35 - R=8: k=16-23, r=35-40 4. **Recurrence-Hops Correlation**: - Higher R values correlate with: - Increased ID region size - More pronounced OOD gradients - Diagonal bands suggest recurrence-hops interaction in OOD detection ### Interpretation The data demonstrates that: 1. **Recurrence Depth Impact**: - Deeper recurrences (higher R) create larger ID regions - OOD detection becomes more gradient-like with increasing R 2. **Hop Recurrence Interaction**: - Diagonal bands indicate that certain (r,k) combinations are more prone to OOD - This suggests recurrence-hops co-dependency in model representations 3. **Threshold Behavior**: - Train recurrence threshold (purple line) aligns with: - Transition from ID to OOD regions - Emergence of red cells in higher R panels 4. **Model Complexity Insights**: - Larger ID regions in higher R panels may indicate: - Better ID representation - Potential overfitting to ID data - Red cells near OOD boundary suggest: - Model uncertainty thresholds - Possible mode collapse in OOD regions The visualization reveals that recurrence depth significantly influences OOD detection patterns, with deeper recurrences creating more complex ID/OOD boundaries and stronger gradient transitions. The diagonal bands of high OOD values suggest that specific recurrence-hops combinations create particularly vulnerable model representations.