## Heatmap: Seed-Specific ID/OOD Boundary and Train Recurrence Analysis
### Overview
The image presents three side-by-side heatmaps (Seed 1, Seed 2, Seed 3) visualizing the relationship between **Recurrence (r)** and **Hops (k)** for different model configurations. Each panel uses a color gradient (blue to red) to represent ID/OOD boundary values, with dashed lines marking critical thresholds: a vertical green dashed line for the ID/OOD boundary and a horizontal purple dashed line for train recurrence.
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### Components/Axes
1. **X-Axis (Hops, k)**:
- Range: 2 to 38 (integer increments).
- Labels: "Hops (k)" at the bottom of each panel.
2. **Y-Axis (Recurrence, r)**:
- Range: 2 to 40 (integer increments).
- Labels: "Recurrence (r)" on the left of each panel.
3. **Color Scale**:
- Blue (0.0) to Red (1.0), representing ID/OOD boundary values.
- Legend on the right:
- **Green dashed line**: ID/OOD boundary.
- **Purple dashed line**: Train recurrence.
4. **Panel Titles**:
- Seed 1 (ID: 22-hop)
- Seed 2 (ID: 21-hop)
- Seed 3 (ID: 19-hop)
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### Detailed Analysis
#### Seed 1 (ID: 22-hop)
- **ID/OOD Boundary**: Vertical green dashed line at **k ≈ 23**.
- **Train Recurrence**: Horizontal purple dashed line at **r ≈ 9**.
- **Color Gradient**:
- Blue dominates the left (low k, low r), transitioning to red in the top-right (high k, high r).
- Strong diagonal gradient from bottom-left (blue) to top-right (red).
#### Seed 2 (ID: 21-hop)
- **ID/OOD Boundary**: Vertical green dashed line at **k ≈ 26**.
- **Train Recurrence**: Horizontal purple dashed line at **r ≈ 10**.
- **Color Gradient**:
- Similar diagonal trend but with a more gradual transition to red.
- Red region starts earlier (lower r) compared to Seed 1.
#### Seed 3 (ID: 19-hop)
- **ID/OOD Boundary**: Vertical green dashed line at **k ≈ 29**.
- **Train Recurrence**: Horizontal purple dashed line at **r ≈ 11**.
- **Color Gradient**:
- Red region dominates the top-right, with a sharper transition from blue to red.
- Higher recurrence values (r > 11) show stronger red intensity.
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### Key Observations
1. **Boundary Shift**:
- As Seed ID decreases (22 → 21 → 19), the ID/OOD boundary moves **rightward** (k increases from 23 → 26 → 29).
- Train recurrence increases (r = 9 → 10 → 11), suggesting higher robustness or complexity in lower-ID seeds.
2. **Color Intensity**:
- Red regions (high ID/OOD values) expand with lower Seed IDs, indicating increased out-of-distribution sensitivity.
3. **Consistency**:
- All panels share the same axis ranges and legend, enabling direct comparison.
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### Interpretation
The data suggests that **lower Seed IDs (e.g., 19-hop)** exhibit:
- **Stronger ID/OOD discrimination** (higher k boundary).
- **Higher train recurrence thresholds** (r ≈ 11 vs. 9), possibly reflecting more robust training dynamics.
- **Greater sensitivity to out-of-distribution data** (expanded red regions).
This trend implies that models with lower ID values may prioritize recurrence over hop count for maintaining performance, highlighting a trade-off between recurrence depth and hop efficiency in ID/OOD boundary delineation.
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### Spatial Grounding & Trend Verification
- **Legend Placement**: Right-aligned, clearly associating colors with boundary types.
- **Dashed Lines**:
- Green (ID/OOD) consistently vertical across panels.
- Purple (Train recurrence) consistently horizontal.
- **Trend Logic Check**:
- Seed 1 (22-hop): Steepest gradient, lowest boundary (k=23).
- Seed 3 (19-hop): Shallowest gradient, highest boundary (k=29).
- Matches expectation: Lower ID correlates with higher k/r thresholds.
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### Content Details
- **No numerical data tables** present; values inferred from axis labels and color gradients.
- **No textual annotations** beyond axis titles and panel labels.
- **No UI elements** (e.g., buttons, menus) visible.
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### Final Notes
The heatmaps emphasize the interplay between recurrence and hop count in defining ID/OOD boundaries. Lower-ID seeds show a clear shift toward higher recurrence and hop thresholds, suggesting a design choice to enhance robustness at the cost of efficiency.
