## Heatmap: Recurrence and Out-of-Distribution (OOD) Boundary ### Overview The image displays a heatmap that visualizes the recurrence of a specific event or pattern across different hops (k) and seeds (ID). The heatmap is divided into three sections, each representing a different seed with varying hop counts. The color gradient indicates the level of recurrence, with darker shades representing higher recurrence and lighter shades indicating lower recurrence. ### Components/Axes - **X-axis (Hops (k))**: Represents the number of hops, ranging from 2 to 38. - **Y-axis (Recurrence (r))**: Represents the recurrence level, ranging from 0 to 1. - **Legend**: Located at the bottom right, it provides color coding for the recurrence levels and OOD boundary. - **ID/OOD boundary**: A dashed green line that separates the in-distribution (ID) and out-of-distribution (OOD) regions. - **Train recurrence**: A dashed purple line that indicates the threshold for train recurrence. ### Detailed Analysis - **Seed 1 (ID: 22-hop)**: The heatmap shows a high recurrence level, especially at the lower end of the hops (2-8). The recurrence level decreases as the hop count increases. - **Seed 2 (ID: 21-hop)**: Similar to Seed 1, Seed 2 also shows a high recurrence level, particularly at the lower end of the hops (2-8). The recurrence level decreases as the hop count increases. - **Seed 3 (ID: 19-hop)**: Seed 3 has a moderate recurrence level, with a slight increase in recurrence as the hop count increases. ### Key Observations - **High Recurrence**: All three seeds show high recurrence levels, especially at the lower end of the hops. - **ID/OOD Boundary**: The ID/OOD boundary is clearly visible, with the ID region being darker and the OOD region being lighter. - **Train Recurrence**: The train recurrence line is consistently above the ID/OOD boundary, indicating that the model is trained to recognize and distinguish between ID and OOD data. ### Interpretation The heatmap suggests that the model is highly effective in recognizing and distinguishing between in-distribution and out-of-distribution data across different seeds and hop counts. The high recurrence levels indicate that the model is consistently able to identify the pattern or event being measured. The ID/OOD boundary is well-defined, which is crucial for the model's ability to generalize and perform well on unseen data. The train recurrence line being consistently above the boundary further confirms that the model is trained to recognize and differentiate between ID and OOD data, which is essential for its performance in real-world applications.

## 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. --- ### 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) --- ### 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. --- ### 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. --- ### 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. --- ### 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. --- ### 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. --- ### 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.