## Heatmap Analysis: Recurrence and Hops ### Overview The image displays three heatmaps, each representing different configurations of recurrence (R=4, R=8, R=dynamic) and hops (k=2, k=4, k=6). The heatmaps are used to visualize the recurrence and hops of a model, with the intensity of the color indicating the level of recurrence or hops. ### Components/Axes - **Recurrence (R)**: The x-axis represents the recurrence level, ranging from 2 to 100. - **Hops (k)**: The y-axis represents the number of hops, ranging from 2 to 100. - **ID/OOD boundary**: A dashed green line indicates the boundary between in-distribution (ID) and out-of-distribution (OOD) data. - **Train recurrence**: A dashed purple line represents the recurrence level of the training data. - **Legend**: The legend on the right side of the image provides color coding for the recurrence and hops levels. ### Detailed Analysis - **R=4**: The heatmap shows a moderate level of recurrence, with the majority of the data points falling within the ID/OOD boundary. The recurrence level is relatively stable across different hops. - **R=8**: The heatmap indicates a higher level of recurrence, with a significant portion of the data points falling outside the ID/OOD boundary. The recurrence level increases with the number of hops. - **R=dynamic**: The heatmap shows a highly dynamic recurrence level, with the majority of the data points falling outside the ID/OOD boundary. The recurrence level fluctuates significantly across different hops. ### Key Observations - **ID/OOD boundary**: The ID/OOD boundary is consistently present in all three heatmaps, indicating that the model's performance is evaluated against a standard distribution. - **Train recurrence**: The train recurrence line is present in all three heatmaps, suggesting that the model's recurrence level is based on the training data. - **Hops**: The number of hops affects the recurrence level, with higher hops generally resulting in higher recurrence levels. ### Interpretation The heatmaps suggest that the model's recurrence level is influenced by both the recurrence level and the number of hops. The ID/OOD boundary indicates that the model's performance is evaluated against a standard distribution, and the train recurrence line suggests that the model's recurrence level is based on the training data. The dynamic recurrence level in the R=dynamic heatmap indicates that the model's performance is highly sensitive to the number of hops, with higher hops resulting in higher recurrence levels. This suggests that the model's performance may be affected by the complexity of the data and the number of hops used in the model.

## Heatmap: Model Performance Across Recurrence and Hops ### Overview The image presents three heatmaps comparing model performance across different recurrence values (r) and hops (k) for three scenarios: fixed R=4, fixed R=8, and dynamic R. Color gradients (blue to red) represent ID/OOD classification probabilities, with dashed lines marking key boundaries. ### Components/Axes - **X-axis (Hops, k)**: Ranges from 2 to 100 in increments of 2. - **Y-axis (Recurrence, r)**: Ranges from 4 to 20 in increments of 2. - **Legends**: - **Green dashed line**: ID/OOD boundary (k=40). - **Purple dashed line**: Train recurrence threshold (r=6). - **Color scale**: Blue (ID, 0.00–0.75) to Red (OOD, 0.75–1.00). ### Detailed Analysis #### R=4 Panel - **ID/OOD Boundary**: Vertical green dashed line at k=40. Left of the line (k<40) shows dominant blue (ID), right (k>40) transitions to red (OOD). - **Train Recurrence**: Horizontal purple dashed line at r=6. Above this line (r>6), blue dominates; below (r<6), red increases. - **Trend**: ID/OOD separation sharpens with higher k. Recurrence values above 6 correlate with higher ID likelihood. #### R=8 Panel - **ID/OOD Boundary**: Same k=40 boundary. Left side (k<40) has stronger blue dominance than R=4. - **Train Recurrence**: Purple line at r=6. Above r=6, blue dominates; below, red increases. - **Trend**: Similar to R=4 but with a more pronounced ID/OOD split at lower k values. #### R=dynamic Panel - **ID/OOD Boundary**: k=40 boundary persists but with less distinct separation. - **Train Recurrence**: Purple line at r=6. Above r=6, blue dominates; below, red increases. - **Trend**: Uniform color distribution across k and r, suggesting reduced model confidence in dynamic R scenarios. ### Key Observations 1. **Consistent Boundaries**: The ID/OOD boundary (k=40) and train recurrence threshold (r=6) are consistent across all panels. 2. **Recurrence Sensitivity**: Higher recurrence values (r>6) correlate with increased ID likelihood, while lower values (r<6) align with OOD. 3. **Hop Threshold**: k=40 acts as a critical point where OOD probability sharply increases. 4. **Dynamic R Uncertainty**: The dynamic R panel shows no clear ID/OOD separation, indicating model instability under variable R. ### Interpretation The data demonstrates that model performance is highly sensitive to recurrence and hop thresholds. Fixed R values (4 and 8) show predictable ID/OOD boundaries, with higher recurrence and lower hops favoring ID. The dynamic R scenario, however, lacks clear boundaries, suggesting that variable R introduces uncertainty, potentially increasing OOD risk. This highlights the importance of recurrence and hop constraints in maintaining model reliability.