## Heatmap: Fixed Recurrence Seed 2 ### Overview The image displays a heatmap titled "Fixed Recurrence Seed 2," which appears to be a visualization of data related to recurrence rates and hops in a certain context. The heatmap is organized into two rows, each with four subplots, representing different values of "R" (recurrence rate) and "ID" (identifier or ID). The x-axis represents "Hops (k)," and the y-axis represents "Recurrence (t)." The color gradient indicates the intensity of the recurrence rate, with darker shades representing higher recurrence rates. ### Components/Axes - **X-Axis**: Labeled "Hops (k)" with values ranging from 2 to 23. - **Y-Axis**: Labeled "Recurrence (t)" with values ranging from 0 to 1. - **Legend**: Located at the bottom right corner, indicating the color gradient for the recurrence rate. - **Subplots**: Each subplot represents a different combination of "R" and "ID," with the color intensity varying across the "Hops (k)" axis. ### Detailed Analysis - **Subplot 1 (R=1, ID=3-hop)**: The heatmap shows a relatively uniform color intensity across the "Hops (k)" axis, indicating a consistent recurrence rate. - **Subplot 2 (R=2, ID=6-hop)**: The color intensity is slightly higher, suggesting a higher recurrence rate compared to Subplot 1. - **Subplot 3 (R=3, ID=9-hop)**: The color intensity is even higher, indicating a significant increase in recurrence rate. - **Subplot 4 (R=4, ID=10-hop)**: The color intensity is the highest, showing the maximum recurrence rate among the subplots. - **Subplot 5 (R=5, ID=12-hop)**: The color intensity is moderate, indicating a moderate recurrence rate. - **Subplot 6 (R=6, ID=13-hop)**: The color intensity is slightly lower than Subplot 5, suggesting a lower recurrence rate. - **Subplot 7 (R=7, ID=14-hop)**: The color intensity is lower, indicating a further decrease in recurrence rate. - **Subplot 8 (R=8, ID=13-hop)**: The color intensity is the lowest, showing the minimum recurrence rate among the subplots. ### Key Observations - **Trend**: As the value of "R" increases, the recurrence rate generally increases. - **Outliers**: There are no significant outliers in the data, as the color intensity varies smoothly across the "Hops (k)" axis. - **Anomalies**: There are no anomalies in the data, as the color intensity does not show any sudden jumps or drops. ### Interpretation The heatmap suggests that the recurrence rate is influenced by the value of "R" and the identifier "ID." As "R" increases, the recurrence rate also increases, indicating a positive correlation between these two variables. The identifier "ID" appears to have a moderating effect, with some subplots showing a higher recurrence rate for certain IDs compared to others. The color gradient provides a visual representation of the recurrence rate, with darker shades indicating higher recurrence rates. This visualization can be useful for identifying patterns and trends in the data, which can inform further analysis and decision-making.

## Heatmap: Fixed Recurrence Seed 2 ### Overview The image is a composite heatmap consisting of 8 panels arranged in two rows (4 panels per row). Each panel represents a different recurrence value (R=1 to R=8) and corresponding ID hop counts (3-hop to 13-hop). The heatmap visualizes the relationship between recurrence (r), hops (k), and out-of-distribution (OOD) performance, with color intensity indicating OOD values (0.0 to 1.0). ### Components/Axes - **X-axis (Hops, k)**: Labeled "Hops (k)" with values ranging from 2 to 23. - **Y-axis (Recurrence, r)**: Labeled "Recurrence (r)" with values ranging from 1 to 40. - **Legend**: - **Blue**: ID/OOD boundary (dashed vertical line). - **Purple**: Train recurrence (dashed horizontal line). - **Color bar**: OOD values from 0.0 (blue) to 1.0 (red). - **Panel Titles**: Each panel is labeled with "R=X (ID Y-hop)", where X is the recurrence value and Y is the ID hop count (e.g., "R=1 (ID 3-hop)"). ### Detailed Analysis - **R=1 (ID 3-hop)**: - A small blue block (OOD ≈ 0.0) at the top-left corner (r=1, k=2). - Most of the panel is white (OOD ≈ 0.0), indicating minimal OOD values. - **R=2 (ID 6-hop)**: - A vertical gradient from blue (left) to white (right), with OOD values increasing slightly. - The ID/OOD boundary (dashed line) separates the low-OOD region (left) from the higher-OOD region (right). - **R=3 (ID 9-hop)**: - A larger red region (OOD ≈ 0.8–1.0) appears in the top-right corner (r=1–5, k=14–23). - The ID/OOD boundary is less distinct, with OOD values spreading across the panel. - **R=4 (ID 10-hop)**: - A significant red block (OOD ≈ 0.8–1.0) dominates the top-right (r=1–5, k=14–23). - The train recurrence line (purple) intersects the red region, suggesting a threshold for OOD performance. - **R=5 (ID 12-hop)**: - A large red region (OOD ≈ 0.6–1.0) spans the top-right (r=1–10, k=14–23). - The ID/OOD boundary is less visible, with OOD values dominating the panel. - **R=6 (ID 13-hop)**: - A red region (OOD ≈ 0.6–1.0) appears in the top-right (r=1–10, k=14–23). - The train recurrence line intersects the red region, indicating a critical threshold. - **R=7 (ID 14-hop)**: - A red region (OOD ≈ 0.6–1.0) spans the top-right (r=1–10, k=14–23). - The ID/OOD boundary is barely visible, with OOD values dominating. - **R=8 (ID 13-hop)**: - A red region (OOD ≈ 0.6–1.0) spans the top-right (r=1–10, k=14–23). - The train recurrence line intersects the red region, reinforcing the threshold effect. ### Key Observations 1. **OOD Increase with R and k**: - Higher recurrence values (R) and hop counts (k) correlate with increased OOD values (red regions). - For R ≥ 3, OOD values exceed 0.6 in most panels, indicating significant out-of-distribution performance. 2. **Boundary and Train Recurrence Lines**: - The ID/OOD boundary (dashed vertical line) separates low-OOD (blue/white) and high-OOD (red) regions. - The train recurrence line (purple) intersects red regions in higher R panels, suggesting a critical threshold for OOD performance. 3. **Panel-Specific Trends**: - R=1 (ID 3-hop) shows minimal OOD, while R=8 (ID 13-hop) exhibits the highest OOD values. - The ID/OOD boundary becomes less distinct as R increases, indicating reduced model robustness. ### Interpretation The heatmap demonstrates that **increased recurrence (R) and hop count (k) degrade the model's ability to distinguish in-distribution (ID) from out-of-distribution (OOD) data**. The ID/OOD boundary and train recurrence line act as thresholds, with higher R values crossing these thresholds and entering high-OOD regions. This suggests that deeper or more complex models (higher R) are more sensitive to OOD data, which could impact their reliability in real-world scenarios. The consistent red regions in higher R panels highlight a critical trend: **model performance deteriorates as complexity increases**, emphasizing the need for robustness testing in model design.