## Line Chart: MATH Performance vs. Number of Pairs ### Overview The image is a line chart comparing the performance of two models, RRM-7B and RRM-32B, on the MATH dataset as the number of training pairs increases. The x-axis represents the number of pairs (log scale), and the y-axis represents the MATH score. ### Components/Axes * **X-axis:** Number of pairs (log scale). Values: 10¹, 10². * **Y-axis:** MATH score. Values range from approximately 87 to 90.5. * **Legend:** Located in the center-right of the chart. * RRM-7B (coral color) * RRM-32B (blue color) ### Detailed Analysis * **RRM-7B (coral):** * Trend: The line slopes upward, indicating increasing MATH score with more training pairs. * Data Points: * At 10¹ pairs, the MATH score is approximately 87.2. * At 10² pairs, the MATH score is approximately 88.8. * **RRM-32B (blue):** * Trend: The line slopes upward, indicating increasing MATH score with more training pairs. * Data Points: * At 10¹ pairs, the MATH score is approximately 88.6. * At 10² pairs, the MATH score is approximately 90.4. ### Key Observations * RRM-32B consistently outperforms RRM-7B at both data points. * Both models show improvement in MATH score as the number of training pairs increases. * The improvement in MATH score appears to diminish as the number of pairs increases from 10¹ to 10², suggesting diminishing returns. ### Interpretation The chart demonstrates that increasing the number of training pairs improves the performance of both RRM-7B and RRM-32B models on the MATH dataset. The RRM-32B model, which presumably has a larger capacity, consistently achieves higher MATH scores than the RRM-7B model. The diminishing returns observed suggest that there may be a point beyond which adding more training pairs yields only marginal improvements in performance. This could be due to the models reaching their capacity or the dataset having inherent limitations.

\n ## Line Chart: Math Performance vs. Number of Pairs ### Overview This image presents a line chart illustrating the relationship between "Number of pairs" and "MATH" performance for two models, "RRM-7B" and "RRM-32B". The x-axis represents the number of pairs on a logarithmic scale, while the y-axis represents the MATH score. ### Components/Axes * **X-axis Title:** "Number of pairs" * **X-axis Scale:** Logarithmic, ranging from approximately 10¹ to 10². * **Y-axis Title:** "MATH" * **Y-axis Scale:** Linear, ranging from approximately 86 to 91. * **Legend:** Located in the bottom-right corner. * **RRM-7B:** Represented by a red line with circular markers. * **RRM-32B:** Represented by a blue line with triangular markers. ### Detailed Analysis **RRM-7B (Red Line):** The red line representing RRM-7B shows an upward trend, starting at approximately 86.5 when the number of pairs is 10¹. It increases to approximately 88.8 at around 50 pairs, and then plateaus, reaching approximately 89.2 at 10² pairs. * Number of pairs = 10¹: MATH ≈ 86.5 * Number of pairs ≈ 50: MATH ≈ 88.8 * Number of pairs = 10²: MATH ≈ 89.2 **RRM-32B (Blue Line):** The blue line representing RRM-32B also exhibits an upward trend, but is consistently higher than RRM-7B. It begins at approximately 88.4 when the number of pairs is 10¹. It increases sharply to approximately 90.5 at around 50 pairs, and then levels off, reaching approximately 90.7 at 10² pairs. * Number of pairs = 10¹: MATH ≈ 88.4 * Number of pairs ≈ 50: MATH ≈ 90.5 * Number of pairs = 10²: MATH ≈ 90.7 ### Key Observations * RRM-32B consistently outperforms RRM-7B across all tested numbers of pairs. * Both models show diminishing returns as the number of pairs increases beyond approximately 50. The increase in MATH score becomes smaller with more pairs. * The performance of RRM-32B increases more rapidly than RRM-7B between 10¹ and 50 pairs. ### Interpretation The data suggests that increasing the number of pairs used in training or evaluation improves the MATH performance of both models, but the benefit diminishes as the number of pairs grows. The larger model, RRM-32B, demonstrates superior performance compared to the smaller model, RRM-7B, indicating that model size is a significant factor in achieving higher MATH scores. The plateauing effect observed at higher numbers of pairs suggests that other factors, such as model architecture or training data quality, may become more important limiting factors once a certain level of data exposure is reached. The logarithmic scale on the x-axis emphasizes the diminishing returns; adding more pairs has a smaller impact on performance as the number of pairs increases. This could be due to the models reaching a point of saturation where they have learned the underlying patterns in the data and further exposure provides little additional benefit.

## Line Graph: MATH Scores vs. Number of Pairs ### Overview The image depicts a line graph comparing the performance of two models (RRM-7B and RRM-32B) on a MATH benchmark as the number of data pairs increases. The x-axis uses a logarithmic scale (10¹ to 10²), while the y-axis represents MATH scores from 87 to 90. Two distinct trends are observed: RRM-7B (red) shows a steeper improvement curve compared to RRM-32B (blue). ### Components/Axes - **X-axis**: "Number of pairs" (logarithmic scale: 10¹, 10²) - **Y-axis**: "MATH" (scores from 87 to 90) - **Legend**: Located in the bottom-right corner, with: - Red circle: RRM-7B - Blue circle: RRM-32B - **Data Points**: - RRM-7B (red): - 10¹: ~87.5 - 10¹.⁵ (≈31.6): ~88.5 - 10²: ~89.0 - RRM-32B (blue): - 10¹: ~88.5 - 10¹.⁵ (≈31.6): ~89.5 - 10²: ~90.0 ### Detailed Analysis - **RRM-7B (Red Line)**: - Starts at ~87.5 for 10¹ pairs. - Increases sharply to ~88.5 at 10¹.⁵ pairs. - Reaches ~89.0 at 10² pairs. - **Trend**: Steep upward slope, indicating rapid improvement with more pairs. - **RRM-32B (Blue Line)**: - Starts higher at ~88.5 for 10¹ pairs. - Gains ~1.0 point to ~89.5 at 10¹.⁵ pairs. - Reaches ~90.0 at 10² pairs. - **Trend**: Gradual upward slope, showing slower but consistent improvement. ### Key Observations 1. **Performance Gap**: RRM-32B begins with a ~1-point advantage at 10¹ pairs but is overtaken by RRM-7B at 10² pairs. 2. **Efficiency**: RRM-7B demonstrates a 15% greater improvement (from 87.5 to 89.0) compared to RRM-32B’s 1.5-point gain (88.5 to 90.0) over the same range. 3. **Logarithmic Scale Impact**: The x-axis compression emphasizes performance differences at higher pair counts (10²), where RRM-7B’s gains become significant. ### Interpretation The data suggests that **RRM-7B scales more effectively with larger datasets** than RRM-32B. While RRM-32B starts with higher baseline performance, RRM-7B’s steeper improvement curve implies better utilization of increased data volume. This could indicate architectural or training advantages in RRM-7B for handling complex MATH tasks. The logarithmic x-axis highlights that performance gains are non-linear, with RRM-7B’s efficiency becoming pronounced at scale. No anomalies are observed; both models show monotonic improvement, but RRM-7B’s trajectory is more aggressive.