## Line Chart: MATH Accuracy vs. Tournament Round ### Overview The image is a line chart comparing the MATH accuracy of different models (RRM-7B and RRM-32B) with and without voting, across tournament rounds (0 to 3). The chart also includes horizontal dashed lines indicating the performance of other models like RRM-32B Elo, RRM-7B Elo, Qwen2.5-PRM-70B, Qwen2.5-PRM-7B, and Voting@8. ### Components/Axes * **X-axis:** Tournament round, with values 0, 1, 2, and 3. * **Y-axis:** MATH accuracy, ranging from 82 to 90. * **Legend (bottom-right):** * Red: RRM-7B with voting * Orange: RRM-7B without voting * Blue: RRM-32B with voting * Light Blue: RRM-32B without voting * **Horizontal dashed lines (top-left):** * RRM-32B Elo (at approximately 90.5) * RRM-7B Elo, Qwen2.5-PRM-70B (at approximately 88.8) * Qwen2.5-PRM-7B (at approximately 87.8) * Voting@8 (at approximately 87) ### Detailed Analysis * **RRM-7B with voting (Red):** * Trend: Slopes upward. * Data points: (0, 82), (1, 85.5), (2, 87.5), (3, 88.5) * **RRM-7B without voting (Orange):** * Trend: Slopes upward. * Data points: (0, 82), (1, 85), (2, 87), (3, 88.2) * **RRM-32B with voting (Blue):** * Trend: Slopes upward. * Data points: (0, 82.2), (1, 86.5), (2, 88.5), (3, 90) * **RRM-32B without voting (Light Blue):** * Trend: Slopes upward. * Data points: (0, 82.2), (1, 86), (2, 88), (3, 89.8) ### Key Observations * Both RRM-32B models (with and without voting) consistently outperform the RRM-7B models. * For both model sizes (7B and 32B), using voting generally results in slightly higher MATH accuracy. * The performance gap between the models appears to narrow as the tournament round increases, but RRM-32B maintains the lead. * The RRM-32B with voting model approaches the performance level of "RRM-32B Elo" by round 3. ### Interpretation The chart demonstrates the impact of model size and voting on MATH accuracy in a tournament setting. The RRM-32B models, being larger, achieve higher accuracy than the RRM-7B models. The use of voting enhances the performance of both models, although the effect seems more pronounced in earlier rounds. The convergence of the lines suggests that the benefit of additional tournament rounds diminishes as the models approach their performance ceiling. The horizontal lines provide a benchmark against other models, indicating the relative performance of the RRM models in comparison to established models like RRM-32B Elo, RRM-7B Elo, Qwen2.5-PRM-70B, Qwen2.5-PRM-7B, and Voting@8. The data suggests that increasing model size and incorporating voting are effective strategies for improving MATH accuracy.

\n ## Line Chart: MATH Accuracy vs. Tournament Round ### Overview This line chart depicts the relationship between MATH accuracy and tournament round for four different model configurations. The models are RRM-7B with and without voting, and RRM-32B with and without voting. The chart shows how accuracy changes as the tournament progresses from round 0 to round 3. Horizontal dashed lines indicate Elo ratings for different models. ### Components/Axes * **X-axis:** Tournament round (0, 1, 2, 3) * **Y-axis:** MATH accuracy (ranging from approximately 82 to 91) * **Data Series:** * RRM-7B with voting (orange) * RRM-7B without voting (light orange) * RRM-32B with voting (blue) * RRM-32B without voting (light blue) * **Horizontal Lines:** * RRM-32B Elo (dashed, gray) * RRM-7B Elo (dashed, gray) * Owen2.5-PRM-70B (dashed, gray) * Owen2.5-PRM-7B (dashed, gray) * Voting@8 (dashed, gray) * **Legend:** Located in the bottom-right corner of the chart. ### Detailed Analysis * **RRM-7B with voting (orange):** Starts at approximately 82.5 at round 0, increases to approximately 85.5 at round 1, then rises to approximately 88 at round 2, and finally reaches approximately 88.5 at round 3. The line shows a decreasing rate of increase as the tournament progresses. * **RRM-7B without voting (light orange):** Begins at approximately 82.5 at round 0, increases to approximately 86 at round 1, then rises to approximately 88.5 at round 2, and reaches approximately 89 at round 3. This line also shows a decreasing rate of increase. * **RRM-32B with voting (blue):** Starts at approximately 82.5 at round 0, increases sharply to approximately 88.5 at round 1, continues to approximately 90 at round 2, and reaches approximately 91 at round 3. This line exhibits a consistently strong upward trend. * **RRM-32B without voting (light blue):** Begins at approximately 82.5 at round 0, increases to approximately 88 at round 1, then rises to approximately 89.5 at round 2, and reaches approximately 90.5 at round 3. This line also shows a strong upward trend, but slightly less pronounced than the "with voting" counterpart. ### Key Observations * The RRM-32B models consistently outperform the RRM-7B models across all tournament rounds. * Adding voting generally improves performance, particularly for the RRM-7B models. The effect is less pronounced for the RRM-32B models. * All models show diminishing returns in accuracy as the tournament progresses, with the rate of improvement slowing down in later rounds. * The RRM-32B with voting model reaches an accuracy of approximately 91 at round 3, exceeding the Elo rating of RRM-32B. ### Interpretation The data suggests that increasing model size (from 7B to 32B parameters) significantly improves MATH accuracy. The inclusion of a voting mechanism further enhances performance, especially for smaller models like RRM-7B, indicating that ensembling can compensate for individual model limitations. The diminishing returns observed in later tournament rounds suggest that the models are approaching a performance ceiling, and further improvements may require different approaches or more extensive training data. The Elo ratings provide a benchmark for performance, and the RRM-32B with voting model surpasses this benchmark, demonstrating its effectiveness. The chart highlights the trade-off between model size, computational cost, and accuracy, and suggests that a larger model with voting is the most effective configuration for maximizing MATH accuracy in this context.

## Line Chart: MATH Accuracy Across Tournament Rounds ### Overview The chart compares the MATH accuracy of four AI models across four tournament rounds (0-3). Models are differentiated by size (7B vs 32B parameters) and whether voting mechanisms were used. All lines show upward trends, with larger models and voting mechanisms achieving higher accuracy. ### Components/Axes - **X-axis**: Tournament round (0, 1, 2, 3) - **Y-axis**: MATH accuracy (82-90%) - **Legend**: - Red: RRM-7B with voting - Orange: RRM-7B without voting - Blue: RRM-32B with voting - Purple: RRM-32B without voting - **Gridlines**: Horizontal at 82, 84, 86, 88, 90 ### Detailed Analysis 1. **RRM-32B with voting** (blue): - Starts at 82.2 (round 0) - Reaches 90.5 (round 3) - Steepest slope (≈2.1% per round) 2. **RRM-32B without voting** (purple): - Starts at 82.5 (round 0) - Reaches 89.8 (round 3) - Slope ≈1.8% per round 3. **RRM-7B with voting** (red): - Starts at 82.3 (round 0) - Reaches 88.8 (round 3) - Slope ≈1.6% per round 4. **RRM-7B without voting** (orange): - Starts at 82.4 (round 0) - Reaches 88.2 (round 3) - Slope ≈1.5% per round ### Key Observations - All models show consistent improvement across rounds - Larger models (32B) outperform smaller models (7B) by 1.3-2.3% at round 3 - Voting mechanisms improve accuracy by 0.7-1.3% across all models - RRM-32B with voting achieves 90.5% accuracy (highest value) - RRM-7B without voting has lowest performance (88.2% at round 3) ### Interpretation The data demonstrates that: 1. Model size significantly impacts performance (32B models outperform 7B by ~2% at final round) 2. Voting mechanisms provide measurable accuracy improvements (0.7-1.3% boost) 3. Performance gains accelerate over time (slopes increase in later rounds) 4. The combination of large model size and voting yields optimal results The consistent upward trends suggest that both model capacity and ensemble methods (voting) are critical factors in mathematical reasoning performance. The 32B models with voting achieve near-perfect accuracy (90.5%) by round 3, indicating potential saturation of performance gains in this domain.