## Line Graph: Accuracy vs. Completion Tokens (Average Per Question) ### Overview The graph compares the accuracy of four different methods (ReST-MCTS*, PRM+Best-of-N, ORM+Best-of-N, Self-Consistency) across varying numbers of completion tokens (average per question). Accuracy is measured on the y-axis (0.12–0.22), while the x-axis represents completion tokens in increments of ~9,174 (0, 9,174, 18,348, 27,522). Error bars indicate variability in accuracy measurements. ### Components/Axes - **X-axis**: Completion Tokens (Average Per Question) Labels: 0, 9,174, 18,348, 27,522 - **Y-axis**: Accuracy (0.12–0.22) - **Legend**: Top-left corner, with four entries: - ReST-MCTS* (orange, "x" markers) - PRM+Best-of-N (red, "+" markers) - ORM+Best-of-N (blue, "o" markers) - Self-Consistency (green, "□" markers) ### Detailed Analysis 1. **ReST-MCTS*** - Starts at ~0.175 accuracy at 0 tokens, rising steadily to ~0.225 at 27,522 tokens. - Error bars shrink slightly as token count increases. - **Trend**: Consistent upward slope. 2. **PRM+Best-of-N** - Begins at ~0.165 accuracy at 0 tokens, increasing to ~0.215 at 27,522 tokens. - Error bars remain moderate throughout. - **Trend**: Steeper upward trajectory than ReST-MCTS*. 3. **ORM+Best-of-N** - Starts at ~0.125 accuracy at 0 tokens, jumps to ~0.185 at 9,174 tokens, then plateaus. - Error bars are large initially, stabilizing after 9,174 tokens. - **Trend**: Sharp initial increase, followed by flatline. 4. **Self-Consistency** - Begins at ~0.12 accuracy at 0 tokens, rising to ~0.145 at 27,522 tokens. - Error bars are smallest among all methods. - **Trend**: Gradual, linear increase. ### Key Observations - **ReST-MCTS* and PRM+Best-of-N** show the strongest performance, with ReST-MCTS* achieving the highest accuracy (~0.225) at maximum tokens. - **ORM+Best-of-N** exhibits a plateau after 9,174 tokens, suggesting diminishing returns. - **Self-Consistency** has the lowest accuracy but also the smallest error margins, indicating higher reliability in its measurements. - All methods improve with more tokens, but the rate of improvement varies significantly. ### Interpretation The data suggests that **ReST-MCTS* and PRM+Best-of-N** are the most effective methods for improving accuracy with increased computational resources (tokens). ORM+Best-of-N’s plateau implies it may not benefit from additional tokens beyond 9,174. Self-Consistency’s steady but modest gains highlight its limitations compared to other methods. The error bars suggest that ReST-MCTS* and PRM+Best-of-N have higher variability in performance, potentially due to more complex or stochastic processes. This graph underscores the trade-off between token efficiency and accuracy across different approaches.