\n ## Line Chart: Pass Rate vs. Number of Patches ### Overview The image presents two line charts comparing the "Pass Rate (%)" of two methods, "Self-play" and "Pass@N" (or "Majority Voting" in the left chart), across different "Number of patches: BF x TW" configurations. The x-axis represents the number of patches, with values 1x1, 3x3, 5x5, 10x10, 20x20, and 40x40. The y-axis represents the Pass Rate, ranging from 45% to 75%. ### Components/Axes * **X-axis Label:** "Number of patches: BF x TW" * **Y-axis Label:** "Pass Rate (%)" * **Left Chart Legend:** * Blue Line: "Self-play" * Green Line: "Majority Voting" * **Right Chart Legend:** * Blue Line: "Self-play" * Orange Line: "Pass@N" * **X-axis Markers:** 1x1, 3x3, 5x5, 10x10, 20x20, 40x40 * **Y-axis Markers:** 45.0, 47.5, 50.0, 52.5, 55.0, 57.5, 60.0, 62.5 (Left Chart), 45.0, 48.0, 50.0, 52.5, 55.0, 57.5, 60.0, 62.5, 65.0, 67.5, 70.0, 72.5, 75.0 (Right Chart) ### Detailed Analysis or Content Details **Left Chart: Majority Voting vs. Self-play** * **Self-play (Blue Line):** The line slopes upward initially, then plateaus. * 1x1: ~48.0% * 3x3: ~52.6% * 5x5: ~55.4% * 10x10: ~58.8% * 20x20: ~60.4% * 40x40: ~60.4% * **Majority Voting (Green Line):** The line initially increases, then decreases and plateaus. * 1x1: ~48.8% * 3x3: ~50.0% * 5x5: ~51.0% * 10x10: ~51.4% * 20x20: ~51.2% * 40x40: ~51.2% **Right Chart: Pass@N vs. Self-play** * **Self-play (Blue Line):** The line slopes upward initially, then plateaus. * 1x1: ~48.0% * 3x3: ~52.6% * 5x5: ~55.4% * 10x10: ~58.8% * 20x20: ~60.4% * 40x40: ~60.4% * **Pass@N (Orange Line):** The line slopes upward consistently. * 1x1: ~48.0% * 3x3: ~60.4% * 5x5: ~64.0% * 10x10: ~67.4% * 20x20: ~71.6% * 40x40: ~74.8% ### Key Observations * In both charts, the "Self-play" method shows diminishing returns as the number of patches increases, plateauing around 60%. * The "Majority Voting" method (left chart) performs poorly compared to "Self-play" and plateaus at a lower pass rate. * The "Pass@N" method (right chart) consistently outperforms "Self-play" and shows a positive correlation between the number of patches and the pass rate. * The "Pass@N" method demonstrates a significant improvement in pass rate as the number of patches increases, suggesting that more patches lead to better performance. ### Interpretation The data suggests that increasing the number of patches (BF x TW) generally improves the pass rate for both methods, but the effect is more pronounced for the "Pass@N" method. The "Pass@N" method appears to be a more effective strategy than "Majority Voting" and eventually outperforms "Self-play" as the number of patches increases. The plateauing of the "Self-play" method indicates that there is a limit to its improvement with more patches, while "Pass@N" continues to benefit. This could be due to the "Pass@N" method's ability to leverage information from multiple patches more effectively. The initial similar performance of both methods at 1x1 suggests that the benefit of the "Pass@N" method is only realized with a larger patch size. The consistent upward trend of "Pass@N" suggests that further increasing the number of patches could lead to even higher pass rates.