## Line Graph: Pass@k Performance Comparison ### Overview The image depicts a line graph comparing the performance of two token selection strategies ("critical tokens" and "random tokens") across varying sample sizes (k). The y-axis represents "pass@k(%)", while the x-axis shows the "number of sample k". Error bars indicate measurement uncertainty for each data point. ### Components/Axes - **X-axis**: "number of sample k" (ranges from 10 to 40 in increments of 10) - **Y-axis**: "pass@k(%)" (ranges from 50% to 85% in 5% increments) - **Legend**: Located at bottom-right, with: - Red triangles: "critical tokens" - Purple stars: "random tokens" - **Error bars**: Vertical lines with caps at both ends, representing ± uncertainty for each data point ### Detailed Analysis **Critical Tokens (Red):** - At k=10: 70% ±3% (error bar spans 67–73%) - At k=20: 78% ±2% (66–80%) - At k=30: 82% ±1% (81–83%) - At k=40: 85% ±2% (83–87%) **Random Tokens (Purple):** - At k=10: 50% ±5% (45–55%) - At k=20: 58% ±4% (54–62%) - At k=30: 62% ±3% (59–65%) - At k=40: 64% ±4% (60–68%) ### Key Observations 1. **Performance Gap**: Critical tokens consistently outperform random tokens by 16–21 percentage points across all k values. 2. **Error Trends**: - Random tokens show larger error margins (4–5%) compared to critical tokens (1–3%). - Error margins for critical tokens decrease as k increases. 3. **Saturation Point**: Both strategies plateau near k=30–40, with diminishing returns in performance gains. ### Interpretation The data demonstrates that critical token selection significantly improves performance reliability compared to random selection. The narrowing performance gap at higher k values suggests diminishing returns for both strategies, but critical tokens maintain a clear advantage. The smaller error margins for critical tokens indicate more consistent results, making them preferable for applications requiring stable performance. The plateau observed at k≥30 implies that increasing sample size beyond this point yields minimal practical benefits for either strategy.