## 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.