## Chart: Pass@k vs. k for different n and n' values ### Overview The image is a line chart showing the relationship between "pass@k (%)" on the y-axis and "k" on the x-axis for different values of "n" and "n'". There are three lines representing different combinations of n and n': (n=1, n'=1), (n=4, n'=1), and (n=4, n'=4). The chart uses a logarithmic scale for both axes. ### Components/Axes * **X-axis:** "k" (logarithmic scale), with markers at 1, 10, 100, and 1000. * **Y-axis:** "pass@k (%)" (logarithmic scale), with markers at 0.2, 0.5, 1.0, 2.0, 5.0, and 10.0. * **Legend:** Located on the right side of the chart, identifying the lines: * Solid orange line: "n=1, n'=1" * Dashed dark blue line: "n=4, n'=1" * Dotted light green line: "n=4, n'=4" ### Detailed Analysis * **n=1, n'=1 (Solid Orange Line):** * Trend: The line slopes upward, indicating that "pass@k (%)" increases as "k" increases. * Data Points: * k=1, pass@k ≈ 0.25% * k=10, pass@k ≈ 1.0% * k=100, pass@k ≈ 4.0% * k=1000, pass@k ≈ 10.0% * **n=4, n'=1 (Dashed Dark Blue Line):** * Trend: The line slopes upward, indicating that "pass@k (%)" increases as "k" increases. * Data Points: * k=1, pass@k ≈ 0.3% * k=10, pass@k ≈ 1.5% * k=100, pass@k ≈ 5.5% * k=1000, pass@k ≈ 11.0% * **n=4, n'=4 (Dotted Light Green Line):** * Trend: The line slopes upward, indicating that "pass@k (%)" increases as "k" increases. * Data Points: * k=1, pass@k ≈ 0.25% * k=10, pass@k ≈ 1.2% * k=100, pass@k ≈ 4.5% * k=1000, pass@k ≈ 10.0% ### Key Observations * For smaller values of k (e.g., k=1), the "n=4, n'=1" configuration yields the highest "pass@k (%)". * As k increases, the differences between the three configurations become smaller. * For larger values of k (e.g., k=1000), the "n=4, n'=1" configuration still yields the highest "pass@k (%)", but the "n=1, n'=1" and "n=4, n'=4" configurations are very close. ### Interpretation The chart illustrates how the "pass@k (%)" metric changes with respect to "k" for different configurations of "n" and "n'". The data suggests that increasing "k" generally improves "pass@k (%)" regardless of the "n" and "n'" values. The "n=4, n'=1" configuration appears to perform slightly better than the other configurations, especially for smaller values of "k". The logarithmic scale indicates that the rate of increase in "pass@k (%)" slows down as "k" increases. The values of n and n' seem to have a more significant impact at lower values of k.

## Line Graph: pass@k (%) vs. k ### Overview The image depicts a line graph comparing the performance metric "pass@k (%)" across different values of `k` (x-axis) for three configurations of parameters `n` and `n'`. The y-axis represents the percentage of successful outcomes, while the x-axis spans a logarithmic scale from 1 to 1000. Three distinct lines represent different parameter combinations, with the legend positioned in the bottom-right corner. --- ### Components/Axes - **Y-Axis**: Labeled "pass@k (%)", ranging from 0.2 to 10.0 in increments of 1.0. - **X-Axis**: Labeled "k", spanning a logarithmic scale from 1 to 1000. - **Legend**: Located in the bottom-right corner, with three entries: - **Solid Red**: `n=1, n'=1` - **Dashed Black**: `n=4, n'=1` - **Dotted Green**: `n=4, n'=4` --- ### Detailed Analysis 1. **Solid Red Line (`n=1, n'=1`)**: - Starts near the origin (0.2% at `k=1`). - Gradually increases, reaching ~5.0% at `k=100` and ~9.5% at `k=1000`. - Exhibits the slowest growth rate among the three lines. 2. **Dashed Black Line (`n=4, n'=1`)**: - Begins slightly above the red line (0.3% at `k=1`). - Outperforms the red line, reaching ~6.5% at `k=100` and ~10.0% at `k=1000`. - Shows a steeper slope than the red line but less than the green line. 3. **Dotted Green Line (`n=4, n'=4`)**: - Starts at ~0.4% at `k=1`. - Demonstrates the steepest growth, surpassing the black line by `k=10`. - Reaches ~9.0% at `k=100` and ~10.0% at `k=1000`. --- ### Key Observations - All three lines exhibit **monotonic growth**, with no declines observed across the range of `k`. - The **green line (`n=4, n'=4`)** consistently outperforms the other two configurations, suggesting that higher values of `n` and `n'` improve performance. - The **red line (`n=1, n'=1`)** lags significantly behind, indicating that lower parameter values result in poorer outcomes. - The logarithmic scale on the x-axis emphasizes performance differences at larger `k` values (e.g., `k=1000`). --- ### Interpretation The graph demonstrates that increasing both `n` and `n'` parameters enhances the "pass@k" metric, likely reflecting improved efficiency or accuracy in a system (e.g., recommendation algorithms, search engines, or classification models). The logarithmic x-axis highlights that performance gains are more pronounced at higher `k` thresholds, where the system's ability to handle larger-scale data becomes critical. The divergence between configurations suggests that parameter tuning (specifically increasing `n` and `n'`) is crucial for optimizing outcomes in scenarios requiring high recall or precision at scale. No outliers or anomalies are present, as all lines follow predictable growth patterns.