## Line Chart: MATH Performance Comparison
### Overview
The image contains two line charts comparing the performance of different models on a MATH task. The top chart shows the "Pass Rate" as a function of "# Checkpoints" for "Iterative Learning" (Pass@1 and Cumulative), "Sampling Only" (Cumulative), and "SFT Baseline" (Pass@1). The bottom chart shows "Accuracy" as a function of "k" for "Sampling Only" (SC@k) and "SFT Baseline" (Pass@1).
### Components/Axes
**Top Chart:**
* **Title:** MATH
* **Y-axis:** Pass Rate, ranging from 30 to 65 in increments of 5.
* **X-axis:** # Checkpoints, ranging from 0 to 10 in increments of 2.
* **Legend (Top-Left):**
* Green triangle: Iterative Learning (Pass@1)
* Dark green star: Iterative Learning (Cumulative)
* Blue star: Sampling Only (Cumulative)
* Purple dashed line: SFT Baseline (Pass@1)
**Bottom Chart:**
* **Y-axis:** Accuracy, ranging from 30 to 65 in increments of 5.
* **X-axis:** k, ranging from 4 to 10 in increments of 1.
* **Legend (Top-Left):**
* Blue triangle: Sampling Only (SC@k)
* Purple dashed line: SFT Baseline (Pass@1)
### Detailed Analysis
**Top Chart:**
* **Iterative Learning (Pass@1) - Green Triangles:** The pass rate generally increases with the number of checkpoints.
* 0 Checkpoints: 29.0
* 2 Checkpoints: 38.4
* 4 Checkpoints: 46.7
* 6 Checkpoints: 51.6
* 10 Checkpoints: 57.9
* **Iterative Learning (Cumulative) - Dark Green Stars:** The pass rate is relatively stable, hovering around 30.
* 0 Checkpoints: 29.2
* 2 Checkpoints: 30.4
* 6 Checkpoints: 32.2
* 10 Checkpoints: 31.2
* **Sampling Only (Cumulative) - Blue Stars:** The pass rate increases with the number of checkpoints.
* 0 Checkpoints: 34.9
* 2 Checkpoints: 42.4
* 6 Checkpoints: 49.6
* 10 Checkpoints: 57.1
* **SFT Baseline (Pass@1) - Purple Dashed Line:** The pass rate is constant.
* Value: 29.0
**Bottom Chart:**
* **Sampling Only (SC@k) - Blue Triangles:** The accuracy increases with k.
* k = 4: 30.0
* k = 5: 31.5
* k = 6: 32.2
* k = 7: 33.3
* k = 8: 34.2
* k = 10: 35.1
* **SFT Baseline (Pass@1) - Purple Dashed Line:** The accuracy is constant.
* Value: 29.0
### Key Observations
* In the top chart, both "Iterative Learning (Pass@1)" and "Sampling Only (Cumulative)" show a positive correlation between the number of checkpoints and the pass rate. "Iterative Learning (Cumulative)" remains relatively flat.
* In the bottom chart, "Sampling Only (SC@k)" shows a positive correlation between k and accuracy.
* "SFT Baseline (Pass@1)" remains constant in both charts.
### Interpretation
The data suggests that increasing the number of checkpoints improves the performance of "Iterative Learning (Pass@1)" and "Sampling Only (Cumulative)" on the MATH task, as indicated by the increasing pass rates. The "Iterative Learning (Cumulative)" method does not seem to benefit from additional checkpoints. In the bottom chart, increasing 'k' for "Sampling Only (SC@k)" also improves accuracy. The "SFT Baseline (Pass@1)" serves as a constant benchmark for comparison. The "Iterative Learning (Pass@1)" and "Sampling Only (Cumulative)" methods outperform the baseline with a sufficient number of checkpoints.
