## Line Chart: Benchmark AMC23 Validation Scores ### Overview The image is a line chart comparing the validation scores of two methods, **GRPO** (blue) and **MEL** (red), across 140 training steps on the AMC23 benchmark. The y-axis represents validation scores (0.46–0.60), and the x-axis represents training steps (0–140). Both lines exhibit fluctuating trends with peaks and troughs, converging at later steps. --- ### Components/Axes - **X-axis (Training Step)**: Labeled "Training Step," ranging from 0 to 140 in increments of 20. - **Y-axis (Validation Score)**: Labeled "Validation Score," ranging from 0.46 to 0.60 in increments of 0.02. - **Legend**: Located in the **bottom-right corner**, with: - **Blue circles**: GRPO - **Red triangles**: MEL --- ### Detailed Analysis #### GRPO (Blue Line) - **Initial Phase (0–20 steps)**: Starts at ~0.46, rises sharply to ~0.58 by step 20. - **Mid-Phase (20–80 steps)**: Drops to ~0.52 at step 40, rises to ~0.58 at step 60, then dips to ~0.54 at step 80. - **Late Phase (80–140 steps)**: Peaks at ~0.60 at step 100, stabilizes around ~0.58 by step 140. #### MEL (Red Line) - **Initial Phase (0–20 steps)**: Starts at ~0.46, rises sharply to ~0.60 by step 20. - **Mid-Phase (20–80 steps)**: Drops to ~0.50 at step 40, rises to ~0.58 at step 60, dips to ~0.54 at step 80. - **Late Phase (80–140 steps)**: Peaks at ~0.60 at step 100, stabilizes around ~0.58 by step 140. --- ### Key Observations 1. **Initial Divergence**: Both methods start similarly but diverge sharply after step 20, with MEL achieving a higher peak (~0.60) earlier. 2. **Volatility**: GRPO exhibits more frequent fluctuations (e.g., step 40–60), while MEL has sharper drops (e.g., step 20–40). 3. **Convergence**: Both lines stabilize near ~0.58 by step 140, suggesting similar long-term performance. 4. **Outliers**: - GRPO’s peak at step 100 (~0.60) is the highest validation score. - MEL’s drop to ~0.50 at step 40 is the lowest point for either method. --- ### Interpretation The chart demonstrates that both GRPO and MEL improve validation scores over training steps, but with distinct patterns: - **GRPO** shows gradual, sustained improvement with moderate volatility, peaking at step 100. - **MEL** achieves higher early gains but experiences sharper declines, stabilizing later. - The convergence at step 140 implies that extended training mitigates initial disparities, though GRPO’s trajectory suggests better consistency in later stages. This analysis highlights trade-offs between early performance (MEL) and long-term stability (GRPO) in the AMC23 benchmark.