## Line Graph: Benchmark: AIME25 ### Overview The image is a line graph comparing the validation scores of two methods, **GRPO** (blue) and **MEL** (pink), across training steps (0–140). The y-axis represents validation scores (0.025–0.200), while the x-axis represents training steps. The graph highlights performance trends, with MEL generally outperforming GRPO in later stages. --- ### Components/Axes - **Title**: "Benchmark: AIME25" (top center). - **X-axis**: "Training Step" (0–140, increments of 20). - **Y-axis**: "Validation Score" (0.025–0.200, increments of 0.025). - **Legend**: Bottom-right corner, with: - **Blue**: GRPO - **Pink**: MEL --- ### Detailed Analysis #### GRPO (Blue Line) - **Initial Phase (0–30 steps)**: Starts at 0.100, dips sharply to 0.025 at step 30. - **Mid-Phase (30–80 steps)**: Fluctuates between 0.025 and 0.100, with a peak at 0.100 at step 60. - **Late Phase (80–140 steps)**: Rises to 0.175 at step 100, then drops to 0.100 at step 120, ending at 0.075 at step 140. #### MEL (Pink Line) - **Initial Phase (0–40 steps)**: Starts at 0.100, peaks at 0.130 at step 10, remains flat until step 40. - **Mid-Phase (40–80 steps)**: Rises to 0.130 at step 50, stays flat until step 80. - **Late Phase (80–140 steps)**: Jumps to 0.175 at step 110, drops to 0.130 at step 120, peaks at 0.200 at step 130, and ends at 0.165 at step 140. --- ### Key Observations 1. **GRPO Volatility**: The blue line exhibits significant fluctuations, with sharp dips (e.g., 0.025 at steps 30 and 80) and peaks (0.175 at step 100). 2. **MEL Stability**: The pink line shows smoother trends, with gradual increases and fewer extreme drops. 3. **Performance Divergence**: MEL outperforms GRPO in later training steps (e.g., 0.200 at step 130 vs. GRPO’s 0.175 at step 100). 4. **Final Scores**: At step 140, MEL ends at 0.165, while GRPO ends at 0.075. --- ### Interpretation - **Model Reliability**: MEL demonstrates greater consistency and higher validation scores, suggesting it is more robust for the AIME25 benchmark. - **GRPO Instability**: The blue line’s volatility may indicate challenges in learning or overfitting, particularly in early and mid-training phases. - **Late-Stage Advantage**: MEL’s sharp rise after step 100 implies it adapts better to complex patterns in later training stages. - **Practical Implications**: For applications requiring stable performance, MEL is preferable. GRPO’s fluctuations might necessitate further tuning or regularization. --- ### Spatial Grounding - **Legend**: Bottom-right corner, clearly associating colors with methods. - **Data Points**: All values align with legend colors (e.g., pink for MEL, blue for GRPO). - **Axis Labels**: Centered and legible, with numerical increments explicitly marked. --- ### Content Details - **GRPO Data Points**: - 0: 0.100 - 10: 0.100 - 20: 0.100 - 30: 0.025 - 40: 0.075 - 50: 0.075 - 60: 0.100 - 70: 0.075 - 80: 0.025 - 90: 0.100 - 100: 0.175 - 110: 0.100 - 120: 0.100 - 130: 0.075 - 140: 0.075 - **MEL Data Points**: - 0: 0.100 - 10: 0.130 - 20: 0.130 - 30: 0.130 - 40: 0.130 - 50: 0.130 - 60: 0.130 - 70: 0.130 - 80: 0.130 - 90: 0.130 - 100: 0.130 - 110: 0.175 - 120: 0.130 - 130: 0.200 - 140: 0.165 --- ### Final Notes The graph emphasizes the trade-off between stability and performance. While GRPO shows potential in mid-training, MEL’s late-stage dominance suggests it is better suited for tasks requiring sustained accuracy. Further analysis could explore hyperparameter tuning for GRPO to mitigate its volatility.