## Chart: Validation Score vs. Training Step for AMC23 Benchmark ### Overview The image is a line chart comparing the validation scores of two models, GRPO and MEL, over a series of training steps for the AMC23 benchmark. The x-axis represents the training step, and the y-axis represents the validation score. ### Components/Axes * **Title:** Benchmark: AMC23 * **X-axis:** Training Step (ranging from 0 to 140) * **Y-axis:** Validation Score (ranging from 0.55 to 0.80) * **Legend:** Located in the bottom-right corner. * GRPO (blue line) * MEL (pink line) ### Detailed Analysis * **GRPO (blue line):** * Starts at approximately 0.60 at training step 0. * Decreases to approximately 0.53 at training step 40. * Increases to approximately 0.70 at training step 60. * Increases to approximately 0.80 at training step 100. * Decreases to approximately 0.62 at training step 130. * Increases to approximately 0.75 at training step 140. * **MEL (pink line):** * Starts at approximately 0.60 at training step 0. * Increases to approximately 0.75 at training step 40. * Increases to approximately 0.80 at training step 50. * Decreases to approximately 0.75 at training step 60. * Increases to approximately 0.80 at training step 120. * Increases to approximately 0.82 at training step 140. ### Key Observations * MEL generally outperforms GRPO in terms of validation score. * Both models show fluctuations in validation score during training. * MEL's validation score appears to stabilize at a higher level than GRPO's towards the end of the training steps. ### Interpretation The chart compares the performance of two models, GRPO and MEL, on the AMC23 benchmark. The validation scores indicate how well each model generalizes to unseen data during training. MEL consistently achieves higher validation scores than GRPO, suggesting it is a better-performing model for this benchmark. The fluctuations in validation scores suggest that both models experience periods of improvement and decline during training, which is common in machine learning. The stabilization of MEL's validation score at a higher level indicates that it may have converged to a better solution than GRPO.

\n ## Line Chart: Validation Score vs. Training Step (Benchmark: AMC23) ### Overview This image presents a line chart comparing the validation scores of two models, GRPO and MEL, across 140 training steps on the AMC23 benchmark. The chart visualizes the performance of each model as training progresses, allowing for a comparison of their learning curves. ### Components/Axes * **Title:** Benchmark: AMC23 (positioned at the top-center) * **X-axis:** Training Step (ranging from 0 to 140, with tick marks at intervals of 20) * **Y-axis:** Validation Score (ranging from 0.60 to 0.82, with tick marks at intervals of 0.05) * **Legend:** Located in the top-right corner. * GRPO (represented by a light blue line with circular markers) * MEL (represented by a light red line with triangular markers) ### Detailed Analysis **GRPO (Light Blue Line):** The GRPO line exhibits a fluctuating trend. It starts at approximately 0.63, dips to a low of around 0.58 at step 40, then rises to approximately 0.68 at step 80. It then increases to a peak of around 0.79 at step 100, followed by a decline to approximately 0.63 at step 120, and finally recovers slightly to around 0.70 at step 140. * Step 0: ~0.63 * Step 20: ~0.65 * Step 40: ~0.58 * Step 60: ~0.67 * Step 80: ~0.68 * Step 100: ~0.79 * Step 120: ~0.63 * Step 140: ~0.70 **MEL (Light Red Line):** The MEL line shows a generally increasing trend with some fluctuations. It begins at approximately 0.61, rises steadily to a peak of around 0.81 at step 60, then dips to approximately 0.76 at step 80. It then increases again to around 0.80 at step 100, dips to approximately 0.78 at step 120, and finally rises to around 0.81 at step 140. * Step 0: ~0.61 * Step 20: ~0.64 * Step 40: ~0.74 * Step 60: ~0.81 * Step 80: ~0.76 * Step 100: ~0.80 * Step 120: ~0.78 * Step 140: ~0.81 ### Key Observations * MEL consistently outperforms GRPO across all training steps. * Both models exhibit fluctuations in validation score, indicating potential instability during training. * GRPO shows a more pronounced dip in performance around step 40. * Both models appear to converge towards a stable validation score towards the end of the training process (steps 120-140). ### Interpretation The chart demonstrates that the MEL model achieves higher validation scores than the GRPO model on the AMC23 benchmark. This suggests that MEL is a more effective model for this particular task. The fluctuations in validation scores for both models could be attributed to factors such as the stochastic nature of the training process, the learning rate, or the complexity of the dataset. The convergence towards stable scores at the end of training indicates that both models are learning and improving, but MEL consistently maintains a higher level of performance. The initial dip in GRPO's performance might indicate a slower initial learning rate or a greater sensitivity to initial conditions. The overall trend suggests that continued training might lead to further improvements in both models, but MEL is likely to remain the superior performer.

\n ## Line Chart: Benchmark: AMC23 ### Overview The image is a line chart comparing the validation score performance of two methods, "GAPO" and "MEL", over the course of training steps on the AMC23 benchmark. The chart shows that the MEL method demonstrates a generally superior and more stable upward trend compared to the more volatile performance of the GAPO method. ### Components/Axes * **Chart Title:** "Benchmark: AMC23" (centered at the top). * **X-Axis:** * **Label:** "Training Step" * **Scale:** Linear, from 0 to 140. * **Major Tick Marks:** 0, 20, 40, 60, 80, 100, 120, 140. * **Y-Axis:** * **Label:** "Validation Score" * **Scale:** Linear, from 0.55 to 0.80. * **Major Tick Marks:** 0.55, 0.60, 0.65, 0.70, 0.75, 0.80. * **Legend:** Located in the bottom-right corner of the plot area. * **Blue line with circular markers:** "GAPO" * **Red line with circular markers:** "MEL" * **Grid:** Light gray grid lines are present for both major x and y ticks. ### Detailed Analysis **Data Series: MEL (Red Line)** * **Trend Verification:** The red line shows a clear, generally upward trend with moderate fluctuations. It starts at the same point as GAPO but establishes a lead early and maintains it. * **Approximate Data Points (Training Step, Validation Score):** * (0, 0.60) * (10, 0.60) * (20, 0.75) - Sharp increase. * (30, 0.75) * (40, 0.75) * (50, 0.80) - Peak. * (60, 0.77) * (70, 0.80) - Returns to peak. * (80, 0.77) * (90, 0.80) * (100, 0.77) * (110, 0.80) * (120, 0.82) - New peak. * (130, 0.82) * (140, 0.83) - Highest point. **Data Series: GAPO (Blue Line)** * **Trend Verification:** The blue line is highly volatile with significant dips and recoveries. It shows an overall slight upward trend but with much less consistency than MEL. * **Approximate Data Points (Training Step, Validation Score):** * (0, 0.60) * (10, 0.65) * (20, 0.63) * (30, 0.55) - Major dip, lowest point. * (40, 0.65) * (50, 0.63) * (60, 0.70) * (70, 0.60) * (80, 0.68) * (90, 0.68) * (100, 0.80) - Sharp spike, matches MEL's peak at this step. * (110, 0.78) * (120, 0.70) * (130, 0.63) * (140, 0.75) - Final recovery. ### Key Observations 1. **Performance Gap:** After step 20, the MEL (red) line is consistently above the GAPO (blue) line, except for a single convergence at step 100. 2. **Volatility:** GAPO exhibits extreme volatility, with a dramatic drop at step 30 (to ~0.55) and a sharp, isolated spike at step 100 (to ~0.80). 3. **Stability:** MEL shows a more stable learning curve. Its dips are less severe, and it establishes new performance plateaus (e.g., ~0.75 from steps 20-40, ~0.80 from steps 50-110). 4. **Final State:** At the final recorded step (140), MEL achieves its highest score (~0.83), while GAPO recovers to ~0.75, still significantly below MEL. ### Interpretation The data suggests that for the AMC23 benchmark, the **MEL method is significantly more effective and robust than the GAPO method**. MEL's trajectory indicates a more reliable learning process, quickly achieving high performance and maintaining it with minor fluctuations, ultimately reaching a higher final score. The GAPO method's performance is erratic. The severe dip at step 30 could indicate a period of catastrophic forgetting or an unstable update. The isolated spike at step 100 is an interesting anomaly—it suggests GAPO is capable of high performance but cannot sustain it, possibly due to overfitting to a specific batch or instability in its optimization landscape. The key takeaway is that MEL provides a more dependable and superior training outcome for this specific task. The chart effectively argues for the preference of MEL over GAPO in this context, highlighting not just a higher average score, but a more trustworthy and consistent improvement over time.

## Line Chart: Benchmark: AMC23 ### Overview The image is a line chart comparing the validation scores of two models, **GRPO** (blue) and **MEL** (pink), across training steps (0 to 140). The y-axis represents validation scores (0.55 to 0.80), while the x-axis represents training steps. The chart highlights performance trends over time, with notable fluctuations and convergence patterns. --- ### Components/Axes - **Title**: "Benchmark: AMC23" (top center). - **X-axis**: "Training Step" (0 to 140, increments of 20). - **Y-axis**: "Validation Score" (0.55 to 0.80, increments of 0.05). - **Legend**: Located in the bottom-right corner, with: - **GRPO**: Blue line with circular markers. - **MEL**: Pink line with triangular markers. --- ### Detailed Analysis #### GRPO (Blue Line) - **Initial Phase (0–30 steps)**: Starts at 0.60, rises to 0.65 at step 10, then drops sharply to 0.55 at step 30. - **Mid-Phase (30–100 steps)**: Recovers to 0.65 at step 40, peaks at 0.70 at step 60, dips to 0.60 at step 70, then rises to 0.70 at step 80. - **Late Phase (100–140 steps)**: Peaks at 0.80 at step 100, drops to 0.70 at step 120, then rises to 0.75 at step 140. #### MEL (Pink Line) - **Initial Phase (0–30 steps)**: Starts at 0.60, rises steadily to 0.75 by step 30. - **Mid-Phase (30–100 steps)**: Peaks at 0.80 at step 80, dips slightly to 0.75 at step 90, then stabilizes at 0.80 by step 100. - **Late Phase (100–140 steps)**: Maintains 0.80 until step 120, then rises to 0.82 at step 140. --- ### Key Observations 1. **MEL outperforms GRPO** in validation score after step 80, maintaining higher scores (0.80–0.82) compared to GRPO's 0.70–0.75. 2. **GRPO exhibits volatility**, with sharp drops (e.g., step 30) and fluctuations, while **MEL shows smoother growth**. 3. **Convergence**: Both models improve over time, but MEL achieves higher final scores (0.82 vs. 0.75 for GRPO). --- ### Interpretation The chart suggests that **MEL is more stable and efficient** in the AMC23 benchmark, achieving higher validation scores with fewer fluctuations. GRPO's volatility may indicate sensitivity to training dynamics or suboptimal hyperparameters. The divergence after step 80 highlights MEL's superior scalability or architectural advantages. These trends could inform model selection for similar tasks, emphasizing the importance of stability in validation performance.