## Chart: Validation Score vs. Training Step for AIME25 Benchmark ### Overview The image is a line chart comparing the validation scores of two models, GRPO and MEL, over training steps for the AIME25 benchmark. The x-axis represents the training step, and the y-axis represents the validation score. ### Components/Axes * **Title:** Benchmark: AIME25 * **X-axis:** Training Step, ranging from 0 to 140 in increments of 20. * **Y-axis:** Validation Score, ranging from 0.10 to 0.35 in increments of 0.05. * **Legend:** Located in the bottom-right corner. * GRPO (Blue) * MEL (Pink) ### Detailed Analysis * **GRPO (Blue):** * Starts at approximately 0.07 at step 0. * Decreases to approximately 0.10 at step 20. * Increases to approximately 0.17 at step 40. * Increases to approximately 0.23 at step 60. * Remains at approximately 0.23 at step 80. * Decreases to approximately 0.20 at step 100. * Increases to approximately 0.27 at step 120. * Increases to approximately 0.33 at step 140. * **MEL (Pink):** * Starts at approximately 0.07 at step 0. * Increases to approximately 0.17 at step 20. * Increases to approximately 0.17 at step 40. * Increases to approximately 0.23 at step 60. * Decreases to approximately 0.17 at step 80. * Increases to approximately 0.27 at step 100. * Decreases to approximately 0.23 at step 120. * Increases to approximately 0.36 at step 140. ### Key Observations * Both models start with a similar validation score. * GRPO shows a more consistent upward trend towards the end of the training steps. * MEL fluctuates more, with a notable peak at the end. ### Interpretation The chart compares the performance of two models, GRPO and MEL, on the AIME25 benchmark. The validation scores indicate how well each model generalizes to unseen data during training. GRPO appears to have a more stable and consistent improvement in validation score as training progresses, while MEL shows more fluctuation but ultimately reaches a higher validation score at the end of the training steps. This suggests that MEL might be overfitting to the training data or that it requires further regularization. GRPO, on the other hand, might be more robust and generalize better.

\n ## Line Chart: Validation Score vs. Training Step (Benchmark: AIME25) ### Overview This image presents a line chart illustrating the validation score of two models, GRPO and MEL, as a function of the training step. The chart appears to track the performance of these models during a training process on the AIME25 benchmark. ### Components/Axes * **Title:** Benchmark: AIME25 (positioned at the top-center) * **X-axis:** Training Step (ranging from approximately 0 to 140, with markers at intervals of 20) * **Y-axis:** Validation Score (ranging from approximately 0.10 to 0.35, with markers at intervals of 0.05) * **Legend:** Located in the bottom-right corner. * GRPO (represented by a blue line with circular markers) * MEL (represented by a pink line with triangular markers) ### Detailed Analysis **GRPO (Blue Line):** The GRPO line generally slopes upward, indicating an increasing validation score with increasing training steps. However, it exhibits significant fluctuations. * At Training Step 0: Validation Score ≈ 0.13 * At Training Step 20: Validation Score ≈ 0.16 * At Training Step 40: Validation Score ≈ 0.14 * At Training Step 60: Validation Score ≈ 0.24 * At Training Step 80: Validation Score ≈ 0.30 * At Training Step 100: Validation Score ≈ 0.20 * At Training Step 120: Validation Score ≈ 0.28 * At Training Step 140: Validation Score ≈ 0.27 **MEL (Pink Line):** The MEL line also shows an overall upward trend, but with less pronounced fluctuations than GRPO. * At Training Step 0: Validation Score ≈ 0.10 * At Training Step 20: Validation Score ≈ 0.18 * At Training Step 40: Validation Score ≈ 0.18 * At Training Step 60: Validation Score ≈ 0.25 * At Training Step 80: Validation Score ≈ 0.22 * At Training Step 100: Validation Score ≈ 0.24 * At Training Step 120: Validation Score ≈ 0.26 * At Training Step 140: Validation Score ≈ 0.36 ### Key Observations * Both models demonstrate improvement in validation score as training progresses. * GRPO exhibits higher volatility in its validation score compared to MEL. * MEL consistently has a lower validation score than GRPO until approximately Training Step 140, where it surpasses GRPO. * The largest increase in validation score for GRPO occurs between Training Steps 40 and 60. * The largest increase in validation score for MEL occurs between Training Steps 120 and 140. ### Interpretation The chart suggests that both GRPO and MEL are learning from the training data, as evidenced by the increasing validation scores. The higher volatility of GRPO might indicate a more sensitive or unstable training process. The fact that MEL eventually surpasses GRPO in validation score towards the end of the training period suggests that MEL may have a more robust learning algorithm or a better ability to generalize from the data, or that GRPO is overfitting. The AIME25 benchmark appears to be a suitable environment for evaluating these models, as it allows for differentiation in performance. The fluctuations in both lines could be due to the stochastic nature of the training process, the batch size used, or the learning rate schedule. Further investigation would be needed to determine the root cause of these fluctuations and to optimize the training process for both models.

## Line Chart: Benchmark: AIME25 ### Overview The image displays a line chart comparing the performance of two methods, labeled "GAPO" and "MEL," over the course of training. The chart tracks a "Validation Score" against "Training Step," showing how each method's performance evolves. Both methods show a general upward trend, indicating improvement with more training, but with different patterns of volatility. ### Components/Axes * **Chart Title:** "Benchmark: AIME25" (centered at the top). * **X-Axis:** * **Label:** "Training Step" (centered below the axis). * **Scale:** Linear scale from 0 to 140. * **Major Tick Marks:** 0, 20, 40, 60, 80, 100, 120, 140. * **Y-Axis:** * **Label:** "Validation Score" (rotated vertically, left of the axis). * **Scale:** Linear scale from 0.10 to 0.35. * **Major Tick Marks:** 0.10, 0.15, 0.20, 0.25, 0.30, 0.35. * **Legend:** * **Position:** Bottom-right corner of the chart area. * **Entries:** 1. **GAPO:** Represented by a blue line with circular markers. 2. **MEL:** Represented by a red line with triangular markers. ### Detailed Analysis **Data Series: GAPO (Blue Line, Circles)** * **Trend:** The line shows an overall upward trend with significant fluctuations. It starts at a moderate level, dips early, then rises with several peaks and troughs before a final sharp increase. * **Approximate Data Points (Training Step, Validation Score):** * (0, ~0.17) * (10, ~0.17) * (20, ~0.10) - **Notable dip.** * (30, ~0.17) * (40, ~0.13) * (50, ~0.23) * (60, ~0.22) * (70, ~0.25) * (80, ~0.30) - **Local peak.** * (90, ~0.20) * (100, ~0.20) * (110, ~0.25) * (120, ~0.30) * (130, ~0.27) * (140, ~0.33) - **Final value.** **Data Series: MEL (Red Line, Triangles)** * **Trend:** The line shows a strong, albeit volatile, upward trend. It starts lower than GAPO but exhibits more dramatic swings, ultimately reaching a higher final value. * **Approximate Data Points (Training Step, Validation Score):** * (0, ~0.07) * (10, ~0.17) * (20, ~0.17) * (30, ~0.20) * (40, ~0.17) * (50, ~0.27) * (60, ~0.22) * (70, ~0.27) * (80, ~0.20) * (90, ~0.17) * (100, ~0.27) * (110, ~0.23) * (120, ~0.27) * (130, ~0.27) * (140, ~0.36) - **Final value and chart maximum.** ### Key Observations 1. **Initial Performance:** GAPO starts with a higher validation score (~0.17) than MEL (~0.07) at step 0. 2. **Early Divergence:** GAPO experiences a sharp performance drop at step 20, while MEL maintains its score. 3. **Crossover Points:** The lines cross multiple times (e.g., near step 10, step 50, step 110), indicating neither method is consistently superior throughout training. 4. **Volatility:** MEL's performance is more volatile, with larger swings between consecutive steps (e.g., the drop from ~0.27 at step 70 to ~0.17 at step 90). 5. **Final Outcome:** By the final recorded step (140), MEL achieves the highest validation score on the chart (~0.36), surpassing GAPO's final score (~0.33). 6. **General Trend:** Despite the volatility, both methods demonstrate a clear positive correlation between training steps and validation score. ### Interpretation This chart benchmarks two optimization or learning algorithms (GAPO and MEL) on the "AIME25" task. The data suggests that while both methods are effective at learning, as evidenced by their upward trends, they have distinct characteristics. * **GAPO** appears to be a more stable learner initially but is prone to a significant early setback (the dip at step 20). Its recovery and subsequent performance are strong but not the highest. * **MEL** starts poorly but exhibits a "high-risk, high-reward" pattern. Its greater volatility suggests it may be exploring the solution space more aggressively, which leads to larger temporary setbacks but also enables it to discover a better final solution (the peak at step 140). The multiple crossover points imply that the choice between GAPO and MEL might depend on the available training budget. If training must stop early (e.g., before step 50), GAPO might be preferable. For a full training run to step 140, MEL yields a better result. The chart does not provide information on computational cost, stability across multiple runs, or performance beyond 140 steps, which would be critical for a full technical assessment.

## Line Chart: AIME25 Benchmark Validation Scores ### Overview The chart compares the validation performance of two methods, **GRPO** (blue line) and **MEL** (red line), across 140 training steps on the AIME25 benchmark. Both methods exhibit fluctuating performance, with MEL achieving a slightly higher final validation score despite greater volatility. ### Components/Axes - **X-axis (Training Step)**: Ranges from 0 to 140 in increments of 20. - **Y-axis (Validation Score)**: Ranges from 0.05 to 0.35 in increments of 0.05. - **Legend**: Located in the bottom-right corner, with: - **Blue line**: GRPO - **Red line**: MEL ### Detailed Analysis 1. **GRPO (Blue Line)**: - Starts at ~0.05 at step 0. - Dips to ~0.10 at step 20, then rises to ~0.17 at step 40. - Peaks at ~0.30 at step 80, followed by a drop to ~0.20 at step 100. - Final score: ~0.34 at step 140. - **Trend**: Overall upward trajectory with mid-training volatility. 2. **MEL (Red Line)**: - Begins at ~0.05 at step 0. - Rises to ~0.17 at step 40, peaks at ~0.26 at step 60. - Drops to ~0.16 at step 80, then surges to ~0.27 at step 100. - Final score: ~0.36 at step 140. - **Trend**: Highly volatile with two major peaks and sharper fluctuations. ### Key Observations - **Final Performance**: MEL outperforms GRPO by ~0.02 in the last training step. - **Volatility**: MEL shows larger swings (e.g., ~0.10 drops/rises) compared to GRPO’s more gradual changes. - **Early Training**: Both methods start similarly but diverge after step 40. - **Mid-Training Dip**: GRPO’s performance drops sharply at step 80, while MEL recovers strongly. ### Interpretation The data suggests that **MEL achieves higher peak performance** but with greater instability, whereas **GRPO demonstrates steadier improvement** over time. The final scores are close, but MEL’s late-stage surge indicates potential for higher rewards despite its erratic behavior. The AIME25 benchmark likely tests complex reasoning, where MEL’s ability to exploit training dynamics (e.g., late-stage optimization) may explain its edge. However, GRPO’s consistency could be preferable in scenarios requiring reliability over peak performance.