## Chart: Validation Score vs. Training Step for AIME24 Benchmark ### Overview The image is a line chart comparing the validation scores of two models, GRPO and MEL, over training steps for the AIME24 benchmark. The x-axis represents the training step, and the y-axis represents the validation score. ### Components/Axes * **Title:** Benchmark: AIME24 * **X-axis:** Training Step, with markers at 0, 20, 40, 60, 80, 100, 120, and 140. * **Y-axis:** Validation Score, ranging from 0.075 to 0.225, with markers at intervals of 0.025. * **Legend:** Located in the bottom-right corner. * Blue line: GRPO * Pink line: MEL ### Detailed Analysis * **GRPO (Blue):** * Starts at approximately 0.135 at step 0. * Increases to approximately 0.165 by step 20. * Decreases to approximately 0.135 by step 40. * Increases to approximately 0.165 by step 40. * Decreases to approximately 0.100 by step 60. * Increases to approximately 0.165 by step 80. * Remains at approximately 0.165 by step 100. * Remains at approximately 0.165 by step 120. * Increases to approximately 0.165 by step 140. * **MEL (Pink):** * Starts at approximately 0.135 at step 0. * Decreases to approximately 0.070 by step 20. * Increases to approximately 0.135 by step 40. * Decreases to approximately 0.100 by step 60. * Increases to approximately 0.200 by step 80. * Increases to approximately 0.230 by step 100. * Decreases to approximately 0.165 by step 120. * Increases to approximately 0.200 by step 140. ### Key Observations * GRPO shows a more stable validation score compared to MEL. * MEL has a higher peak validation score around step 100, but also exhibits more fluctuation. * Both models start at approximately the same validation score. ### Interpretation The chart compares the performance of two models, GRPO and MEL, on the AIME24 benchmark. GRPO demonstrates more consistent performance across training steps, while MEL shows higher potential but also greater instability. The choice between the two models would depend on the specific requirements of the application, with GRPO being preferable if stability is paramount and MEL being considered if the potential for higher performance outweighs the risk of fluctuation.

## Line Chart: Validation Score vs. Training Step (Benchmark: AIME24) ### Overview The image presents a line chart illustrating the validation score of two models, GRPO and MEL, against the training step. The chart appears to track the performance of these models during a training process on the AIME24 benchmark. ### Components/Axes * **Title:** Benchmark: AIME24 (positioned at the top-center) * **X-axis:** Training Step (ranging from approximately 0 to 140, with gridlines) * **Y-axis:** Validation Score (ranging from approximately 0.075 to 0.225, with gridlines) * **Legend:** Located in the bottom-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 an oscillating trend. It starts at approximately 0.125 at Training Step 0, increases to a peak of around 0.17 at Training Step 20, dips to approximately 0.13 at Step 40, rises again to around 0.16 at Step 60, then fluctuates between approximately 0.13 and 0.17 until Step 120, and finally ends at approximately 0.16 at Step 140. * Step 0: ~0.125 * Step 20: ~0.165 * Step 40: ~0.13 * Step 60: ~0.16 * Step 80: ~0.135 * Step 100: ~0.17 * Step 120: ~0.13 * Step 140: ~0.16 **MEL (Light Red Line):** The MEL line also shows an oscillating pattern, but with a more pronounced peak. It begins at approximately 0.075 at Training Step 0, increases to around 0.13 at Step 20, decreases to a low of approximately 0.10 at Step 40, then experiences a significant rise to a peak of approximately 0.225 at Step 80, before declining to around 0.17 at Step 100, and finally stabilizes around 0.20 at Step 140. * Step 0: ~0.075 * Step 20: ~0.13 * Step 40: ~0.10 * Step 60: ~0.15 * Step 80: ~0.225 * Step 100: ~0.17 * Step 120: ~0.175 * Step 140: ~0.20 ### Key Observations * The MEL model generally achieves higher validation scores than the GRPO model, especially after Training Step 60. * Both models exhibit fluctuations in validation score, suggesting that the training process is not consistently improving performance. * The MEL model shows a significant performance spike around Training Step 80, reaching its highest validation score. * The GRPO model's performance is more stable, with less dramatic fluctuations. ### Interpretation The chart demonstrates the training progress of two models (GRPO and MEL) on the AIME24 benchmark. The validation scores indicate how well each model generalizes to unseen data during training. The oscillating nature of the lines suggests that the models are experiencing periods of improvement and regression, potentially due to factors like learning rate, batch size, or the complexity of the data. The fact that MEL consistently outperforms GRPO suggests that MEL is a more effective model for this particular benchmark, or that it has been trained with more optimal hyperparameters. The peak in MEL's performance at Step 80 could indicate a critical point in the training process where the model learned a significant feature or pattern. The stabilization of both models towards the end of the training process suggests that they are approaching convergence, but further training might not yield substantial improvements. The differences in the curves suggest that the models have different learning dynamics and sensitivities to the training data. Further investigation into the training process and model architectures could reveal the reasons behind these differences and potentially lead to further performance improvements.

## Line Chart: Benchmark: AIME24 ### Overview The image is a line chart titled "Benchmark: AIME24" that plots the "Validation Score" against "Training Step" for two different methods or models, labeled "GAPO" and "MEL". The chart compares their performance over the course of 140 training steps. ### Components/Axes * **Title:** "Benchmark: AIME24" (centered at the top). * **Y-Axis:** * **Label:** "Validation Score" (rotated vertically on the left). * **Scale:** Linear scale ranging from 0.075 to 0.225, with major tick marks at 0.075, 0.100, 0.125, 0.150, 0.175, 0.200, and 0.225. * **X-Axis:** * **Label:** "Training Step" (centered at the bottom). * **Scale:** Linear scale ranging from 0 to 140, with major tick marks at 0, 20, 40, 60, 80, 100, 120, and 140. * **Legend:** Located in the bottom-right corner of the chart area. * **GAPO:** Represented by a blue line with circular markers. * **MEL:** Represented by a red line with square markers. * **Grid:** A light gray grid is present, aligning with the major tick marks on both axes. ### Detailed Analysis **Data Series: GAPO (Blue Line with Circles)** * **Trend:** The GAPO line shows moderate volatility, oscillating within a band between approximately 0.100 and 0.170. It does not exhibit a strong, consistent upward or downward trend over the full 140 steps. * **Approximate Data Points:** * Step 0: ~0.140 * Step 20: ~0.170 * Step 40: ~0.170 * Step 60: ~0.100 (local minimum) * Step 80: ~0.170 * Step 100: ~0.170 * Step 120: ~0.170 * Step 140: ~0.160 **Data Series: MEL (Red Line with Squares)** * **Trend:** The MEL line shows a more dramatic pattern. It starts lower than GAPO, dips to a significant low, then experiences a sharp rise to a peak, followed by a decline and a final recovery. * **Approximate Data Points:** * Step 0: ~0.140 * Step 10: ~0.075 (global minimum for the chart) * Step 20: ~0.140 * Step 40: ~0.100 * Step 60: ~0.125 * Step 70: ~0.200 * Step 80: ~0.175 * Step 90: ~0.225 (global maximum for the chart) * Step 100: ~0.175 * Step 120: ~0.175 * Step 130: ~0.200 * Step 140: ~0.200 ### Key Observations 1. **Performance Crossover:** The two methods start at a similar validation score (~0.140). GAPO quickly takes a lead, maintaining it until approximately step 60, where MEL begins a steep ascent. 2. **Peak Performance:** MEL achieves the highest validation score on the chart (~0.225 at step 90), significantly surpassing GAPO's peak (~0.170). 3. **Volatility:** MEL exhibits much higher volatility, with a range of approximately 0.150 (from 0.075 to 0.225). GAPO's range is smaller, approximately 0.070 (from 0.100 to 0.170). 4. **Late-Stage Convergence:** After step 100, the two lines converge and track closely, with both ending near 0.160-0.200 at step 140. ### Interpretation This chart from the "AIME24" benchmark suggests a fundamental trade-off between the stability and peak performance of the two evaluated methods. * **GAPO** appears to be a more stable, conservative method. It avoids the severe performance collapse seen in MEL early on (step 10) but also fails to reach the highest validation scores. Its performance is relatively consistent after the initial phase. * **MEL** demonstrates a "high-risk, high-reward" profile. It suffers a major early setback but then undergoes a period of rapid improvement, ultimately achieving superior peak performance. Its final performance remains strong, though below its peak. The data implies that the choice between GAPO and MEL could depend on the project's priorities: if consistent, reliable performance is critical, GAPO may be preferable. If the goal is to achieve the absolute best possible score and some instability during training is acceptable, MEL shows greater potential. The convergence at the end might indicate that both methods eventually settle into a similar performance regime given sufficient training steps.

## Line Chart: Validation Scores for GRPO and MEL on AIME24 Benchmark ### Overview The image is a line chart comparing the validation performance of two methods, **GRPO** (blue line) and **MEL** (red line), across 140 training steps on the AIME24 benchmark. The y-axis represents the validation score (ranging from 0.075 to 0.225), while the x-axis represents training steps (0 to 140). Both lines exhibit fluctuating trends, with **MEL** showing sharper peaks and troughs compared to **GRPO**. --- ### Components/Axes - **X-axis (Training Step)**: Labeled "Training Step," with markers at intervals of 20 (0, 20, 40, ..., 140). - **Y-axis (Validation Score)**: Labeled "Validation Score," with increments of 0.025 (0.075, 0.100, ..., 0.225). - **Legend**: Located at the bottom-right corner, with: - **Blue line**: Labeled "GRPO" - **Red line**: Labeled "MEL" --- ### Detailed Analysis #### GRPO (Blue Line) - **Initial Phase (Steps 0–40)**: - Starts at ~0.13, rises to ~0.17 at step 20, then dips to ~0.12 at step 40. - **Mid-Phase (Steps 60–100)**: - Peaks at ~0.17 at step 80, dips to ~0.12 at step 100, then stabilizes around ~0.17. - **Final Phase (Steps 120–140)**: - Drops to ~0.13 at step 120, then remains flat. #### MEL (Red Line) - **Initial Phase (Steps 0–60)**: - Starts at ~0.13, plunges to ~0.075 at step 10, recovers to ~0.13 at step 60. - **Mid-Phase (Steps 80–120)**: - Spikes to ~0.225 at step 90, then stabilizes at ~0.17 until step 120. - **Final Phase (Steps 120–140)**: - Rises sharply to ~0.20 at step 130, then plateaus. --- ### Key Observations 1. **MEL's Volatility**: - MEL exhibits extreme fluctuations, with a dramatic drop to 0.075 at step 10 and a peak of 0.225 at step 90. 2. **GRPO's Stability**: - GRPO shows moderate oscillations but maintains a narrower range (~0.12–0.17). 3. **Crossing Points**: - The lines intersect near step 60 (~0.13) and step 100 (~0.17). 4. **Final Performance**: - By step 140, MEL outperforms GRPO (0.20 vs. 0.13). --- ### Interpretation - **Performance Trade-offs**: - MEL achieves higher validation scores in later stages but with significant instability, suggesting potential overfitting or sensitivity to training dynamics. - GRPO demonstrates robustness but lags in final performance, indicating a conservative learning strategy. - **Benchmark Insights**: - The AIME24 benchmark likely tests complex reasoning, where MEL's peaks may reflect breakthroughs in solving harder problems, while GRPO's consistency suggests reliability for simpler tasks. - **Anomalies**: - MEL's sharp drop at step 10 could indicate an initial misconfiguration or catastrophic forgetting. - The final spike in MEL at step 130 might signal a late-stage optimization surge. This analysis highlights the need to balance exploration (MEL) and exploitation (GRPO) in training strategies for high-stakes benchmarks.