## 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 chart displays the validation score on the y-axis and the training step on the x-axis. ### Components/Axes * **Title:** Benchmark: AIME25 * **X-axis:** Training Step, with markers at 0, 20, 40, 60, 80, 100, 120, and 140. * **Y-axis:** Validation Score, with markers at 0.025, 0.050, 0.075, 0.100, 0.125, 0.150, 0.175, and 0.200. * **Legend:** Located in the bottom-right corner. * GRPO (Blue) * MEL (Pink) ### Detailed Analysis * **GRPO (Blue):** * Starts at approximately 0.100 at training step 0. * Decreases to approximately 0.033 at training step 20. * Relatively stable around 0.067 between training steps 40 and 60. * Decreases to approximately 0.025 at training step 80. * Increases sharply to approximately 0.167 at training step 100. * Decreases to approximately 0.100 at training step 120. * Remains at approximately 0.100 at training step 140. * **MEL (Pink):** * Starts at approximately 0.100 at training step 0. * Increases to approximately 0.133 at training step 20. * Decreases to approximately 0.100 at training step 40. * Relatively stable around 0.133 between training steps 60 and 100. * Decreases to approximately 0.167 at training step 120. * Decreases to approximately 0.133 at training step 120. * Increases sharply to approximately 0.200 at training step 140. * Decreases to approximately 0.167 at training step 140. ### Key Observations * The GRPO model shows more volatility in its validation score compared to the MEL model. * The MEL model generally maintains a higher validation score than the GRPO model, especially in the later training steps. * Both models show fluctuations in their validation scores, indicating potential overfitting or the need for further optimization. ### 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. The MEL model appears to perform better overall, achieving higher validation scores and demonstrating more stability. The GRPO model, while showing some improvement during training, exhibits more significant fluctuations, suggesting it may be more sensitive to the training data or require different hyperparameter tuning. The sharp increase in MEL's validation score near the end of training suggests it may be converging towards a better solution, while GRPO's performance plateaus. These observations can inform decisions about model selection, hyperparameter tuning, and further experimentation to improve the performance of both models.

\n ## Line Chart: Validation Score vs. Training Step (Benchmark: AIME25) ### Overview The image presents a line chart comparing the validation scores of two models, "GRPO" and "MEL", across different training steps. The chart aims to visualize the performance of each model during the 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 tick marks at intervals of 20) * **Y-axis:** Validation Score (ranging from approximately 0.02 to 0.20, with tick marks 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) * **Gridlines:** Present to aid in reading values. ### Detailed Analysis **GRPO (Blue Line):** The GRPO line exhibits a fluctuating trend. It starts at approximately 0.10, dips to a minimum of around 0.025 at a training step of 20, then rises to a peak of approximately 0.175 at a training step of 100. After this peak, it declines to around 0.10 at a training step of 120, and finally drops to approximately 0.06 at a training step of 140. * (0, 0.10) * (20, 0.025) * (40, 0.065) * (60, 0.10) * (80, 0.025) * (100, 0.175) * (120, 0.10) * (140, 0.06) **MEL (Pink Line):** The MEL line shows a generally increasing trend with some fluctuations. It begins at approximately 0.10, rises to a peak of around 0.13 at a training step of 20, then plateaus around 0.10 until a training step of 60. From 60 to 100, it increases to approximately 0.14, and then rises sharply to a maximum of approximately 0.20 at a training step of 140. * (0, 0.10) * (20, 0.13) * (40, 0.10) * (60, 0.10) * (80, 0.13) * (100, 0.14) * (120, 0.15) * (140, 0.20) ### Key Observations * The GRPO model demonstrates significant fluctuations in validation score throughout the training process, indicating potential instability or sensitivity to training data. * The MEL model exhibits a more stable and generally increasing trend, suggesting more consistent learning. * The MEL model consistently outperforms the GRPO model after a training step of 80. * Both models start with similar validation scores. ### Interpretation The chart suggests that the MEL model is more effective at learning from the AIME25 benchmark data compared to the GRPO model. The consistent upward trend of the MEL model indicates that it is successfully generalizing to the validation data as training progresses. The GRPO model's erratic behavior suggests it may be overfitting to the training data or encountering difficulties in convergence. The difference in performance between the two models becomes more pronounced as training continues, highlighting the superior learning capabilities of the MEL model in this specific scenario. The initial similar performance suggests both models start with comparable initial conditions, but their learning dynamics diverge over time. The AIME25 benchmark appears to favor the learning strategy employed by the MEL model.

\n ## Line Chart: Benchmark: AIME25 ### Overview The image is a line chart comparing the validation score performance of two models, labeled "GRPO" and "MEL," over the course of training steps on a benchmark titled "AIME25." The chart displays two distinct line series with markers, plotted against a grid. ### Components/Axes * **Chart Title:** "Benchmark: AIME25" (centered at the top). * **Y-Axis:** Labeled "Validation_Score". The scale runs from 0.025 to 0.200, with major tick marks at intervals of 0.025 (0.025, 0.050, 0.075, 0.100, 0.125, 0.150, 0.175, 0.200). * **X-Axis:** Labeled "Training_Step". The scale runs from 0 to 140, with major tick marks at intervals of 20 (0, 20, 40, 60, 80, 100, 120, 140). * **Legend:** Located in the bottom-right corner of the plot area. * **GRPO:** Represented by a blue line with circular markers. * **MEL:** Represented by a red line with triangular markers. * **Grid:** A light gray grid is present, aligning with the major ticks on both axes. ### Detailed Analysis **Data Series: GRPO (Blue Line, Circle Markers)** * **Trend:** The GRPO line exhibits high volatility, characterized by sharp peaks and deep troughs throughout the training steps. There is no consistent upward or downward trend; performance fluctuates dramatically. * **Approximate Data Points:** * Step 0: ~0.100 * Step 20: ~0.035 (sharp drop) * Step 40: ~0.075 (recovery) * Step 60: ~0.100 (peak) * Step 80: ~0.040 (sharp drop) * Step 100: ~0.165 (highest peak) * Step 120: ~0.100 (drop) * Step 140: ~0.060 (final point) **Data Series: MEL (Red Line, Triangle Markers)** * **Trend:** The MEL line shows a more stable and generally upward trend. After an initial rise, it plateaus, dips slightly, and then climbs to its highest values in the later steps. * **Approximate Data Points:** * Step 0: ~0.100 * Step 20: ~0.130 (rise) * Step 40: ~0.100 (dip) * Step 60: ~0.100 (plateau) * Step 80: ~0.130 (rise) * Step 100: ~0.130 (plateau) * Step 120: ~0.165 (peak, tied with GRPO's peak) * Step 140: ~0.165 (final point, maintains peak) ### Key Observations 1. **Performance Crossover:** The two models start at the same validation score (~0.100). MEL immediately outperforms GRPO at step 20. GRPO only surpasses MEL at its single, dramatic peak at step 100 (~0.165 vs MEL's ~0.130). 2. **Volatility vs. Stability:** GRPO's performance is highly unstable, with a range of approximately 0.035 to 0.165. MEL's performance is more consistent, with a narrower range of approximately 0.100 to 0.165. 3. **Final Performance:** At the final recorded step (140), MEL (~0.165) significantly outperforms GRPO (~0.060). 4. **Peak Alignment:** Both models achieve their highest observed validation score of ~0.165, but at different times (GRPO at step 100, MEL at steps 120 & 140). ### Interpretation The chart suggests a fundamental difference in the training dynamics of the two models on the AIME25 benchmark. The **MEL** model demonstrates more robust and reliable learning, achieving a high validation score and maintaining it. Its trajectory indicates stable convergence. In contrast, the **GRPO** model appears unstable; its performance is erratic, suggesting potential issues like overfitting to specific training batches, sensitivity to hyperparameters, or an unstable optimization process. While GRPO is capable of reaching a high score (step 100), it cannot sustain it. The data implies that for this specific task, MEL is the more dependable model, offering predictable and high performance as training progresses. GRPO's volatility makes its final performance unpredictable and, in this case, poor. The benchmark likely measures a capability where consistent optimization (MEL) is more effective than the approach used by GRPO.

## 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.