## Line Chart: Benchmark AMC23 ### Overview The image is a line chart comparing the validation scores of two models, GRPO and MEL, over training steps. The chart shows how the validation scores change as the models are trained. ### Components/Axes * **Title:** Benchmark: AMC23 * **X-axis:** Training Step (ranging from 0 to 140) * Axis markers: 0, 20, 40, 60, 80, 100, 120, 140 * **Y-axis:** Validation Score (ranging from 0.46 to 0.60) * Axis markers: 0.46, 0.48, 0.50, 0.52, 0.54, 0.56, 0.58, 0.60 * **Legend:** Located in the bottom-right corner. * GRPO (blue line with circle markers) * MEL (pink line with triangle markers) ### Detailed Analysis * **GRPO (blue line):** * Trend: Initially increases, then fluctuates, and finally stabilizes. * Data Points: * (0, 0.45) * (20, 0.50) * (40, 0.525) * (50, 0.50) * (60, 0.575) * (80, 0.55) * (100, 0.60) * (120, 0.575) * (140, 0.575) * **MEL (pink line):** * Trend: Initially increases sharply, plateaus, then fluctuates before stabilizing. * Data Points: * (0, 0.45) * (20, 0.60) * (40, 0.60) * (60, 0.575) * (80, 0.55) * (100, 0.575) * (120, 0.55) * (140, 0.575) ### Key Observations * Both models start with the same validation score at the beginning of training. * MEL initially performs better, reaching a higher validation score faster than GRPO. * Both models appear to converge to a similar validation score 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 shows a faster initial improvement, but both models eventually achieve similar performance levels. The fluctuations in validation scores suggest that both models experience some instability during training, possibly due to overfitting or other factors. The stabilization towards the end indicates that the models are converging and learning effectively.

## Line Chart: Validation Score vs. Training Step (Benchmark: AMC23) ### Overview This 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 AMC23 benchmark. ### Components/Axes * **Title:** Benchmark: AMC23 (positioned at the top-center) * **X-axis:** Training Step (ranging from approximately 0 to 140, with markers at 0, 20, 40, 60, 80, 100, 120, and 140) * **Y-axis:** Validation Score (ranging from approximately 0.46 to 0.61, with markers at 0.46, 0.48, 0.50, 0.52, 0.54, 0.56, 0.58, 0.60) * **Legend:** Located in the bottom-right corner. * GRPO (represented by a light blue line) * MEL (represented by a light red line) ### Detailed Analysis **GRPO (Light Blue Line):** The GRPO line initially slopes upward from approximately 0.47 at a training step of 0 to a peak of approximately 0.58 at a training step of 20. It then declines to approximately 0.52 at a training step of 40, rises again to approximately 0.58 at a training step of 60, dips to approximately 0.55 at a training step of 80, and then rises to approximately 0.59 at a training step of 100. Finally, it plateaus around 0.58 from training step 100 to 140. * Step 0: ~0.47 * Step 20: ~0.58 * Step 40: ~0.52 * Step 60: ~0.58 * Step 80: ~0.55 * Step 100: ~0.59 * Step 120: ~0.56 * Step 140: ~0.58 **MEL (Light Red Line):** The MEL line exhibits a rapid increase from approximately 0.47 at a training step of 0 to approximately 0.60 at a training step of 20. It then declines to approximately 0.52 at a training step of 40, rises to approximately 0.58 at a training step of 60, dips to approximately 0.55 at a training step of 80, peaks at approximately 0.60 at a training step of 100, and then declines to approximately 0.59 at a training step of 140. * Step 0: ~0.47 * Step 20: ~0.60 * Step 40: ~0.52 * Step 60: ~0.58 * Step 80: ~0.55 * Step 100: ~0.60 * Step 120: ~0.56 * Step 140: ~0.59 ### Key Observations * Both models show an initial increase in validation score, followed by fluctuations. * MEL generally achieves a higher validation score than GRPO, especially in the early stages of training (up to step 60). * Both models appear to converge towards a similar validation score around training step 140. * The fluctuations suggest that the training process is not entirely smooth and may be sensitive to the training step. ### Interpretation The chart demonstrates the learning curves of two models (GRPO and MEL) during training on the AMC23 benchmark. The validation score serves as a metric for the model's generalization performance on unseen data. The initial increase in validation score indicates that both models are learning from the training data. The subsequent fluctuations suggest that the models are experiencing some degree of overfitting or are encountering challenges in generalizing to the validation set. The fact that MEL consistently outperforms GRPO suggests that MEL may be a more effective model for this particular benchmark. However, the convergence of the two models towards the end of the training process indicates that GRPO is also improving and may eventually achieve comparable performance. The fluctuations in validation score could be due to several factors, such as the stochastic nature of the training process, the choice of hyperparameters, or the complexity of the dataset. Further analysis would be needed to determine the root cause of these fluctuations and to optimize the training process for better performance. The data suggests that training beyond step 100 provides diminishing returns.

\n ## Line Chart: Benchmark: AMC23 ### Overview The image displays a line chart comparing the validation score performance of two methods, labeled "GRPO" and "MEL," over the course of training steps on the AMC23 benchmark. The chart tracks how the validation score for each method changes as training progresses. ### Components/Axes * **Chart Title:** "Benchmark: AMC23" (centered at the top). * **X-Axis:** Labeled "Training Step." The axis is linear and marked with major ticks at intervals of 20, from 0 to 140. Minor ticks are present at intervals of 10. * **Y-Axis:** Labeled "Validation Score." The axis is linear and marked with major ticks at intervals of 0.02, from 0.46 to 0.60. * **Legend:** Located in the top-right corner of the plot area. * A blue line with circle markers is labeled "GRPO". * A red line with triangle markers is labeled "MEL". * **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 series shows an initial sharp increase, followed by a period of fluctuation, and then stabilizes at a higher level towards the end of the tracked steps. * **Approximate Data Points (Training Step, Validation Score):** * (0, 0.46) * (10, 0.50) * (20, 0.58) * (30, 0.52) * (40, 0.52) * (50, 0.50) * (60, 0.58) * (70, 0.58) * (80, 0.58) * (90, 0.60) - **Peak Value** * (100, 0.56) * (110, 0.58) * (120, 0.58) * (130, 0.58) **Data Series: MEL (Red line, triangle markers)** * **Trend:** The MEL series exhibits a very rapid initial rise to a plateau, followed by a significant drop, a recovery, a second dip, and a final rise to match its earlier peak. * **Approximate Data Points (Training Step, Validation Score):** * (0, 0.46) * (10, 0.60) - **Reaches early plateau** * (20, 0.60) * (30, 0.60) * (40, 0.50) - **Significant drop** * (50, 0.58) * (60, 0.58) * (70, 0.55) * (80, 0.55) - **Second dip** * (90, 0.60) - **Matches early peak** * (100, 0.55) * (110, 0.55) * (120, 0.58) * (130, 0.60) - **Final value matches peak** ### Key Observations 1. **Initial Performance:** Both methods start at the same score (0.46). MEL achieves a much higher score (0.60) by step 10, while GRPO reaches 0.50. 2. **Volatility:** The MEL series shows greater volatility, with two distinct drops (at step 40 and steps 70-80/100-110) compared to GRPO's more moderate fluctuations. 3. **Peak Performance:** Both methods achieve a peak validation score of 0.60. GRPO hits this peak once at step 90. MEL hits this peak at steps 10-30, 90, and 130. 4. **Convergence:** By the final recorded step (130), both methods have converged to very similar scores: GRPO at 0.58 and MEL at 0.60. 5. **Relative Position:** The MEL line is generally above the GRPO line for the first 30 steps, falls below it between steps 40-50 and 70-80, and then intertwines with it for the remainder of the chart. ### Interpretation This chart suggests a comparative analysis of two training methodologies (GRPO and MEL) on the AMC23 benchmark. The data indicates that **MEL learns faster initially**, reaching near-peak performance within 10 steps, but this comes with **less stability**, as evidenced by its sharp performance drops. **GRPO demonstrates a more gradual and stable learning curve**, with its performance improving in a less erratic manner, though it takes longer to reach its peak. The fact that both methods ultimately achieve similar final scores (0.58 vs. 0.60) implies that for this specific benchmark, the choice between them may depend on other factors: if rapid initial convergence is critical, MEL might be preferred despite its instability. If consistent, stable improvement is valued, GRPO could be the better choice. The repeated drops in MEL's performance could indicate sensitivity to certain training phases or batches, warranting further investigation into the training dynamics of that method. The chart effectively communicates that while the endpoints are similar, the journey to get there differs significantly between the two approaches.

## Line Chart: Benchmark AMC23 Validation Scores ### Overview The image is a line chart comparing the validation scores of two methods, **GRPO** (blue) and **MEL** (red), across 140 training steps on the AMC23 benchmark. The y-axis represents validation scores (0.46–0.60), and the x-axis represents training steps (0–140). Both lines exhibit fluctuating trends with peaks and troughs, converging at later steps. --- ### Components/Axes - **X-axis (Training Step)**: Labeled "Training Step," ranging from 0 to 140 in increments of 20. - **Y-axis (Validation Score)**: Labeled "Validation Score," ranging from 0.46 to 0.60 in increments of 0.02. - **Legend**: Located in the **bottom-right corner**, with: - **Blue circles**: GRPO - **Red triangles**: MEL --- ### Detailed Analysis #### GRPO (Blue Line) - **Initial Phase (0–20 steps)**: Starts at ~0.46, rises sharply to ~0.58 by step 20. - **Mid-Phase (20–80 steps)**: Drops to ~0.52 at step 40, rises to ~0.58 at step 60, then dips to ~0.54 at step 80. - **Late Phase (80–140 steps)**: Peaks at ~0.60 at step 100, stabilizes around ~0.58 by step 140. #### MEL (Red Line) - **Initial Phase (0–20 steps)**: Starts at ~0.46, rises sharply to ~0.60 by step 20. - **Mid-Phase (20–80 steps)**: Drops to ~0.50 at step 40, rises to ~0.58 at step 60, dips to ~0.54 at step 80. - **Late Phase (80–140 steps)**: Peaks at ~0.60 at step 100, stabilizes around ~0.58 by step 140. --- ### Key Observations 1. **Initial Divergence**: Both methods start similarly but diverge sharply after step 20, with MEL achieving a higher peak (~0.60) earlier. 2. **Volatility**: GRPO exhibits more frequent fluctuations (e.g., step 40–60), while MEL has sharper drops (e.g., step 20–40). 3. **Convergence**: Both lines stabilize near ~0.58 by step 140, suggesting similar long-term performance. 4. **Outliers**: - GRPO’s peak at step 100 (~0.60) is the highest validation score. - MEL’s drop to ~0.50 at step 40 is the lowest point for either method. --- ### Interpretation The chart demonstrates that both GRPO and MEL improve validation scores over training steps, but with distinct patterns: - **GRPO** shows gradual, sustained improvement with moderate volatility, peaking at step 100. - **MEL** achieves higher early gains but experiences sharper declines, stabilizing later. - The convergence at step 140 implies that extended training mitigates initial disparities, though GRPO’s trajectory suggests better consistency in later stages. This analysis highlights trade-offs between early performance (MEL) and long-term stability (GRPO) in the AMC23 benchmark.