## Line Chart: MATH500 Accuracy vs. Training Steps ### Overview The image is a line chart comparing the MATH500 accuracy of three different methods (GRPO, REC-OneSide-NoIS (0.2), and RED-Weight) over training steps. The chart shows the performance of each method as the training progresses, with the x-axis representing training steps and the y-axis representing MATH500 accuracy. The parameter "sync_interval" is set to 20. ### Components/Axes * **Title:** sync\_interval = 20 * **X-axis:** Training Steps (values ranging from 0 to 400) * **Y-axis:** MATH500 Accuracy (values ranging from 0.40 to 0.50) * **Legend:** Located in the center of the chart. * GRPO (light green) * REC-OneSide-NoIS (0.2) (light purple) * RED-Weight (light orange) ### Detailed Analysis * **GRPO (light green):** The line starts at approximately 0.43 accuracy at 0 training steps. It initially decreases slightly, then increases steadily to approximately 0.51 accuracy at 400 training steps. * **REC-OneSide-NoIS (0.2) (light purple):** The line starts at approximately 0.43 accuracy at 0 training steps. It increases to approximately 0.50 accuracy at 200 training steps, then fluctuates slightly before reaching approximately 0.51 accuracy at 400 training steps. * **RED-Weight (light orange):** The line starts at approximately 0.43 accuracy at 0 training steps. It increases sharply to approximately 0.49 accuracy at 50 training steps, then fluctuates before reaching approximately 0.50 accuracy at 400 training steps. ### Key Observations * All three methods show an increasing trend in MATH500 accuracy as training steps increase. * RED-Weight shows the most rapid initial increase in accuracy. * GRPO has a more gradual and consistent increase in accuracy compared to the other two methods. * At 400 training steps, all three methods converge to approximately the same accuracy level (around 0.51). ### Interpretation The chart demonstrates the performance of three different methods for improving MATH500 accuracy during training. The RED-Weight method initially shows a faster improvement, but all three methods eventually achieve similar accuracy levels after a sufficient number of training steps. The choice of method may depend on the desired speed of initial improvement versus the consistency of the improvement over time. The "sync_interval" parameter being set to 20 suggests that the model parameters are synchronized every 20 training steps, which could influence the learning dynamics of each method.

\n ## Line Chart: MATH500 Accuracy vs. Training Steps ### Overview This line chart depicts the MATH500 accuracy of three different models (GRPO, REC-OneSide-NoIS (0.2), and RED-Weight) as a function of training steps. The chart is labeled with a `sync_interval = 20`. ### Components/Axes * **X-axis:** Training Steps (ranging from 0 to 500, with markers at 0, 200, and 400) * **Y-axis:** MATH500 Accuracy (ranging from 0.40 to 0.52, with markers at 0.40, 0.45, 0.50) * **Legend:** Located in the bottom-left corner. * GRPO (Light Green Line) * REC-OneSide-NoIS (0.2) (Purple Line) * RED-Weight (Orange Line) ### Detailed Analysis * **GRPO (Light Green Line):** The line starts at approximately 0.43 at 0 training steps. It increases to around 0.48 at 200 training steps, then decreases to approximately 0.47 at 400 training steps, and finally reaches around 0.50 at 500 training steps. * **REC-OneSide-NoIS (0.2) (Purple Line):** The line begins at approximately 0.40 at 0 training steps. It rises steadily to around 0.47 at 200 training steps, continues to increase to approximately 0.51 at 400 training steps, and then slightly decreases to around 0.50 at 500 training steps. * **RED-Weight (Orange Line):** The line starts at approximately 0.48 at 0 training steps. It initially decreases to around 0.47 at 100 training steps, then increases to approximately 0.51 at 300 training steps, decreases to around 0.49 at 400 training steps, and finally reaches approximately 0.51 at 500 training steps. ### Key Observations * All three models show an increasing trend in MATH500 accuracy as training steps increase. * The REC-OneSide-NoIS (0.2) model appears to achieve the highest accuracy at 400 training steps, reaching approximately 0.51. * The RED-Weight model starts with the highest accuracy at 0 training steps, but its performance fluctuates more than the other two models. * The GRPO model has the slowest initial increase in accuracy. ### Interpretation The chart demonstrates the learning progress of three different models on the MATH500 dataset. The `sync_interval = 20` suggests that model parameters are synchronized every 20 training steps, which could influence the observed performance. The REC-OneSide-NoIS (0.2) model appears to be the most effective in this experiment, achieving the highest accuracy after 400 training steps. The fluctuations in the RED-Weight model's performance might indicate sensitivity to the training process or a need for parameter tuning. The overall upward trend for all models suggests that continued training could lead to further improvements in accuracy. The data suggests that the models are converging, but further training might be needed to reach a plateau in performance. The initial difference in starting accuracy between the models could be due to different initialization strategies or pre-training.

\n ## Line Chart: Training Steps vs. MATH500 Accuracy (sync_interval = 20) ### Overview The image is a line chart comparing the performance of three different training methods or algorithms over the course of training steps. The performance metric is accuracy on the MATH500 benchmark. The chart title indicates a specific experimental parameter: `sync_interval = 20`. ### Components/Axes * **Chart Title:** `sync_interval = 20` (centered at the top). * **Y-Axis:** * **Label:** `MATH500 Accuracy` (vertical text on the left). * **Scale:** Linear scale from 0.40 to 0.50, with major tick marks at 0.40, 0.45, and 0.50. * **X-Axis:** * **Label:** `Training Steps` (horizontal text at the bottom). * **Scale:** Linear scale from 0 to approximately 450, with major tick marks labeled at 0, 200, and 400. * **Legend:** Located in the bottom-right quadrant of the chart area. It contains three entries, each with a colored line sample and a text label: 1. **Blue Line:** `GRPO` 2. **Purple Line:** `REC-OneSide-NoIS (0.2)` 3. **Orange Line:** `RED-Weight` ### Detailed Analysis The chart plots three data series, each showing the trajectory of MATH500 accuracy as training progresses. 1. **GRPO (Blue Line):** * **Trend:** Starts at a moderate accuracy, experiences a slight initial dip, then shows a steady, consistent upward trend throughout the training steps. * **Approximate Data Points:** * Step 0: ~0.43 * Step ~50: ~0.42 (slight dip) * Step ~150: ~0.44 * Step ~250: ~0.46 * Step ~350: ~0.48 * Step ~450: ~0.50 2. **REC-OneSide-NoIS (0.2) (Purple Line):** * **Trend:** Begins at a higher accuracy than the other two methods. It shows a strong, relatively smooth upward trend, maintaining the highest accuracy for most of the training duration before being closely matched by GRPO at the end. * **Approximate Data Points:** * Step 0: ~0.45 * Step ~100: ~0.47 * Step ~200: ~0.48 * Step ~300: ~0.50 * Step ~400: ~0.51 (peak) * Step ~450: ~0.50 3. **RED-Weight (Orange Line):** * **Trend:** Starts at the lowest accuracy but exhibits the most rapid initial improvement, jumping significantly within the first ~50 steps. After this initial surge, its performance plateaus and fluctuates within a narrow band (approximately 0.48 to 0.49), showing less continued improvement compared to the other two methods. * **Approximate Data Points:** * Step 0: ~0.40 * Step ~50: ~0.48 (sharp increase) * Step ~150: ~0.485 * Step ~250: ~0.48 * Step ~350: ~0.49 * Step ~450: ~0.485 ### Key Observations * **Initial Performance Hierarchy:** At step 0, the order from highest to lowest accuracy is: REC-OneSide-NoIS (0.2) > GRPO > RED-Weight. * **Learning Dynamics:** RED-Weight learns fastest initially but saturates quickly. GRPO learns more slowly but steadily. REC-OneSide-NoIS (0.2) starts strong and maintains a consistent learning rate. * **Convergence:** By the end of the plotted training steps (~450), the performance of GRPO and REC-OneSide-NoIS (0.2) converges to a very similar level (~0.50), while RED-Weight remains slightly below them. * **Volatility:** The RED-Weight line shows more minor fluctuations (ups and downs) after its initial rise compared to the smoother trajectories of the other two methods. ### Interpretation This chart demonstrates the comparative learning efficiency and final performance of three algorithms on the MATH500 task under a specific synchronization setting (`sync_interval = 20`). * **REC-OneSide-NoIS (0.2)** appears to be the most robust method, offering both a strong starting point (possibly due to better initialization or a more effective early-stage update rule) and sustained improvement. Its final performance is among the best. * **GRPO** shows a classic, steady learning curve. While it starts slower, its consistent improvement suggests it is a reliable method that continues to benefit from extended training, ultimately matching the top performer. * **RED-Weight** is characterized by extremely rapid early gains, which could be advantageous if training compute is severely limited. However, its early plateau indicates it may get stuck in a local optimum or lack the mechanisms for fine-grained later-stage improvement that the other methods possess. The key takeaway is that the choice of method involves a trade-off: **RED-Weight** for fast, early results, **GRPO** for steady, predictable improvement, and **REC-OneSide-NoIS (0.2)** for strong performance throughout. The `sync_interval` parameter is a critical experimental condition, and these relative performances might change under different synchronization settings.

## Line Chart: Algorithm Performance on MATH500 Accuracy (sync_interval = 20) ### Overview The chart compares the training performance of three algorithms (GRPO, REC-OneSide-NoIS (0.2), and RED-Weight) on the MATH500 accuracy metric over 400 training steps. The y-axis represents accuracy (0.40–0.50), and the x-axis represents training steps (0–400). All lines converge near 0.50 accuracy by the final step, but exhibit distinct trajectories. ### Components/Axes - **X-axis (Training Steps)**: Labeled "Training Steps," with markers at 0, 200, and 400. - **Y-axis (MATH500 Accuracy)**: Labeled "MATH500 Accuracy," scaled from 0.40 to 0.50 in 0.05 increments. - **Legend**: Located in the bottom-right corner, with three entries: - **GRPO**: Green line. - **REC-OneSide-NoIS (0.2)**: Purple line. - **RED-Weight**: Orange line. - **Title**: "sync_interval = 20" is displayed at the top. ### Detailed Analysis 1. **GRPO (Green Line)**: - Starts at ~0.40 accuracy at 0 steps. - Sharp upward trend to ~0.45 accuracy by 200 steps. - Plateaus at ~0.45 accuracy for the remainder of training (200–400 steps). 2. **REC-OneSide-NoIS (0.2) (Purple Line)**: - Begins at ~0.40 accuracy at 0 steps. - Gradual upward trend, reaching ~0.45 accuracy at 200 steps. - Continues rising to ~0.50 accuracy by 400 steps. 3. **RED-Weight (Orange Line)**: - Starts at ~0.45 accuracy at 0 steps. - Dips to ~0.43 accuracy at 200 steps. - Recovers to ~0.50 accuracy by 400 steps, with minor fluctuations. ### Key Observations - **GRPO** shows the fastest initial improvement but plateaus earlier than the other algorithms. - **REC-OneSide-NoIS (0.2)** demonstrates steady, consistent growth, achieving the highest final accuracy (~0.50). - **RED-Weight** exhibits volatility, with a notable dip at 200 steps before recovering to match the final accuracy of REC-OneSide-NoIS. - All algorithms converge near 0.50 accuracy by 400 steps, but REC-OneSide-NoIS (0.2) maintains the most stable upward trajectory. ### Interpretation The chart suggests that **REC-OneSide-NoIS (0.2)** is the most effective algorithm for this task, as it achieves the highest final accuracy with minimal volatility. **GRPO** performs well initially but stagnates, while **RED-Weight**'s fluctuations indicate potential instability in its training process. The "sync_interval = 20" parameter may influence these dynamics, though its exact role is not explained in the chart. The convergence at ~0.50 accuracy implies that all algorithms reach a similar ceiling, but REC-OneSide-NoIS (0.2) does so more efficiently.