## Line Chart: Accuracy Reward vs. Global Step for Different GRPO Methods ### Overview The image is a line chart comparing the accuracy reward of three different Guided Reinforcement Policy Optimization (GRPO) methods: Vanilla GRPO, Naive Guided GRPO, and G²RPO-A, over a range of global steps. The chart displays how the accuracy reward changes with the global step for each method. ### Components/Axes * **X-axis:** Global step, with markers at intervals of 20, ranging from 0 to 140. * **Y-axis:** Accuracy reward, ranging from 0.0 to 0.5, with markers at intervals of 0.1. * **Legend (top-left):** * Vanilla GRPO (light blue line) * Naive Guided GRPO (light green line) * G²RPO-A (dark blue line) ### Detailed Analysis * **Vanilla GRPO (light blue line):** * Trend: Initially increases slowly, plateaus around 0.2 between steps 40 and 80, then increases to approximately 0.25 around step 100, and decreases to approximately 0.05 at step 140. * Data Points: Starts at approximately 0.07 at step 0, reaches approximately 0.25 at step 100, and ends at approximately 0.05 at step 140. * **Naive Guided GRPO (light green line):** * Trend: Starts low, increases to a peak around step 60, dips slightly, then rises to a higher peak around step 100, and decreases to approximately 0.0 at step 140. * Data Points: Starts at approximately 0.1 at step 0, reaches approximately 0.37 at step 60, peaks at approximately 0.5 at step 100, and ends at approximately 0.0 at step 140. * **G²RPO-A (dark blue line):** * Trend: Starts low, increases to a peak around step 60, dips slightly, then rises to a higher peak around step 100, and decreases to approximately 0.05 at step 140. * Data Points: Starts at approximately 0.11 at step 0, reaches approximately 0.38 at step 60, peaks at approximately 0.42 at step 100, and ends at approximately 0.05 at step 140. ### Key Observations * The Naive Guided GRPO and G²RPO-A methods generally outperform Vanilla GRPO in terms of accuracy reward. * All three methods experience a significant drop in accuracy reward towards the end of the global step range. * The Naive Guided GRPO method achieves the highest peak accuracy reward around step 100. * The G²RPO-A method has a more stable performance compared to the Naive Guided GRPO method, especially in the initial steps. ### Interpretation The chart suggests that both Naive Guided GRPO and G²RPO-A are more effective than Vanilla GRPO in achieving higher accuracy rewards, particularly during the middle stages of the global step range. The eventual decline in accuracy reward for all methods indicates a potential limitation or instability in the learning process as the global step increases. The G²RPO-A method's relatively stable performance in the initial steps might indicate a more robust learning process compared to the Naive Guided GRPO method. The data implies that guiding the reinforcement policy optimization can lead to better performance, but further investigation is needed to understand the cause of the eventual decline in accuracy reward.

\n ## Line Chart: Accuracy Reward vs. Global Step ### Overview This image presents a line chart comparing the accuracy reward of three different algorithms – Vanilla GRPO, Naive Guided GRPO, and G²RPO-A – over a series of global steps. The chart visualizes the performance of each algorithm as it progresses, allowing for a comparison of their learning curves. ### Components/Axes * **X-axis:** "Global step" ranging from 0 to 140, with tick marks at intervals of 20. * **Y-axis:** "Accuracy reward" ranging from 0.0 to 0.5, with tick marks at intervals of 0.1. * **Legend:** Located in the top-left corner, identifying the three data series: * Vanilla GRPO (Light Blue) * Naive Guided GRPO (Green) * G²RPO-A (Dark Blue) ### Detailed Analysis The chart displays three lines representing the accuracy reward for each algorithm over the global steps. * **Vanilla GRPO (Light Blue):** The line starts at approximately 0.08 at step 0. It generally slopes upward, reaching a peak of around 0.36 at step 90. After step 90, the line declines, ending at approximately 0.05 at step 140. There are some fluctuations, with a dip around step 40 to approximately 0.16. * **Naive Guided GRPO (Green):** This line begins at approximately 0.11 at step 0. It exhibits a more pronounced upward trend than Vanilla GRPO, peaking at around 0.42 at step 100. Following the peak, the line declines sharply, reaching approximately 0.03 at step 140. * **G²RPO-A (Dark Blue):** The line starts at approximately 0.09 at step 0. It shows a steady increase, reaching a peak of around 0.38 at step 60, then fluctuates between 0.30 and 0.40 until step 100. After step 100, the line declines, ending at approximately 0.10 at step 140. ### Key Observations * Naive Guided GRPO consistently outperforms Vanilla GRPO and G²RPO-A for the majority of the global steps, achieving the highest accuracy reward. * All three algorithms exhibit a similar trend: an initial increase in accuracy reward followed by a decline after reaching a peak. * The decline in accuracy reward is most pronounced for Naive Guided GRPO, suggesting potential overfitting or instability. * G²RPO-A demonstrates a more stable performance compared to the other two algorithms, with less fluctuation after the initial increase. ### Interpretation The data suggests that Naive Guided GRPO is the most effective algorithm for improving accuracy reward in the initial stages of training. However, its performance deteriorates significantly after reaching a peak, indicating a potential issue with generalization or long-term stability. Vanilla GRPO and G²RPO-A exhibit more moderate performance, with G²RPO-A showing greater stability. The decline in accuracy reward for all algorithms after a certain point could be attributed to factors such as diminishing returns, overfitting, or the exploration of less rewarding states. The chart highlights the trade-off between initial performance and long-term stability in these algorithms. Further investigation is needed to understand the reasons behind the decline in accuracy reward and to explore strategies for improving the generalization capabilities of Naive Guided GRPO.

## Line Chart: Accuracy Reward vs. Global Step for Three GRPO Variants ### Overview The image is a line chart comparing the performance of three different methods—Vanilla GRPO, Naive Guided GRPO, and G²RPO-A—over the course of training. The performance metric is "Accuracy reward," plotted against "Global step," which likely represents training iterations or time. The chart shows that all three methods follow a similar general trend of increasing reward, peaking around step 100, and then declining sharply, but with distinct differences in their peak values and volatility. ### Components/Axes * **Chart Type:** Line chart with three data series. * **X-Axis:** * **Title:** "Global step" * **Scale:** Linear, ranging from 0 to 140. * **Major Tick Marks:** 0, 20, 40, 60, 80, 100, 120, 140. * **Y-Axis:** * **Title:** "Accuracy reward" * **Scale:** Linear, ranging from 0.0 to 0.5. * **Major Tick Marks:** 0.0, 0.1, 0.2, 0.3, 0.4, 0.5. * **Legend:** * **Position:** Top-left corner of the chart area. * **Entries:** 1. **Vanilla GRPO:** Represented by a light blue line. 2. **Naive Guided GRPO:** Represented by a green line. 3. **G²RPO-A:** Represented by a dark blue line. ### Detailed Analysis **Trend Verification & Data Point Extraction (Approximate Values):** | Method | Step 0 | Step 40 | Step 60 | Step 80 | Step 100 (Global Peak) | Step 120 | Step 140 | | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | | **Vanilla GRPO** | ~0.07 | ~0.13 | ~0.25 (Local Peak) | ~0.22 | ~0.40 | ~0.23 | ~0.04 | | **Naive Guided GRPO** | ~0.10 | ~0.10 (Trough) | ~0.38 (Local Peak) | ~0.22 (Trough) | ~0.48 (Highest value) | ~0.26 | ~0.01 (Lowest final) | | **G²RPO-A** | ~0.10 | ~0.16 | ~0.34 | ~0.35 | ~0.42 | ~0.25 | ~0.09 (Highest final) | **Trend Descriptions:** 1. **Vanilla GRPO (Light Blue Line):** * **Trend:** Starts lowest, shows a gradual, relatively smooth increase with minor fluctuations, reaches a moderate peak, and then declines steeply. 2. **Naive Guided GRPO (Green Line):** * **Trend:** Starts in the middle, exhibits the most volatility with pronounced peaks and troughs, achieves the highest overall peak, and then experiences the most severe decline. 3. **G²RPO-A (Dark Blue Line):** * **Trend:** Starts slightly above Vanilla GRPO, shows a steadier and more consistent upward trend with less volatility than Naive Guided GRPO, peaks at a value between the other two, and maintains a higher reward than the others during the final decline. ### Key Observations 1. **Common Trajectory:** All three methods follow a macro pattern of rise, peak, and fall. The peak for all occurs around Global Step 100. 2. **Performance Hierarchy at Peak:** At the peak (~Step 100), Naive Guided GRPO > G²RPO-A > Vanilla GRPO. 3. **Volatility:** Naive Guided GRPO is the most volatile, with the largest swings between local maxima and minima. Vanilla GRPO is the smoothest. 4. **Final Performance:** After the peak, all methods degrade. However, G²RPO-A degrades the slowest, ending with the highest reward at Step 140. Naive Guided GRPO degrades the fastest, ending near zero. 5. **Early Training:** In the first 40 steps, G²RPO-A establishes a clear lead over Vanilla GRPO, while Naive Guided GRPO lags initially before catching up. ### Interpretation This chart likely visualizes the training dynamics of different reinforcement learning or optimization algorithms (variants of "GRPO") on a task where performance is measured by an accuracy-based reward signal. * **What the data suggests:** The "guided" variants (Naive Guided and G²RPO-A) generally outperform the "Vanilla" baseline, indicating that incorporating guidance improves learning efficiency and peak performance. However, the guidance in "Naive Guided GRPO" appears to introduce instability, leading to higher peaks but also more severe crashes, possibly due to overfitting or aggressive policy updates. G²RPO-A seems to strike a better balance, achieving strong performance with more stability, as evidenced by its smoother curve and better final retention of reward. * **The Decline Phase:** The sharp, synchronized decline after Step 100 is a critical feature. This could indicate several scenarios: 1) The training task becomes progressively harder after this point, 2) The learning rate or another hyperparameter causes divergence, 3) The agents have overfitted to a certain phase of the environment and fail to generalize, or 4) This is an intentional part of the experimental design (e.g., a curriculum that resets or changes). The fact that G²RPO-A retains more reward suggests it may be more robust to whatever causes this decline. * **Peircean Reading:** The chart is an indexical sign of the learning process. The jaggedness of the green line is a direct trace of a more reactive, less stable learning policy. The synchronized peak and fall across all three lines point to a common external factor (the environment or training protocol) exerting a strong influence, over and above the differences between the algorithms themselves. The key takeaway for a researcher is not just that G²RPO-A has a good peak, but that its performance profile suggests a more robust and reliable learning trajectory.

## Line Graph: Accuracy Reward vs. Global Step ### Overview The image is a line graph comparing the accuracy reward of three reinforcement learning methods (Vanilla GRPO, Naive Guided GRPO, and G²RPO-A) across 140 global steps. The y-axis represents accuracy reward (0.0–0.5), and the x-axis represents global steps (0–140). Three colored lines (blue, green, purple) correspond to the methods in the legend. ### Components/Axes - **X-axis (Global Step)**: Labeled "Global step," with ticks at 0, 20, 40, 60, 80, 100, 120, 140. - **Y-axis (Accuracy Reward)**: Labeled "Accuracy reward," with ticks at 0.0, 0.1, 0.2, 0.3, 0.4, 0.5. - **Legend**: Located at the top, with: - **Blue**: Vanilla GRPO - **Green**: Naive Guided GRPO - **Purple**: G²RPO-A ### Detailed Analysis 1. **Vanilla GRPO (Blue)**: - Starts at ~0.05 accuracy reward at step 0. - Gradually increases to a peak of ~0.35 at step 100. - Declines sharply to ~0.1 by step 140. - Shows moderate fluctuations (e.g., minor dips at steps 40–60). 2. **Naive Guided GRPO (Green)**: - Begins at ~0.1 at step 0. - Rises to a peak of ~0.45 at step 100. - Drops sharply to ~0.05 by step 140. - Exhibits volatility (e.g., oscillations between 0.2–0.3 at steps 40–80). 3. **G²RPO-A (Purple)**: - Starts at ~0.1 at step 0. - Increases steadily to ~0.4 at step 100. - Declines gradually to ~0.15 by step 140. - Smoother trajectory with fewer fluctuations compared to others. ### Key Observations - All three methods peak near step 100, but G²RPO-A maintains higher accuracy post-peak. - Naive Guided GRPO has the highest peak (~0.45) but the steepest decline. - Vanilla GRPO shows the most gradual rise and fall, with intermediate performance. - No data points fall below 0.0 or exceed 0.5. ### Interpretation The graph suggests that **G²RPO-A** outperforms the other methods in maintaining accuracy over time, particularly after the global step 100. The Naive Guided GRPO achieves the highest peak accuracy but suffers from instability, leading to a rapid decline. Vanilla GRPO demonstrates moderate performance with fewer fluctuations. The sharp drop in Naive Guided GRPO after step 100 may indicate overfitting or sensitivity to hyperparameters. The trends imply that G²RPO-A balances exploration and exploitation more effectively, making it robust for longer training durations.