## Line Chart: Accuracy vs. Step for Different Models ### Overview The image is a line chart comparing the accuracy of three different models (RLVR, RLME, and RLME-NoCheat) over a series of steps. The x-axis represents the step number, and the y-axis represents the accuracy, ranging from 0 to 1. The chart displays the performance of each model as a line, allowing for a visual comparison of their learning curves. ### Components/Axes * **X-axis:** "Step", ranging from 0 to 150 in increments of 50. * **Y-axis:** "Accuracy", ranging from 0 to 1 in increments of 0.2. * **Legend:** Located in the top-left corner of the chart. * **RLVR:** Represented by a gray dotted line. * **RLME:** Represented by a solid blue line. * **RLME-NoCheat:** Represented by a dashed green line. ### Detailed Analysis * **RLVR (Gray Dotted Line):** * Starts at approximately 0.12 accuracy at step 0. * Increases to approximately 0.32 accuracy around step 30. * Gradually decreases to approximately 0.02 accuracy by step 150. * Trend: Initially increases, then steadily declines. * **RLME (Solid Blue Line):** * Starts at approximately 0.13 accuracy at step 0. * Increases to approximately 0.40 accuracy around step 30. * Decreases to approximately 0.03 accuracy by step 150. * Trend: Initially increases, then steadily declines. * **RLME-NoCheat (Dashed Green Line):** * Starts at approximately 0.30 accuracy at step 0. * Increases to approximately 0.45 accuracy around step 30. * Experiences a sharp increase in accuracy around step 80. * Fluctuates between approximately 0.70 and 0.90 accuracy from step 100 to step 160. * Trend: Initially increases, then shows a significant and sustained increase. ### Key Observations * RLME-NoCheat consistently outperforms RLVR and RLME after approximately step 80. * RLVR and RLME show a similar trend of initial increase followed by a decline in accuracy. * RLME-NoCheat exhibits a significant jump in accuracy around step 80, suggesting a change in learning dynamics. ### Interpretation The chart illustrates the learning performance of three different models. RLME-NoCheat demonstrates a clear advantage, achieving significantly higher accuracy compared to RLVR and RLME, especially after a certain number of steps. The decline in accuracy for RLVR and RLME suggests that these models may be overfitting or failing to generalize effectively as the number of steps increases. The "NoCheat" aspect of RLME-NoCheat likely contributes to its superior performance, possibly by preventing the model from exploiting unintended shortcuts or biases in the training data. The jump in accuracy around step 80 for RLME-NoCheat could indicate a critical point in its learning process, where it begins to leverage learned features more effectively.

## Line Chart: Accuracy vs. Step for RLVR, RLME, and RLME-NoCheat ### Overview This chart illustrates the performance, measured as "Accuracy," of three distinct reinforcement learning methods—RLVR, RLME, and RLME-NoCheat—across a training duration of approximately 160 steps. The chart demonstrates a clear divergence in performance between the "NoCheat" variant and the other two methods. ### Components/Axes * **Y-Axis:** Labeled "Accuracy," representing a normalized scale from 0 to 1.0. * **X-Axis:** Labeled "Step," representing the training progression from 0 to 160. * **Legend:** Positioned in the top-left quadrant of the chart area. * **RLVR:** Represented by a grey dotted line. * **RLME:** Represented by a solid blue line. * **RLME-NoCheat:** Represented by a dashed green line. ### Detailed Analysis The chart displays three distinct data series plotted against the axes: 1. **RLVR (Grey Dotted Line):** * **Trend:** Starts at ~0.15, rises to a peak of ~0.3 at step 25, then exhibits a steady, consistent decline. * **Values:** By step 75, accuracy drops to ~0.1. By step 120, it approaches 0.0, with a minor, transient spike to ~0.05 at step 130 before returning to near 0.0 by step 160. 2. **RLME (Solid Blue Line):** * **Trend:** Starts at ~0.15, rises to a peak of ~0.4 at step 25 (the highest initial peak of the three). Following this peak, it trends downward with significant volatility. * **Values:** It exhibits a sharp drop-off, with notable, jagged spikes at step 90 (~0.15) and step 125 (~0.05). It trends toward 0.0 by step 160. 3. **RLME-NoCheat (Dashed Green Line):** * **Trend:** Starts at ~0.3, dips slightly to ~0.25 at step 15, and then initiates a strong, sustained upward trend. * **Values:** It crosses the 0.4 threshold at step 50, the 0.6 threshold at step 90, and the 0.8 threshold at step 130. It finishes at approximately 0.85 at step 160. ### Key Observations * **Early Convergence:** All three methods show similar performance characteristics between steps 0 and 30, with RLME and RLVR peaking around step 25. * **Divergence:** After step 30, the RLME-NoCheat method diverges significantly from the other two, showing a positive slope, while RLVR and RLME show negative slopes. * **Failure Modes:** Both RLVR and RLME appear to fail to converge or maintain accuracy, trending toward zero as the step count increases. * **Volatility:** The RLME (solid blue) line is the most volatile, showing frequent, sharp fluctuations compared to the smoother decline of the RLVR (grey dotted) line. ### Interpretation The data suggests that the "NoCheat" variant is the only successful approach among the three tested. The naming convention "NoCheat" implies that the other two methods (RLVR and RLME) may be relying on "cheating"—likely utilizing privileged information or shortcuts during training that do not generalize to the task, leading to eventual performance collapse. The fact that RLVR and RLME peak early and then decline suggests they may be overfitting to initial conditions or failing to learn a robust policy. Conversely, the RLME-NoCheat method demonstrates a successful learning curve, indicating that removing the "cheating" mechanism allows the agent to learn the underlying task effectively, resulting in high accuracy by the end of the training period.

## Line Graph: Model Accuracy Over Training Steps ### Overview The graph depicts the accuracy of three reinforcement learning models (RLVR, RLME, RLME-NoCheat) across 150 training steps. Accuracy is measured on a scale from 0 to 1, with distinct trends observed for each model. ### Components/Axes - **X-axis (Step)**: Labeled "Step," with markers at 0, 50, 100, and 150. - **Y-axis (Accuracy)**: Labeled "Accuracy," scaled from 0 to 1 in increments of 0.2. - **Legend**: Located in the top-left corner, associating: - **RLVR**: Dotted gray line - **RLME**: Solid blue line - **RLME-NoCheat**: Dashed green line ### Detailed Analysis 1. **RLVR (Dotted Gray Line)**: - Starts at ~0.2 accuracy at step 0. - Peaks at ~0.35 around step 25. - Declines sharply to near 0 by step 150. - Intermediate fluctuations observed between steps 50–100 (~0.1–0.2). 2. **RLME (Solid Blue Line)**: - Begins at ~0.15 accuracy at step 0. - Rises to ~0.4 around step 25. - Gradual decline to ~0.1 by step 150. - Notable volatility between steps 50–100 (~0.2–0.3). 3. **RLME-NoCheat (Dashed Green Line)**: - Starts at ~0.2 accuracy at step 0. - Steady upward trend, reaching ~0.8 by step 150. - Minor fluctuations observed (e.g., ~0.75 at step 100, ~0.85 at step 125). ### Key Observations - **RLME-NoCheat** consistently outperforms other models, maintaining high accuracy throughout training. - **RLVR** and **RLME** exhibit early promise but degrade significantly over time, suggesting instability or overfitting. - **RLME-NoCheat** shows resilience to training noise, with no sharp drops in accuracy. ### Interpretation The data suggests that the "NoCheat" variant of RLME (RLME-NoCheat) is more robust and effective for this task, likely due to architectural or training modifications that mitigate overfitting. In contrast, RLVR and RLME degrade as training progresses, indicating potential issues with generalization or reward hacking. The steady rise of RLME-NoCheat implies it balances exploration and exploitation effectively, making it a preferable choice for long-term training scenarios.