## Bar Charts: Reflection Frequency Before and After GRPO ### Overview The image contains two side-by-side bar charts comparing reflection frequency (%) across different numbers of blanks (9–54). The left chart shows data "Before GRPO," while the right chart shows data "After GRPO." Both charts use a red dashed vertical line at 54 blanks as a reference point. --- ### Components/Axes - **X-axis**: "number of blanks" (discrete values: 9, 18, 27, 36, 45, 54). - **Y-axis**: "reflection frequency (%)" (continuous scale from 0.0 to 1.0 in increments of 0.2). - **Legend**: No explicit legend, but the red dashed line at 54 blanks is consistent across both charts. - **Titles**: - Left chart: "Before GRPO" - Right chart: "After GRPO" --- ### Detailed Analysis #### Before GRPO - **Trend**: Reflection frequency remains consistently low (≤0.2%) across all blank counts. - **Values**: - 9 blanks: ~0.15% - 18 blanks: ~0.18% - 27 blanks: ~0.12% - 36 blanks: ~0.15% - 45 blanks: ~0.18% - 54 blanks: ~0.12% - **Red Dashed Line**: At 54 blanks, reflection frequency is ~0.12%. #### After GRPO - **Trend**: Reflection frequency increases monotonically with the number of blanks, reaching 100% at 54 blanks. - **Values**: - 9 blanks: ~0.70% - 18 blanks: ~0.75% - 27 blanks: ~0.80% - 36 blanks: ~0.85% - 45 blanks: ~0.95% - 54 blanks: ~1.00% - **Red Dashed Line**: At 54 blanks, reflection frequency is ~1.00%. --- ### Key Observations 1. **Before GRPO**: Reflection frequency is uniformly low (<0.2%), with minor fluctuations but no clear pattern. 2. **After GRPO**: Reflection frequency increases sharply with the number of blanks, achieving 100% at 54 blanks. 3. **Red Dashed Line**: Marks the threshold at 54 blanks, where the effect of GRPO becomes maximal (100% reflection frequency post-GRPO vs. ~0.12% pre-GRPO). --- ### Interpretation The data demonstrates that GRPO significantly enhances reflection frequency as the number of blanks increases. Pre-GRPO, reflection frequency remains negligible regardless of blank count, suggesting a lack of responsiveness. Post-GRPO, reflection frequency scales linearly with blanks, indicating a direct proportional relationship. The red dashed line at 54 blanks highlights a critical threshold where GRPO’s impact plateaus at 100%, implying that beyond this point, additional blanks do not further improve reflection frequency. This could reflect a saturation effect or a design constraint in the system being analyzed. The stark contrast between the two charts underscores GRPO’s transformative role in optimizing reflection efficiency.