## Histogram: Reward Score Distribution Comparison ### Overview The image displays a comparative histogram showing the distribution of reward scores for two AI models: Deepseek-R1 (blue) and Gemini Flash Thinking (orange). The x-axis represents reward scores (0.0–1.0), and the y-axis represents density (0–4). The distributions overlap between 0.4–0.6, with distinct peaks in separate regions. ### Components/Axes - **X-axis (Reward Score)**: Labeled "Reward Score," scaled from 0.0 to 1.0 in increments of 0.2. - **Y-axis (Density)**: Labeled "Density," scaled from 0 to 4 in increments of 1. - **Legend**: Located in the top-left corner, with: - Blue: Deepseek-R1 - Orange: Gemini Flash Thinking ### Detailed Analysis 1. **Deepseek-R1 (Blue)**: - **Peak Density**: ~3.5 at reward score ~0.75. - **Spread**: Distinct bimodal distribution with secondary peaks near 0.6 and 0.85. - **Tail Behavior**: Extends to ~0.95 with low-density tails. - **Overlap Region**: Minimal overlap with Gemini Flash Thinking (0.4–0.6), where density drops to ~0.5. 2. **Gemini Flash Thinking (Orange)**: - **Peak Density**: ~2.5 at reward score ~0.3. - **Spread**: Unimodal distribution with a sharp decline after 0.4. - **Tail Behavior**: Tapers off sharply below 0.5, with negligible density beyond 0.6. - **Overlap Region**: Overlaps with Deepseek-R1 in 0.4–0.6, but with much lower combined density (~1.0). ### Key Observations - **Distinct Peaks**: Deepseek-R1 dominates higher reward scores (0.6–0.9), while Gemini Flash Thinking concentrates in lower scores (0.0–0.4). - **Overlap Region**: Both models show weak performance between 0.4–0.6, but Deepseek-R1 maintains higher density here. - **Tail Differences**: Deepseek-R1 exhibits a long right tail (up to 0.95), suggesting occasional high-reward outliers, whereas Gemini Flash Thinking has no significant tail beyond 0.6. ### Interpretation The data suggests **Deepseek-R1 consistently outperforms Gemini Flash Thinking in reward scores**, with a clear dominance in the 0.6–0.9 range. The overlap region (0.4–0.6) indicates a narrow band of comparable performance, but Gemini Flash Thinking lacks the capacity to achieve the highest rewards. The sharp decline in Gemini’s distribution after 0.4 implies a fundamental limitation in reaching higher reward thresholds, while Deepseek-R1’s bimodal structure hints at specialized capabilities for high-reward scenarios. This could reflect architectural differences, training data, or optimization strategies between the models.