## Scatter Plot: Reasoning Tokens vs. Problem Size for o3-mini ### Overview The image is a scatter plot comparing the number of reasoning tokens used by the o3-mini model against problem size, differentiated by success/failure outcomes. Two data series are represented: blue circles for successful runs and orange squares for failed runs. The plot spans problem sizes from 0 to 400 and reasoning tokens from 0 to 50,000. ### Components/Axes - **X-axis (Problem Size)**: Labeled "Problem Size," ranging from 0 to 400 in increments of 100. - **Y-axis (Reasoning Tokens)**: Labeled "Reasoning Tokens," ranging from 0 to 50,000 in increments of 10,000. - **Legend**: Located in the top-right corner, with: - **Blue circles**: "o3-mini (Successful)" - **Orange squares**: "o3-mini (Failed)" ### Detailed Analysis - **Blue Circles (Successful)**: - Clustered primarily in the lower-left quadrant. - Problem sizes range from ~0 to ~100. - Reasoning tokens range from ~0 to ~25,000. - Density decreases as problem size increases. - **Orange Squares (Failed)**: - Distributed across the entire plot but concentrated in the upper-right quadrant. - Problem sizes range from ~50 to ~400. - Reasoning tokens range from ~5,000 to ~50,000. - Notable outliers: A few orange squares at problem size ~100 with reasoning tokens ~50,000. ### Key Observations 1. **Successful Runs**: Dominated by smaller problem sizes (<100) and lower token usage (<25,000). 2. **Failed Runs**: More variable, with larger problem sizes (>200) and higher token usage (>10,000). 3. **Outliers**: A small subset of failed runs at problem size ~100 required ~50,000 tokens, suggesting inefficiency or edge cases. ### Interpretation The data suggests that successful reasoning by o3-mini is strongly correlated with smaller problem sizes and efficient token usage. Failed runs, however, exhibit a broader range of problem sizes and token consumption, indicating potential challenges with scalability or resource allocation. The outliers at problem size ~100 with high token usage may represent edge cases where the model struggles despite smaller inputs, possibly due to algorithmic complexity or data quality issues. This highlights a trade-off between problem size, computational resources, and success rates for the o3-mini model.