## Line Graphs: Model Accuracy vs. Recursion Depth
### Overview
The image contains three line graphs comparing the accuracy of three AI models (o4-mini, Goedel-Prover-SFT, Kimina-Prover-Preview-Distill-7B) across varying recursion depths. Each graph uses a distinct color-coded line with markers to represent performance trends.
### Components/Axes
- **X-axis**: "Recursion Depth" (integer values from 0 to 4 or 6, depending on the model).
- **Y-axis**: "Accuracy (%)" (ranging from ~58% to 75%).
- **Legends**:
- **Blue line with circles**: o4-mini.
- **Red line with triangles**: Goedel-Prover-SFT.
- **Purple line with squares**: Kimina-Prover-Preview-Distill-7B.
- **Gridlines**: Present for all graphs to aid in value estimation.
### Detailed Analysis
#### o4-mini (Blue Line)
- **Trend**: Steep initial increase followed by plateau.
- **Data Points**:
- Depth 0: ~7% accuracy.
- Depth 1: ~35% accuracy.
- Depth 2: ~40% accuracy.
- Depth 3: ~43% accuracy.
- Depth 4: ~45% accuracy.
#### Goedel-Prover-SFT (Red Line)
- **Trend**: Gradual, near-linear improvement with slight deceleration.
- **Data Points**:
- Depth 0: ~58% accuracy.
- Depth 1: ~60% accuracy.
- Depth 2: ~63% accuracy.
- Depth 3: ~64% accuracy.
- Depth 4: ~65% accuracy.
- Depth 5: ~65% accuracy.
- Depth 6: ~65% accuracy.
#### Kimina-Prover-Preview-Distill-7B (Purple Line)
- **Trend**: Steady increase with plateau after depth 3.
- **Data Points**:
- Depth 0: ~68% accuracy.
- Depth 1: ~70% accuracy.
- Depth 2: ~72% accuracy.
- Depth 3: ~74% accuracy.
- Depth 4: ~75% accuracy.
- Depth 5: ~75% accuracy.
- Depth 6: ~75% accuracy.
### Key Observations
1. **o4-mini** shows the most dramatic early improvement but plateaus sharply after depth 1.
2. **Goedel-Prover-SFT** demonstrates consistent, incremental gains but reaches a ceiling at ~65% accuracy.
3. **Kimina-Prover-Preview-Distill-7B** achieves the highest peak accuracy (~75%) but requires deeper recursion to plateau.
### Interpretation
The data suggests that recursion depth significantly impacts model performance, with all models improving as depth increases. However, the rate and ceiling of improvement vary:
- **o4-mini** prioritizes rapid early gains but offers diminishing returns.
- **Goedel-Prover-SFT** balances steady progress with moderate efficiency.
- **Kimina-Prover-Preview-Distill-7B** achieves the highest accuracy but requires deeper recursion, indicating potential trade-offs between computational cost and performance.
The differences in trends may reflect architectural choices (e.g., model complexity, training data) or optimization strategies for recursion handling. For applications requiring high accuracy, Kimina’s model is optimal despite higher computational demands, while o4-mini suits scenarios with limited recursion depth.
