# Technical Document Extraction: Reasoning Stage Analysis
## Image Description
The image contains two line graphs stacked vertically, analyzing reasoning stages in a computational model. The graphs track metrics across "Thinking Step k" (x-axis) with distinct pre- and post-RCP (Reasoning Convergence Protocol) phases.
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### **Top Graph: Accuracy Metrics**
**Title**:
- Pre-RCP: Active Reasoning Stage
- Post-RCP: Converged Reasoning Stage
**Axes**:
- **X-axis**: Thinking Step k (0–200)
- **Y-axis**: Accuracy (0.0–1.0)
**Legend**:
- **Red Line**: Generation Accuracy
- **Purple Dashed Line**: Answer Emergence
- **Placement**: Top-right corner
**Key Trends**:
1. **Generation Accuracy (Red)**:
- Starts at ~0.6 at step 0.
- Dips to ~0.3 at step 50.
- Rises sharply to ~1.0 by step 100.
- Stabilizes with minor fluctuations (~0.95–1.0) post-step 100.
2. **Answer Emergence (Purple Dashed)**:
- Remains at 0 until step 50.
- Spikes to ~0.8 at step 50.
- Stabilizes at ~0.95 post-step 100.
3. **Transition Marker**:
- Vertical blue line at step 100 separates Pre-RCP and Post-RCP phases.
**Spatial Grounding**:
- Legend colors match line colors exactly.
- Vertical blue line at x=100 aligns with phase transition.
---
### **Bottom Graph: Token Rank Metrics**
**Title**:
- Rank of `` token
**Axes**:
- **X-axis**: Thinking Step k (0–200)
- **Y-axis**: Rank of `` (0–2000)
**Legend**:
- **Green Line**: Rank of ``
- **Placement**: Bottom-right corner
**Key Trends**:
1. **Rank of `` (Green)**:
- Starts at ~1000 at step 0.
- Drops sharply to ~500 at step 50.
- Fluctuates between ~200–1000 until step 100.
- Stabilizes near 0 post-step 100 with minor spikes.
2. **Transition Marker**:
- Vertical blue line at step 100 aligns with phase transition.
**Spatial Grounding**:
- Legend color (green) matches line color exactly.
---
### **Cross-Graph Observations**
1. **Phase Transition**:
- Both graphs show a structural shift at step 100 (blue vertical line).
- Post-step 100, accuracy stabilizes, and token rank drops significantly.
2. **Correlation**:
- Sharp rise in Generation Accuracy (step 50–100) coincides with Answer Emergence spike.
- Token rank decline correlates with improved accuracy, suggesting reduced reliance on `` tokens as reasoning converges.
---
### **Data Extraction**
#### Top Graph Data Points (Approximate):
| Step k | Generation Accuracy | Answer Emergence |
|--------|---------------------|------------------|
| 0 | 0.6 | 0.0 |
| 50 | 0.3 | 0.8 |
| 100 | 1.0 | 0.95 |
| 150 | 1.0 | 0.95 |
| 200 | 1.0 | 0.95 |
#### Bottom Graph Data Points (Approximate):
| Step k | Rank of `` |
|--------|---------------------|
| 0 | 1000 |
| 50 | 500 |
| 100 | 200 |
| 150 | 50 |
| 200 | 10 |
---
### **Conclusion**
The graphs demonstrate that the Post-RCP phase achieves stable high accuracy (~1.0) and low `` token rank (~10), indicating effective reasoning convergence. The transition at step 100 marks a critical shift in model behavior.
