## Line Chart: Cumulative Distribution Function (CDF) vs. Recomputed Tokens per Request
### Overview
The chart illustrates the relationship between the cumulative distribution function (CDF) and recomputed tokens per request for four different window sizes (32, 64, 128, 256). The CDF represents the probability that a request will use up to a specified number of tokens. Larger window sizes correspond to higher token thresholds before reaching a CDF of 1.0.
### Components/Axes
- **X-axis**: "Recomputed Tokens per Request" (range: 0–1750, increments of 250).
- **Y-axis**: "CDF" (range: 0.0–1.0, increments of 0.2).
- **Legend**: Located in the bottom-right corner, with four colored lines:
- Blue: Window Size = 32
- Orange: Window Size = 64
- Green: Window Size = 128
- Red: Window Size = 256
### Detailed Analysis
1. **Blue Line (Window Size = 32)**:
- Steepest slope, reaching CDF = 1.0 at approximately **250 tokens**.
- Rapidly plateaus after 250 tokens.
2. **Orange Line (Window Size = 64)**:
- Reaches CDF = 1.0 at approximately **300 tokens**.
- Slope is less steep than the blue line but steeper than green/red lines.
3. **Green Line (Window Size = 128)**:
- Reaches CDF = 1.0 at approximately **400 tokens**.
- Slope is gentler than orange and blue lines.
4. **Red Line (Window Size = 256)**:
- Reaches CDF = 1.0 at approximately **500 tokens**.
- Flattest slope among all lines.
All lines plateau at CDF = 1.0 beyond their respective token thresholds, indicating no further increase in probability for higher token counts.
### Key Observations
- **Inverse Relationship**: Larger window sizes correlate with higher token thresholds before reaching CDF = 1.0.
- **Steepness Gradient**: Smaller window sizes (e.g., 32) exhibit steeper curves, indicating a sharper transition to maximum probability.
- **Consistency**: All lines eventually reach CDF = 1.0, suggesting a hard upper limit on token usage per request.
### Interpretation
The data demonstrates that window size directly impacts the token capacity a system can handle before reaching maximum probability (CDF = 1.0). Larger windows (e.g., 256) allow significantly more tokens per request compared to smaller windows (e.g., 32), reflecting a trade-off between window size and computational efficiency. The CDF approaching 1.0 implies that beyond these thresholds, the likelihood of exceeding token limits becomes negligible. This could inform system design decisions, such as optimizing window sizes for specific workloads or balancing resource allocation.
