## Line Graphs: Model Performance Across Math Benchmarks
### Overview
The image contains 10 line graphs arranged in a 4x3 grid (with one missing in the bottom-right corner), comparing the performance of five AI models across various math benchmarks. Each graph plots "Score" against "Tokens (B)" for different datasets: `average`, `GKMathUnion`, `UGMathBench`, `college_math`, `gsm8k`, `gsm_plus`, `math`, `math500`, `mathbench`, and `mgsm_ZH`. The models compared are:
- Finemath-3plus (blue)
- Nemotron-3plus (orange)
- Inf-mm-webmath (green)
- Megamath-web (red)
- Ling-math-web (purple)
### Components/Axes
- **X-axis**: "Tokens (B)" (0 to 300 in increments of 50)
- **Y-axis**: "Score" (varies by graph, typically 0–25)
- **Legend**: Located in the bottom-right corner of each graph, with color-coded labels for each model.
- **Graph Titles**: Each subplot is labeled with the benchmark name (e.g., "average", "GKMathUnion").
### Detailed Analysis
#### 1. `average` Graph
- **Trend**: All models show upward trends. Finemath-3plus (blue) and Nemotron-3plus (orange) perform best, reaching ~12–14 by 300B tokens. Megamath-web (red) lags, peaking at ~6.
- **Data Points**:
- 50B: Finemath-3plus (~6), Megamath-web (~3)
- 150B: Finemath-3plus (~10), Nemotron-3plus (~9)
- 300B: Finemath-3plus (~14), Nemotron-3plus (~13)
#### 2. `GKMathUnion` Graph
- **Trend**: Ling-math-web (purple) dominates early, peaking at ~18. Finemath-3plus (blue) and Nemotron-3plus (orange) plateau at ~12–14.
- **Data Points**:
- 100B: Ling-math-web (~16), Finemath-3plus (~10)
- 250B: Ling-math-web (~17), Nemotron-3plus (~12)
#### 3. `UGMathBench` Graph
- **Trend**: Finemath-3plus (blue) and Nemotron-3plus (orange) show erratic growth, peaking at ~12. Megamath-web (red) remains flat (~4–6).
- **Data Points**:
- 200B: Finemath-3plus (~11), Megamath-web (~5)
- 300B: Finemath-3plus (~12), Nemotron-3plus (~10)
#### 4. `college_math` Graph
- **Trend**: Finemath-3plus (blue) and Nemotron-3plus (orange) rise steadily to ~20. Ling-math-web (purple) fluctuates but peaks at ~25.
- **Data Points**:
- 150B: Finemath-3plus (~16), Ling-math-web (~22)
- 300B: Finemath-3plus (~20), Nemotron-3plus (~19)
#### 5. `gsm8k` Graph
- **Trend**: Finemath-3plus (blue) and Nemotron-3plus (orange) show sharp increases, peaking at ~18. Megamath-web (red) lags at ~8.
- **Data Points**:
- 100B: Finemath-3plus (~12), Megamath-web (~6)
- 250B: Finemath-3plus (~16), Nemotron-3plus (~14)
#### 6. `gsm_plus` Graph
- **Trend**: Finemath-3plus (blue) and Nemotron-3plus (orange) plateau at ~12–14. Ling-math-web (purple) peaks at ~14.
- **Data Points**:
- 200B: Finemath-3plus (~11), Ling-math-web (~13)
- 300B: Finemath-3plus (~12), Nemotron-3plus (~11)
#### 7. `math` Graph
- **Trend**: Finemath-3plus (blue) and Nemotron-3plus (orange) rise to ~14. Megamath-web (red) remains flat (~4–6).
- **Data Points**:
- 150B: Finemath-3plus (~10), Megamath-web (~5)
- 300B: Finemath-3plus (~14), Nemotron-3plus (~12)
#### 8. `math500` Graph
- **Trend**: Finemath-3plus (blue) and Nemotron-3plus (orange) peak at ~16. Megamath-web (red) fluctuates between 3–6.
- **Data Points**:
- 200B: Finemath-3plus (~12), Megamath-web (~4)
- 300B: Finemath-3plus (~16), Nemotron-3plus (~14)
#### 9. `mathbench` Graph
- **Trend**: Finemath-3plus (blue) and Nemotron-3plus (orange) rise steadily to ~14. Megamath-web (red) remains flat (~3–5).
- **Data Points**:
- 100B: Finemath-3plus (~8), Megamath-web (~3)
- 300B: Finemath-3plus (~14), Nemotron-3plus (~12)
#### 10. `mgsm_ZH` Graph
- **Trend**: Finemath-3plus (blue) and Nemotron-3plus (orange) peak at ~12. Ling-math-web (purple) fluctuates but peaks at ~15.
- **Data Points**:
- 150B: Finemath-3plus (~9), Ling-math-web (~13)
- 300B: Finemath-3plus (~12), Nemotron-3plus (~10)
### Key Observations
1. **Finemath-3plus** consistently outperforms other models across most benchmarks, especially in `college_math` and `gsm8k`.
2. **Ling-math-web** excels in `GKMathUnion` and `mgsm_ZH` but underperforms in `mathbench`.
3. **Megamath-web** (red) lags in all benchmarks, suggesting limited scalability with token count.
4. **Nemotron-3plus** (orange) shows moderate performance, often second to Finemath-3plus.
5. **Inf-mm-webmath** (green) is rarely visible, implying minimal data or low scores.
### Interpretation
The data suggests that **Finemath-3plus** and **Nemotron-3plus** are the most robust models for math tasks, with performance improving as token count increases. **Ling-math-web** performs well in specific benchmarks (e.g., `GKMathUnion`) but lacks consistency. **Megamath-web**’s flat trends indicate potential architectural limitations. The `average` graph highlights a general trend where higher token counts correlate with better scores, but model-specific optimizations (e.g., Ling-math-web in `GKMathUnion`) create outliers. The absence of Inf-mm-webmath in most graphs suggests it may not be a competitive model for these tasks.
