## Line Chart: Scaling training data: MATH-500 ### Overview The chart illustrates the relationship between the number of training solutions (x-axis) and accuracy percentage (y-axis) for different model configurations. Four data series are compared, showing performance trends as training data scales from 1 solution (2⁰) to 32 solutions (2⁵). ### Components/Axes - **X-axis**: "Number of solutions" (logarithmic scale: 2⁰ to 2⁵) - **Y-axis**: "Accuracy (%)" (linear scale: 50% to 85%) - **Legend**: - Orange stars: ThinkPRM-14B (1K) - Green circles: DiscPRM-14B - Purple diamonds: ThinkPRM-14B (65K) - Beige squares: Majority - **Title**: "Scaling training data: MATH-500" (top-center) ### Detailed Analysis 1. **ThinkPRM-14B (1K)** (orange stars): - Starts at ~50% at 2⁰ - Sharp rise to ~60% at 2¹ - Gradual increase to ~82% at 2⁵ - Steady upward trend with no plateaus 2. **DiscPRM-14B** (green circles): - Begins at ~50% at 2⁰ - Rapid growth to ~75% at 2³ - Plateaus at ~75% from 2³ to 2⁵ - Slight dip to ~73% at 2⁵ 3. **ThinkPRM-14B (65K)** (purple diamonds): - Starts at ~50% at 2⁰ - Consistent upward trajectory - Reaches ~85% at 2⁴ - Maintains ~85% at 2⁵ - Highest performance across all scales 4. **Majority** (beige squares): - Flat line at ~50% until 2² - Sharp rise to ~73% at 2³ - Slight decline to ~72% at 2⁵ - Most volatile trend with initial stagnation ### Key Observations - **Performance Correlation**: All models show improved accuracy with increased training data, but ThinkPRM-14B (65K) demonstrates the strongest scaling efficiency. - **DiscPRM-14B Plateau**: Performance stabilizes after 2³ solutions, suggesting diminishing returns at higher data volumes. - **Majority Method Limitations**: Initial stagnation (50% until 2²) indicates poor generalization without sufficient data. - **Model Variants**: The 65K variant of ThinkPRM-14B outperforms the 1K version by ~25% at maximum scale (2⁵). ### Interpretation The data suggests that model performance on MATH-500 is highly sensitive to training data quantity. ThinkPRM-14B (65K) achieves near-optimal results with 32 solutions, while DiscPRM-14B shows saturation at 8 solutions. The Majority method's poor initial performance highlights the importance of diverse training data over simple majority voting. The logarithmic x-axis emphasizes exponential scaling benefits, with most gains occurring between 2¹ and 2³ solutions. The chart underscores the value of large-scale training data for complex reasoning tasks, with ThinkPRM-14B (65K) representing the most effective configuration for this benchmark.