# Technical Document Extraction: ORM Versus PRM Performance Analysis ## 1. Document Metadata * **Title:** ORM Versus PRM * **Language:** English * **Image Type:** Line graph with shaded confidence intervals/error bands * **Primary Subject:** Comparison of MATH Test Accuracy across different sampling methods and reward models ## 2. Component Isolation ### A. Header * **Main Title:** ORM Versus PRM ### B. Main Chart Area * **Y-Axis Label:** MATH Test Accuracy (%) * **Y-Axis Scale:** Linear, ranging from 10 to 40 with increments of 5 * **X-Axis Label:** Number of Samples * **X-Axis Scale:** Logarithmic (Base 2), with markers at $2^1, 2^3, 2^5, 2^7, 2^9, 2^{11}$ * **Legend Location:** Top-left quadrant ### C. Legend Data | Color | Label | | :--- | :--- | | **Blue** | PRM best-of-N weighted | | **Orange** | Base-LM Majority | | **Green** | ORM best-of-N weighted | --- ## 3. Trend Verification and Data Extraction ### Series 1: PRM best-of-N weighted (Blue Line) * **Visual Trend:** This series shows the highest overall performance. It follows a steep upward trajectory from $2^0$ to $2^5$, after which the slope decreases but remains consistently positive, ending at the highest point on the graph. * **Estimated Data Points:** * $2^0$ (1 sample): ~10.5% * $2^3$ (8 samples): ~25.5% * $2^5$ (32 samples): ~31.8% * $2^7$ (128 samples): ~35.3% * $2^{11}$ (2048 samples): ~39.8% ### Series 2: ORM best-of-N weighted (Green Line) * **Visual Trend:** Initially tracks very closely with the PRM (Blue) line for low sample counts ($2^0$ to $2^3$). However, after $2^3$, the growth rate slows down significantly compared to PRM, eventually plateauing between $2^9$ and $2^{11}$. * **Estimated Data Points:** * $2^0$ (1 sample): ~10.5% * $2^3$ (8 samples): ~25.0% * $2^5$ (32 samples): ~30.5% * $2^7$ (128 samples): ~33.0% * $2^{11}$ (2048 samples): ~34.8% ### Series 3: Base-LM Majority (Orange Line) * **Visual Trend:** This is the baseline series and performs the worst of the three. It shows a steady but much shallower upward slope. It lacks the initial "burst" of accuracy seen in the reward-model-guided series. * **Estimated Data Points:** * $2^0$ (1 sample): ~10.5% * $2^3$ (8 samples): ~18.5% * $2^5$ (32 samples): ~25.5% * $2^7$ (128 samples): ~28.1% * $2^{11}$ (2048 samples): ~29.6% --- ## 4. Key Findings and Observations 1. **Convergence at Origin:** All three methods start at approximately the same accuracy (~10.5%) when the number of samples is 1 ($2^0$). 2. **PRM Superiority:** The Process Reward Model (PRM) weighted best-of-N consistently outperforms the Outcome Reward Model (ORM) and the Base-LM Majority vote as the number of samples increases. 3. **Scaling Efficiency:** Both ORM and PRM provide a significant "boost" over simple majority voting. However, the PRM scales better with more samples, whereas the ORM shows signs of diminishing returns (plateauing) earlier. 4. **Statistical Variance:** Shaded regions around each line indicate confidence intervals. The variance appears relatively stable across the sample sizes, with no significant widening or narrowing as $N$ increases.

# Technical Document Analysis: ORM Verses PRM Line Chart ## 1. Chart Title - **Title**: "ORM Verses PRM" ## 2. Axes - **X-Axis**: - Label: "Number of Samples" - Scale: Logarithmic (2¹ to 2¹¹) - Tick Marks: 2¹, 2³, 2⁵, 2⁷, 2⁹, 2¹¹ - **Y-Axis**: - Label: "MATH Test Accuracy (%)" - Range: 10% to 40% - Tick Marks: 10%, 15%, 20%, 25%, 30%, 35%, 40% ## 3. Legend - **Placement**: Top-left corner - **Entries**: - **Blue Circle**: "PRM best-of-N weighted" - **Orange Circle**: "Base-LM Majority" - **Green Circle**: "ORM best-of-N weighted" ## 4. Data Series & Trends ### A. PRM best-of-N weighted (Blue Line) - **Trend**: Steady upward slope from 10% to 40%. - **Key Data Points**: - 2¹: 10% - 2³: 26% - 2⁵: 32% - 2⁷: 35% - 2⁹: 38% - 2¹¹: 40% ### B. Base-LM Majority (Orange Line) - **Trend**: Rapid initial increase, then plateau. - **Key Data Points**: - 2¹: 10% - 2³: 18% - 2⁵: 25% - 2⁷: 28% - 2⁹: 29% - 2¹¹: 30% ### C. ORM best-of-N weighted (Green Line) - **Trend**: Consistent upward slope, slightly less steep than PRM. - **Key Data Points**: - 2¹: 10% - 2³: 24% - 2⁵: 30% - 2⁷: 33% - 2⁹: 34% - 2¹¹: 35% ## 5. Spatial Grounding - **Legend Coordinates**: Top-left corner (exact [x, y] unspecified in image). - **Main Chart Area**: Central region bounded by axes and gridlines. ## 6. Data Table Reconstruction | Number of Samples | PRM best-of-N weighted (%) | Base-LM Majority (%) | ORM best-of-N weighted (%) | |--------------------|----------------------------|----------------------|----------------------------| | 2¹ (2) | 10 | 10 | 10 | | 2³ (8) | 26 | 18 | 24 | | 2⁵ (32) | 32 | 25 | 30 | | 2⁷ (128) | 35 | 28 | 33 | | 2⁹ (512) | 38 | 29 | 34 | | 2¹¹ (2048) | 40 | 30 | 35 | ## 7. Verification Notes - **Color Consistency**: All data points match legend colors (blue = PRM, orange = Base-LM, green = ORM). - **Trend Logic**: - PRM (blue) and ORM (green) lines show continuous improvement with scale. - Base-LM (orange) plateaus after 2⁷ samples, confirming diminishing returns. ## 8. Missing Elements - No additional text, heatmaps, or diagrams present. - No non-English content detected. ## 9. Summary The chart compares three models (PRM, Base-LM, ORM) across increasing sample sizes (logarithmic scale). PRM achieves the highest accuracy (40% at 2¹¹ samples), followed by ORM (35%) and Base-LM (30%), which plateaus early. All models start at 10% accuracy for 2¹ samples.