# Technical Document Extraction: Compute Optimal Search Chart ## 1. Metadata and Header Information * **Title:** Compute Optimal Search * **Language:** English (100%) * **Image Type:** Line Graph with markers * **Primary Subject:** Performance comparison of different search/ranking methods for mathematical problem solving across varying computational budgets. ## 2. Axis and Scale Identification * **Y-Axis (Vertical):** * **Label:** MATH Test Accuracy (%) * **Range:** 10 to 40 * **Markers:** 10, 15, 20, 25, 30, 35, 40 * **X-Axis (Horizontal):** * **Label:** Generation Budget * **Scale:** Logarithmic (Base 2) * **Markers:** $2^1, 2^3, 2^5, 2^7, 2^9$ (with intermediate grid lines representing $2^0, 2^2, 2^4, 2^6, 2^8$) ## 3. Legend and Component Isolation The legend is located in the bottom-right quadrant of the main chart area. | Legend Label | Color | Marker Style | | :--- | :--- | :--- | | **Majority** | Red | Solid line with circle | | **ORM Best-of-N Weighted** | Purple | Solid line with circle | | **PRM Best-of-N Weighted** | Green | Solid line with circle | | **PRM Compute Optimal Oracle** | Blue | Solid line with circle | | **PRM Compute Optimal Predicted** | Orange | Solid line with circle | ## 4. Trend Verification and Data Extraction All data series exhibit a positive correlation: as the "Generation Budget" increases, the "MATH Test Accuracy (%)" also increases, though most series show diminishing returns at higher budgets. ### Data Series Analysis #### A. Majority (Red Line) * **Trend:** The lowest performing baseline. It shows a steady, nearly linear increase on the log scale but remains significantly below all other methods. * **Approximate Data Points:** * $2^0$: ~10.5% * $2^2$: ~14% * $2^4$: ~23% * $2^9$: ~29% #### B. ORM Best-of-N Weighted (Purple Line) * **Trend:** Slopes upward sharply until $2^4$, then decelerates, ending as the second-lowest performer at high budgets. * **Approximate Data Points:** * $2^0$: ~10.5% * $2^4$: ~28% * $2^9$: ~34.5% #### C. PRM Best-of-N Weighted (Green Line) * **Trend:** Consistently outperforms the ORM and Majority baselines. It maintains a steady upward trajectory throughout the budget range. * **Approximate Data Points:** * $2^0$: ~10.5% * $2^4$: ~29% * $2^9$: ~38% #### D. PRM Compute Optimal Oracle (Blue Line) * **Trend:** The highest performing series. It shows a very steep initial climb and reaches the highest recorded accuracy (~39.5%) at a budget of $2^8$. Note: This line ends at $2^8$. * **Approximate Data Points:** * $2^0$: ~10.5% * $2^2$: ~27% * $2^4$: ~33.5% * $2^8$: ~39.5% #### E. PRM Compute Optimal Predicted (Orange Line) * **Trend:** Closely tracks the "Oracle" (Blue) line at lower budgets ($2^0$ to $2^4$). Between $2^4$ and $2^8$, it plateaus significantly compared to the Oracle, eventually converging with the PRM Best-of-N Weighted (Green) line. * **Approximate Data Points:** * $2^0$: ~10.5% * $2^2$: ~27% * $2^4$: ~33% * $2^8$: ~37% ## 5. Summary of Findings The chart demonstrates that Process-based Reward Models (PRM) significantly outperform Outcome-based Reward Models (ORM) and simple Majority voting. The "Compute Optimal Oracle" suggests that with perfect selection, accuracy can reach nearly 40% within a $2^8$ budget. The "Predicted" model successfully mimics the Oracle at low budgets but loses its competitive edge as the budget exceeds $2^4$, falling back toward the standard PRM weighted performance.

# Technical Document: Compute Optimal Search Analysis ## Chart Description The image is a **line chart** titled **"Compute Optimal Search"**, visualizing the relationship between **Generation Budget** (x-axis) and **MATH Test Accuracy (%)** (y-axis). The chart compares five distinct algorithms across increasing computational budgets. --- ### Axis Details - **X-Axis (Generation Budget)**: - Logarithmic scale with markers at `2^1`, `2^3`, `2^5`, `2^7`, `2^9`. - Labels: `2^1`, `2^3`, `2^5`, `2^7`, `2^9`. - **Y-Axis (MATH Test Accuracy %)**: - Linear scale from `10%` to `40%` in increments of `5%`. - Labels: `10%`, `15%`, `20%`, `25%`, `30%`, `35%`, `40%`. --- ### Legend - **Location**: Bottom-right corner. - **Labels and Colors**: 1. **Majority** (Red) 2. **ORM Best-of-N Weighted** (Purple) 3. **PRM Best-of-N Weighted** (Green) 4. **PRM Compute Optimal Oracle** (Blue) 5. **PRM Compute Optimal Predicted** (Orange) --- ### Data Series and Trends #### 1. **Majority (Red Line)** - **Trend**: Gradual upward slope. - **Key Points**: - `2^1`: `10.0%` - `2^3`: `18.0%` - `2^5`: `22.5%` - `2^7`: `27.8%` - `2^9`: `28.5%` #### 2. **ORM Best-of-N Weighted (Purple Line)** - **Trend**: Steeper upward slope than "Majority". - **Key Points**: - `2^1`: `10.0%` - `2^3`: `24.5%` - `2^5`: `30.2%` - `2^7`: `32.8%` - `2^9`: `34.2%` #### 3. **PRM Best-of-N Weighted (Green Line)** - **Trend**: Steeper than "ORM", with consistent growth. - **Key Points**: - `2^1`: `10.0%` - `2^3`: `25.5%` - `2^5`: `31.8%` - `2^7`: `35.3%` - `2^9`: `37.8%` #### 4. **PRM Compute Optimal Oracle (Blue Line)** - **Trend**: Sharpest upward trajectory, reaching the highest accuracy. - **Key Points**: - `2^1`: `10.0%` - `2^3`: `32.0%` - `2^5`: `33.5%` - `2^7`: `36.8%` - `2^9`: `39.5%` #### 5. **PRM Compute Optimal Predicted (Orange Line)** - **Trend**: Moderate upward slope, plateauing near `2^7`. - **Key Points**: - `2^1`: `10.0%` - `2^3`: `27.0%` - `2^5`: `32.5%` - `2^7`: `35.0%` - `2^9`: `37.0%` --- ### Cross-Reference Verification - **Legend Colors**: All line colors match their corresponding labels in the legend. - **Spatial Grounding**: - Legend is positioned in the **bottom-right** corner, outside the plot area. - Data points align with their respective lines and axes. --- ### Summary of Key Trends 1. **PRM Compute Optimal Oracle (Blue)** achieves the highest accuracy, surpassing all other methods at `2^9` (`39.5%`). 2. **PRM Best-of-N Weighted (Green)** and **PRM Compute Optimal Predicted (Orange)** show similar performance, with slight differences in growth rates. 3. **ORM Best-of-N Weighted (Purple)** and **Majority (Red)** exhibit slower growth, with "Majority" having the lowest final accuracy (`28.5%`). --- ### Notes - All lines originate at `(2^1, 10.0%)`, indicating a baseline accuracy of `10%` for all algorithms at the minimum budget. - No textual data tables or non-English content are present. - The chart emphasizes computational efficiency, with higher budgets enabling better performance for most algorithms.