# Technical Data Extraction: Model Accuracy vs. Generation Budget ## 1. Image Overview This image is a line graph plotting the **Accuracy** of four different Process Reward Models (PRMs) against a varying **Budget (# of model generations)**. The chart uses a logarithmic scale for the x-axis and a linear scale for the y-axis. ## 2. Axis and Legend Specifications ### Axis Labels * **Y-Axis:** "Accuracy" (Linear scale ranging from approximately 0.15 to 0.65). * **X-Axis:** "Budget (# of model generations)" (Logarithmic scale base 2, ranging from $2^0$ to $2^7$). ### Axis Markers * **Y-Axis Markers:** 0.2, 0.3, 0.4, 0.5, 0.6. * **X-Axis Markers:** $2^0$ (1), $2^1$ (2), $2^2$ (4), $2^3$ (8), $2^4$ (16), $2^5$ (32), $2^6$ (64), $2^7$ (128). ### Legend | Color | Marker Shape | Label | | :--- | :--- | :--- | | **Blue** | Circle (●) | Qwen2.5-Math-PRM-7B | | **Red** | Square (■) | Llama3.1-8B-PRM-Deepseek-Data | | **Purple** | Triangle (▲) | EurusPRM-Stage2 | | **Green** | Diamond (◆) | math-shepherd-mistral-7b-prm | --- ## 3. Data Series Analysis and Trends ### Series 1: Qwen2.5-Math-PRM-7B (Blue, Circle) * **Trend:** This model consistently maintains the highest accuracy across almost all budget levels. It shows a sharp upward slope from $2^0$ to $2^2$, plateaus/peaks between $2^3$ and $2^4$, experiences a slight dip at $2^6$, and recovers at $2^7$. * **Estimated Data Points:** * $2^0$: 0.40 * $2^1$: 0.46 * $2^2$: 0.62 * $2^3$: 0.63 * $2^4$: 0.64 (Peak) * $2^5$: 0.61 * $2^6$: 0.58 * $2^7$: 0.61 ### Series 2: EurusPRM-Stage2 (Purple, Triangle) * **Trend:** Shows the most consistent and steepest positive linear growth relative to the log-scale budget. It starts as the second-lowest performer and ends as the second-highest, nearly converging with the Qwen model at the highest budget. * **Estimated Data Points:** * $2^0$: 0.20 * $2^1$: 0.27 * $2^2$: 0.35 * $2^3$: 0.44 * $2^4$: 0.49 * $2^5$: 0.57 * $2^6$: 0.58 * $2^7$: 0.59 ### Series 3: Llama3.1-8B-PRM-Deepseek-Data (Red, Square) * **Trend:** Starts with the lowest accuracy at $2^0$. It shows a significant jump at $2^2$, followed by a generally upward but volatile trend, including a notable dip at $2^5$. * **Estimated Data Points:** * $2^0$: 0.15 * $2^1$: 0.27 * $2^2$: 0.40 * $2^3$: 0.41 * $2^4$: 0.46 * $2^5$: 0.42 * $2^6$: 0.44 * $2^7$: 0.46 ### Series 4: math-shepherd-mistral-7b-prm (Green, Diamond) * **Trend:** This is the lowest-performing model overall for budgets $> 2^1$. The trend is generally upward but very shallow compared to the others, with a peak at $2^6$ followed by a decline at $2^7$. * **Estimated Data Points:** * $2^0$: 0.24 * $2^1$: 0.25 * $2^2$: 0.28 * $2^3$: 0.35 * $2^4$: 0.32 * $2^5$: 0.35 * $2^6$: 0.39 * $2^7$: 0.34 --- ## 4. Summary Table of Extracted Values (Approximate) | Budget ($2^x$) | Qwen2.5 (Blue) | EurusPRM (Purple) | Llama3.1 (Red) | Math-Shepherd (Green) | | :--- | :--- | :--- | :--- | :--- | | **1 ($2^0$)** | 0.40 | 0.20 | 0.15 | 0.24 | | **2 ($2^1$)** | 0.46 | 0.27 | 0.27 | 0.25 | | **4 ($2^2$)** | 0.62 | 0.35 | 0.40 | 0.28 | | **8 ($2^3$)** | 0.63 | 0.44 | 0.41 | 0.35 | | **16 ($2^4$)** | 0.64 | 0.49 | 0.46 | 0.32 | | **32 ($2^5$)** | 0.61 | 0.57 | 0.42 | 0.35 | | **64 ($2^6$)** | 0.58 | 0.58 | 0.44 | 0.39 | | **128 ($2^7$)** | 0.61 | 0.59 | 0.46 | 0.34 |