# Technical Data Extraction: MATH Test Accuracy Analysis This document provides a comprehensive extraction of data and trends from two technical charts analyzing MATH test accuracy based on sequential/parallel processing ratios and problem difficulty. --- ## Chart 1: Varying Sequential/Parallel with Verifier ### Component Isolation * **Header:** Title "Varying Sequential/Parallel with Verifier" * **Main Chart:** A line graph with multiple data series plotted against a logarithmic X-axis. * **Legend (Right Side):** A vertical color bar representing the "Number of Generations" on a log scale from $10^0$ (1) to $10^2$ (100+). ### Axis Definitions * **Y-Axis:** "MATH Test Accuracy (%)" * Scale: Linear, from 15 to 45 in increments of 5. * **X-Axis:** "Sequential/Parallel Ratio" * Scale: Logarithmic (base 2), markers at $2^{-7}, 2^{-5}, 2^{-3}, 2^{-1}, 2^1, 2^3, 2^5, 2^7$. ### Data Series and Trends The chart contains several lines, color-coded by the number of generations. Darker purple indicates more generations; lighter orange indicates fewer. 1. **High Generation Count (Dark Purple, ~128-256 generations):** * **Trend:** Starts at ~40% accuracy at $2^{-8}$, dips slightly, then rises to a peak of ~44% at $2^4$ before declining slightly. * **Key Points:** Peak accuracy is achieved when the Sequential/Parallel ratio is approximately $2^4$ (16). 2. **Mid-Range Generation Count (Magenta/Pink, ~16-64 generations):** * **Trend:** These lines are generally flatter and lower than the dark purple line. They show a slight upward trend as the ratio moves from $2^{-3}$ toward $2^3$. * **Key Points:** Accuracy ranges between 33% and 40%. 3. **Low Generation Count (Orange/Light Peach, 1-4 generations):** * **Trend:** These appear as short segments or single points at the bottom center of the graph. * **Key Points:** * Single point (1 generation) at ratio $2^0$ (1) shows ~18% accuracy. * Short line (approx. 2-4 generations) at ratio $2^{-1}$ to $2^1$ shows ~24% accuracy. ### Summary of Findings Accuracy increases significantly with the number of generations. For high generation counts, there is an optimal "sweet spot" for the Sequential/Parallel ratio around $2^4$, where performance is maximized. --- ## Chart 2: Revisions@128, Varying the Sequential to Parallel Ratio ### Component Isolation * **Header:** Title "Revisions@128, Varying the Sequential to Parallel Ratio" * **Main Chart:** A grouped bar chart showing accuracy across five difficulty levels. * **Legend (Right Side):** A vertical color bar representing "Sequential to Parallel Ratio" on a log scale from $10^{-2}$ (0.01) to $10^2$ (100). ### Axis Definitions * **Y-Axis:** "MATH Test Accuracy (%)" * Scale: Linear, from 0 to 80+ in increments of 20. * **X-Axis:** "Test Questions Binned by Increasing Difficulty Level" * Categories: 1, 2, 3, 4, 5 (where 1 is easiest, 5 is hardest). ### Data Table Reconstruction Each difficulty bin contains approximately 10 bars, representing different Sequential to Parallel ratios (from orange/low ratio to dark purple/high ratio). | Difficulty Level | Trend Description | Approximate Accuracy Range | | :--- | :--- | :--- | | **1 (Easiest)** | Very high accuracy; relatively stable across all ratios. | ~90% - 92% | | **2** | High accuracy; slight improvement as the ratio increases (darker bars). | ~58% - 63% | | **3** | Moderate accuracy; clear upward trend as the ratio increases. | ~35% - 42% | | **4** | Low accuracy; performance peaks at mid-to-high ratios then drops for the highest ratio. | ~12% - 18% | | **5 (Hardest)** | Very low accuracy; performance is negligible for low ratios, peaking slightly for mid-high ratios. | ~1% - 4% | ### Summary of Findings 1. **Difficulty Impact:** There is a sharp, inverse correlation between question difficulty and accuracy. 2. **Ratio Impact:** Increasing the Sequential to Parallel ratio (moving toward more sequential processing) generally improves accuracy, particularly for mid-difficulty problems (Levels 2 and 3). 3. **Diminishing Returns:** For the hardest problems (Level 5), even high sequential ratios fail to bring accuracy above ~5%.