# Technical Document Extraction: MATH Test Accuracy Analysis ## 1. Document Metadata * **Title:** Revisions Best-of-128 Weighted, Varying the Sequential to Parallel Ratio * **Chart Type:** Grouped Bar Chart with Color Gradient Mapping * **Primary Language:** English ## 2. Component Isolation ### A. Header * **Main Title:** "Revisions Best-of-128 Weighted, Varying the Sequential to Parallel Ratio" ### B. Main Chart Area (Axes and Labels) * **Y-Axis Label:** MATH Test Accuracy (%) * **Y-Axis Scale:** Linear, ranging from 0 to 80 (with markers at 0, 10, 20, 30, 40, 50, 60, 70, 80). * **X-Axis Label:** Test Questions Binned with Unsupervised Difficulty Bins * **X-Axis Categories:** 1, 2, 3, 4, 5 (representing difficulty levels from easiest to hardest). ### C. Legend / Color Scale (Spatial Grounding: Right Side) * **Legend Title:** Sequential to Parallel Ratio * **Legend Type:** Vertical Color Bar (Heatmap scale) * **Scale Type:** Logarithmic * **Markers:** $10^{-2}$ (Light Orange), $10^{-1}$ (Salmon/Pink), $10^{0}$ (Magenta), $10^{1}$ (Purple), $10^{2}$ (Dark Purple). * **Visual Mapping:** Within each difficulty bin on the x-axis, there are 9 bars. These bars transition from light orange (left-most in the group) to dark purple (right-most in the group), representing an increasing Sequential to Parallel Ratio. ## 3. Data Extraction and Trend Analysis ### Trend Verification Across all difficulty bins, the primary trend is a **sharp decline in accuracy as difficulty increases** (moving from Bin 1 to Bin 5). Within each bin, the "Sequential to Parallel Ratio" (represented by the color gradient) shows varying effects, but generally, higher ratios (darker purple bars) tend to correlate with slightly higher performance in more difficult tasks, though this is non-linear. ### Data Table Reconstruction (Estimated Values) | Difficulty Bin | Ratio: $10^{-2}$ (Orange) | Ratio: $10^{-1}$ (Pink) | Ratio: $10^{0}$ (Magenta) | Ratio: $10^{1}$ (Purple) | Ratio: $10^{2}$ (Dark Purple) | | :--- | :--- | :--- | :--- | :--- | :--- | | **1 (Easiest)** | ~81% | ~80% | ~80% | ~82% | ~81% | | **2** | ~58% | ~59% | ~66% | ~62% | ~69% | | **3** | ~35% | ~36% | ~39% | ~41% | ~36% | | **4** | ~20% | ~20% | ~21% | ~22% | ~19% | | **5 (Hardest)** | ~6% | ~7% | ~7% | ~11% | ~7% | *Note: Each bin contains 9 bars; the table above samples the key points along the gradient for clarity.* ## 4. Detailed Observations by Category * **Bin 1 (Difficulty 1):** Performance is highest and most stable. Accuracy remains consistently above 80% regardless of the Sequential to Parallel Ratio. The variance between the lowest and highest ratio is minimal. * **Bin 2 (Difficulty 2):** Accuracy drops to the 58-69% range. There is a noticeable upward trend as the ratio increases, with the highest ratio (darkest purple) showing a significant peak compared to the lowest ratio. * **Bin 3 (Difficulty 3):** Accuracy drops further to the 35-41% range. The peak performance appears to occur at a mid-to-high ratio (magenta/purple) rather than the absolute highest ratio. * **Bin 4 (Difficulty 4):** Accuracy is low, centered around 20%. The distribution is relatively flat, though a slight peak is visible in the mid-purple range. * **Bin 5 (Difficulty 5):** Accuracy is lowest, mostly under 10%. There is a distinct outlier peak at a high Sequential to Parallel Ratio (purple bar), reaching approximately 11%, while others hover around 6-7%. ## 5. Summary of Findings The data indicates that the "Best-of-128 Weighted" method is highly effective for low-difficulty math problems (Bin 1). As problem difficulty increases, the Sequential to Parallel Ratio becomes a more significant factor in performance. Generally, increasing the sequential component (moving toward dark purple) provides a marginal to moderate accuracy boost in mid-to-high difficulty tiers, though the absolute accuracy remains low for the most difficult questions.