# Technical Document Extraction: Performance Metrics by Population Size ## 1. Image Overview This image is a line graph illustrating the relationship between "Population size N" and the "Pass@1" performance metric across five distinct datasets/benchmarks. The chart includes shaded error bands (confidence intervals) for each data series. ## 2. Component Isolation ### A. Header / Axis Labels * **Y-Axis Title:** `Pass@1` (Vertical orientation, range approximately 0.3 to 0.8). * **X-Axis Title:** `Population size N` (Horizontal orientation). * **X-Axis Markers:** `4`, `8`, `16`, `32` (Logarithmic-style spacing). * **Y-Axis Markers:** `0.4`, `0.5`, `0.6`, `0.7` (with horizontal grid lines). ### B. Legend (Spatial Grounding: Bottom Center) The legend is located in a boxed area below the x-axis. * **Blue Line (Circle marker):** `LiveCodeBench-v6` * **Gold/Yellow Line (Circle marker):** `AIME-25` * **Green Line (Circle marker):** `HMMT-25` * **Orange/Brown Line (Circle marker):** `RG Games` * **Pink/Purple Line (Circle marker):** `RG Cognition + ARC` ## 3. Data Series Analysis and Trend Verification ### Series 1: RG Games (Orange/Brown) * **Trend:** This series starts as the highest performer at N=4. It remains relatively flat/stable across all population sizes, showing very little sensitivity to increases in N. * **Data Points (Approximate):** * N=4: ~0.68 * N=8: ~0.69 * N=16: ~0.69 * N=32: ~0.69 ### Series 2: AIME-25 (Gold/Yellow) * **Trend:** Significant upward slope between N=4 and N=16. It overtakes RG Games at N=16 to become the top performer before showing a slight decline/plateau at N=32. It has the widest confidence interval (shaded area). * **Data Points (Approximate):** * N=4: ~0.60 * N=8: ~0.68 * N=16: ~0.73 (Peak) * N=32: ~0.71 ### Series 3: LiveCodeBench-v6 (Blue) * **Trend:** Very slight upward slope, essentially plateauing after N=8. High stability. * **Data Points (Approximate):** * N=4: ~0.55 * N=8: ~0.56 * N=16: ~0.57 * N=32: ~0.57 ### Series 4: RG Cognition + ARC (Pink/Purple) * **Trend:** Extremely stable with a very marginal upward trend. The performance is consistent across the population range. * **Data Points (Approximate):** * N=4: ~0.50 * N=8: ~0.51 * N=16: ~0.52 * N=32: ~0.52 ### Series 5: HMMT-25 (Green) * **Trend:** Strongest positive correlation with population size. It starts as the lowest performer but shows a consistent upward slope across the entire range (N=4 to N=32). * **Data Points (Approximate):** * N=4: ~0.37 * N=8: ~0.44 * N=16: ~0.48 * N=32: ~0.50 ## 4. Reconstructed Data Table (Estimated Values) | Population size N | RG Games (Orange) | AIME-25 (Gold) | LiveCodeBench-v6 (Blue) | RG Cognition + ARC (Pink) | HMMT-25 (Green) | | :--- | :--- | :--- | :--- | :--- | :--- | | **4** | 0.68 | 0.60 | 0.55 | 0.50 | 0.37 | | **8** | 0.69 | 0.68 | 0.56 | 0.51 | 0.44 | | **16** | 0.69 | 0.73 | 0.57 | 0.52 | 0.48 | | **32** | 0.69 | 0.71 | 0.57 | 0.52 | 0.50 | ## 5. Key Observations * **Scaling Sensitivity:** `HMMT-25` and `AIME-25` benefit the most from increasing the population size from 4 to 16. * **Saturation Point:** Most benchmarks reach a performance plateau by N=16, with `AIME-25` even showing a slight decrease in the mean value at N=32. * **Variance:** `AIME-25` (Gold) and `HMMT-25` (Green) exhibit the largest variance (shaded error bands), particularly at lower population sizes for HMMT-25 and higher sizes for AIME-25.

# Technical Document: Line Chart Analysis ## Chart Overview The image is a line chart comparing the performance of four different systems across varying population sizes. The y-axis represents the metric "Pass@1" (ranging from 0.35 to 0.75), and the x-axis represents "Population size N" (values: 4, 8, 16, 32). Four data series are plotted with distinct colors and markers, each representing a system. --- ## Axes and Labels - **X-axis (Population size N)**: - Tick marks at 4, 8, 16, 32. - Label: "Population size N". - **Y-axis (Pass@1)**: - Range: 0.35 to 0.75. - Label: "Pass@1". --- ## Legend The legend is located at the bottom of the chart and maps colors to systems: 1. **Blue (●)**: LiveCodeBench-v6 2. **Orange (●)**: RG Games 3. **Pink (●)**: RG Cognition + ARC 4. **Green (●)**: HMMT-25 --- ## Data Series and Trends ### 1. **LiveCodeBench-v6 (Blue)** - **Trend**: Starts at ~0.55 (N=4), increases slightly to ~0.57 (N=8), then plateaus. - **Data Points**: - N=4: 0.55 - N=8: 0.57 - N=16: 0.57 - N=32: 0.57 ### 2. **RG Games (Orange)** - **Trend**: Starts at ~0.65 (N=4), peaks at ~0.72 (N=16), then slightly declines. - **Data Points**: - N=4: 0.65 - N=8: 0.70 - N=16: 0.72 - N=32: 0.70 ### 3. **RG Cognition + ARC (Pink)** - **Trend**: Starts at ~0.50 (N=4), increases to ~0.52 (N=16), then stabilizes. - **Data Points**: - N=4: 0.50 - N=8: 0.51 - N=16: 0.52 - N=32: 0.52 ### 4. **HMMT-25 (Green)** - **Trend**: Starts at ~0.35 (N=4), increases to ~0.48 (N=16), then plateaus. - **Data Points**: - N=4: 0.35 - N=8: 0.45 - N=16: 0.48 - N=32: 0.48 --- ## Confidence Intervals - Shaded regions around each line represent confidence intervals: - **RG Games (Orange)**: Widest intervals (e.g., ~0.65–0.75 at N=4, ~0.70–0.75 at N=16). - **LiveCodeBench-v6 (Blue)**: Narrower intervals (~0.55–0.60 at N=4, ~0.57–0.60 at N=16). - **RG Cognition + ARC (Pink)**: Moderate intervals (~0.50–0.55 at N=4, ~0.51–0.55 at N=16). - **HMMT-25 (Green)**: Narrowest intervals (~0.35–0.40 at N=4, ~0.45–0.50 at N=16). --- ## Spatial Grounding - **Legend Position**: Bottom of the chart. - **Color Consistency**: All lines match their legend labels (e.g., blue = LiveCodeBench-v6). --- ## Key Observations 1. **RG Games** achieves the highest Pass@1 scores, peaking at N=16. 2. **HMMT-25** shows the lowest performance but improves significantly with larger population sizes. 3. **LiveCodeBench-v6** and **RG Cognition + ARC** exhibit similar trends, with minimal variation across population sizes. --- ## Notes - No non-English text is present in the chart. - All data points and trends are visually extracted; no numerical tables are embedded.