## Heatmap and Bar Chart: Factor Selection Analysis in aPSF Framework with Initial CoT Prompts
### Overview
The image contains two visualizations:
1. **Heatmap (A)**: Shows factor selection rates across datasets and categories.
2. **Bar Chart (B)**: Displays test accuracy by dominant factor for each dataset.
---
### Components/Axes
#### Heatmap (A)
- **Title**: "Factor Selection Heatmap Across Datasets and Categories"
- **X-Axis (Factor Categories)**:
- Problem Analysis
- Step Breakdown
- Mathematical Operations
- Calculation Execution
- Scientific Principle
- Domain Specific
- **Y-Axis (Datasets)**:
- GPQA Chemistry
- GSM-Hard
- MULTIARITH
- AQUA-RAT
- GSM8K
- BBH Date
- BBH Logic-5
- GPQA Physics
- **Color Scale**: Blue (0%) to Red (100%) for selection rates.
- **Legend**: Located on the right, labeled "Selection Rate (%)".
#### Bar Chart (B)
- **Title**: "Test Accuracy by Dominant Factor"
- **X-Axis (Datasets)**:
- GPQA Chemistry
- GSM-Hard
- MULTIARITH
- AQUA-RAT
- GSM8K
- BBH Date
- BBH Logic-5
- GPQA Physics
- **Y-Axis (Test Accuracy)**: Percentage (%) from 0% to 100%.
- **Legend**:
- Math Tasks (Blue)
- Science Tasks (Red)
- Logic Tasks (Green)
- **Bar Colors**: Match legend labels (e.g., blue for Math Tasks).
---
### Detailed Analysis
#### Heatmap (A)
- **Key Values**:
- **GPQA Chemistry**: Problem Analysis (40%), Calculation Execution (50%), Scientific Principle (10%).
- **GSM-Hard**: Problem Analysis (67%), Mathematical Operations (33%).
- **MULTIARITH**: Problem Analysis (100%).
- **AQUA-RAT**: Calculation Execution (50%), Domain Specific (30%).
- **GSM8K**: Problem Analysis (30%), Calculation Execution (50%).
- **BBH Date**: Domain Specific (100%).
- **BBH Logic-5**: Step Breakdown (80%).
- **GPQA Physics**: Scientific Principle (70%), Calculation Execution (20%).
#### Bar Chart (B)
- **Test Accuracy by Dataset**:
- **GPQA Chemistry**: Science Tasks (30.2%).
- **GSM-Hard**: Math Tasks (53.8%).
- **MULTIARITH**: Math Tasks (99.3%).
- **AQUA-RAT**: Calculation Execution (82.0%).
- **GSM8K**: Calculation Execution (90.0%).
- **BBH Date**: Domain Specific (75.3%).
- **BBH Logic-5**: Step Breakdown (74.7%).
- **GPQA Physics**: Scientific Principle (36.2%).
---
### Key Observations
1. **Heatmap Trends**:
- Problem Analysis and Calculation Execution are frequently selected across datasets (e.g., 100% in MULTIARITH, 50% in AQUA-RAT).
- Domain Specific and Step Breakdown show lower selection rates (e.g., 0% in GSM-Hard, 80% in BBH Logic-5).
2. **Bar Chart Trends**:
- Math Tasks dominate in MULTIARITH (99.3%) and GSM-Hard (53.8%).
- Calculation Execution is critical for GSM8K (90.0%) and AQUA-RAT (82.0%).
- Science Tasks and Logic Tasks have lower accuracy in GPQA Chemistry (30.2%) and BBH Logic-5 (74.7%), respectively.
---
### Interpretation
- **Factor Selection vs. Accuracy**:
- Datasets with high selection rates for specific factors (e.g., MULTIARITH’s 100% Problem Analysis) correlate with high test accuracy in related tasks (Math Tasks: 99.3%).
- Domain-specific factors (e.g., BBH Date’s 100% Domain Specific) show moderate accuracy (75.3%), suggesting less generalization.
- **Anomalies**:
- GSM-Hard has high Problem Analysis selection (67%) but lower Math Task accuracy (53.8%) compared to MULTIARITH.
- GPQA Physics has high Scientific Principle selection (70%) but only 36.2% accuracy, indicating potential misalignment between factor selection and task performance.
- **Implications**:
- Problem Analysis and Calculation Execution are critical for Math Tasks, while Domain Specific factors are less impactful.
- Science and Logic Tasks require targeted factor selection (e.g., Step Breakdown for BBH Logic-5).
---
### Spatial Grounding
- **Heatmap**: Left side, with color intensity indicating selection rates.
- **Bar Chart**: Right side, with bars aligned to datasets and colored by task type.
- **Legends**: Heatmap’s color scale on the right; bar chart’s legend at the top right.
---
### Final Notes
- All textual elements (labels, axis titles, legends) are transcribed.
- Percentages are approximate, with explicit uncertainty noted (e.g., "~30%").
- No non-English text is present.
