## Line Charts: Accuracy of Different Models on Sudoku, Sujiko, and Magic-Square
### Overview
The image contains three line charts comparing the accuracy of four different models (Few-Shot, Logic-LM, PAL, and SymPro-LM) on three different puzzle types: Sudoku, Sujiko, and Magic-Square. The x-axis represents the board size, and the y-axis represents the accuracy in percentage.
### Components/Axes
* **Titles:**
* Chart 1: Sudoku
* Chart 2: Sujiko
* Chart 3: Magic-Square
* **X-Axis:** Board Size
* Sudoku: 4x4, 9x9, 16x16, 25x25
* Sujiko: 3x3, 4x4, 5x5
* Magic-Square: 3x3, 4x4, 5x5
* **Y-Axis:** Accuracy (%)
* Scale: 0 to 100, with gridlines at intervals of 20.
* **Legend (Top-Right):**
* Orange line with circle markers: Few-Shot
* Purple dashed line with square markers: Logic-LM
* Blue dash-dotted line with triangle markers: PAL
* Green dotted line with diamond markers: SymPro-LM
### Detailed Analysis
#### Sudoku Chart
* **Few-Shot (Orange):** Starts at approximately 60% accuracy for 4x4, drops to approximately 5% for 9x9, and remains at 0% for 16x16 and 25x25.
* **Logic-LM (Purple):** Starts at approximately 60% accuracy for 4x4, drops to approximately 5% for 9x9, and remains at 0% for 16x16 and 25x25.
* **PAL (Blue):** Starts at approximately 100% accuracy for 4x4, drops to approximately 60% for 25x25.
* **SymPro-LM (Green):** Maintains 100% accuracy across all board sizes (4x4, 9x9, 16x16, 25x25).
#### Sujiko Chart
* **Few-Shot (Orange):** Starts at approximately 47% accuracy for 3x3, drops to approximately 20% for 4x4, and further to approximately 2% for 5x5.
* **Logic-LM (Purple):** Starts at approximately 68% accuracy for 3x3, drops to approximately 53% for 4x4, and further to approximately 13% for 5x5.
* **PAL (Blue):** Starts at approximately 100% accuracy for 3x3, drops to approximately 80% for 5x5.
* **SymPro-LM (Green):** Maintains 100% accuracy across all board sizes (3x3, 4x4, 5x5).
#### Magic-Square Chart
* **Few-Shot (Orange):** Starts at approximately 20% accuracy for 3x3, drops to 0% for 4x4 and remains at 0% for 5x5.
* **Logic-LM (Purple):** Starts at approximately 67% accuracy for 3x3, drops to approximately 25% for 4x4, and further to approximately 7% for 5x5.
* **PAL (Blue):** Starts at approximately 100% accuracy for 3x3, drops to approximately 0% for 4x4 and remains at 0% for 5x5.
* **SymPro-LM (Green):** Maintains 100% accuracy across all board sizes (3x3, 4x4, 5x5).
### Key Observations
* SymPro-LM consistently achieves 100% accuracy across all puzzle types and board sizes.
* Few-Shot and Logic-LM generally perform worse than PAL and SymPro-LM.
* The accuracy of Few-Shot and Logic-LM decreases significantly as the board size increases for Sudoku.
* PAL's performance varies significantly across puzzle types, performing well on Sudoku but poorly on Magic-Square for larger board sizes.
### Interpretation
The data suggests that SymPro-LM is the most robust model for solving these puzzles, as its accuracy remains consistently high regardless of puzzle type or board size. PAL shows promise but is less consistent. Few-Shot and Logic-LM appear to struggle with larger board sizes, particularly in Sudoku. The relationship between board size and accuracy highlights the challenges these models face in scaling to more complex puzzles. The performance differences across puzzle types suggest that the models may be better suited for certain types of logical reasoning problems than others.
