## Bar Chart: Effect of RL Fine-Tuning on Game-Specific Performance ### Overview The image is a bar chart comparing the performance (accuracy) of three different methods – Zero-shot, Per-Game-RL, and ALL-Game-RL – across six different logic games: Sudoku, Nonogram, Cryptarithm, Magic Square, Zebra Puzzle, Graph, and Knight & Knaves. The chart visualizes how fine-tuning with reinforcement learning (RL) impacts the performance on these games. ### Components/Axes * **Title:** Effect of RL Fine-Tuning on Game-Specific Performance * **X-axis:** Logic Game (Categories: Sudoku, Nonogram, Cryptarithm, Magic Square, Zebra Puzzle, Graph, Knight & Knaves) * **Y-axis:** Accuracy (Scale: 0.0 to 1.0, with gridlines at intervals of 0.2) * **Legend:** Located at the bottom of the chart. * Zero-shot (Gray) * Per-Game-RL (Orange) * ALL-Game-RL (Blue) ### Detailed Analysis Here's a breakdown of the accuracy for each game and method: * **Sudoku:** * Zero-shot: 0.18 * Per-Game-RL: 0.68 * ALL-Game-RL: 0.96 * **Nonogram:** * Zero-shot: 0.09 * Per-Game-RL: 0.50 * ALL-Game-RL: 0.38 * **Cryptarithm:** * Zero-shot: 0.08 * Per-Game-RL: 0.46 * ALL-Game-RL: 0.13 * **Magic Square:** * Zero-shot: 0.11 * Per-Game-RL: 0.78 * ALL-Game-RL: 0.50 * **Zebra Puzzle:** * Zero-shot: 0.27 * Per-Game-RL: 0.95 * ALL-Game-RL: 0.96 * **Graph:** * Zero-shot: 0.74 * Per-Game-RL: 0.87 * ALL-Game-RL: 0.99 * **Knight & Knaves:** * Zero-shot: 0.34 * Per-Game-RL: 0.93 * ALL-Game-RL: 0.74 ### Key Observations * **ALL-Game-RL generally outperforms Zero-shot:** In most games, the blue bars (ALL-Game-RL) are significantly higher than the gray bars (Zero-shot), indicating that fine-tuning with RL improves performance compared to no fine-tuning. * **Per-Game-RL shows mixed results:** The orange bars (Per-Game-RL) sometimes outperform ALL-Game-RL (e.g., Knight & Knaves), but not always. * **Significant performance variation across games:** The accuracy varies greatly depending on the game, suggesting that the effectiveness of RL fine-tuning is game-dependent. * **Outlier:** For the "Graph" game, the Zero-shot performance is relatively high (0.74) compared to other games. ### Interpretation The chart demonstrates the impact of reinforcement learning (RL) fine-tuning on the performance of AI agents across different logic games. The results suggest that fine-tuning, especially with the ALL-Game-RL approach, generally improves performance compared to a Zero-shot approach. However, the effectiveness of each method varies depending on the specific game. The high Zero-shot performance on the "Graph" game could indicate that the initial model is already well-suited for this type of problem, reducing the need for extensive fine-tuning. The mixed results of Per-Game-RL suggest that fine-tuning on individual games might not always generalize well, and a more comprehensive approach like ALL-Game-RL could be more effective in some cases. Overall, the data highlights the potential benefits of RL fine-tuning for improving AI performance on logic games, but also emphasizes the importance of considering the specific characteristics of each game when choosing a fine-tuning strategy.

\n ## Bar Chart: Effect of RL Fine-Tuning on Game-Specific Performance ### Overview This bar chart compares the accuracy of a model on several logic games under three different training conditions: Zero-shot, Per-Game-RL (Reinforcement Learning), and ALL-Game-RL. The accuracy is measured on a scale from 0.0 to 1.0. The chart displays the performance for Sudoku, Nonogram, Cryptarithm, Magic Square, Zebra Puzzle, Graph, and Knight & Knaves. ### Components/Axes * **Title:** Effect of RL Fine-Tuning on Game-Specific Performance * **X-axis:** Logic Game (Sudoku, Nonogram, Cryptarithm, Magic Square, Zebra Puzzle, Graph, Knight & Knaves) * **Y-axis:** Accuracy (Scale from 0.0 to 1.0) * **Legend:** * Zero-shot (Grey) * Per-Game-RL (Orange) * ALL-Game-RL (Blue) ### Detailed Analysis The chart consists of groups of three bars for each logic game, representing the accuracy achieved under each training condition. **Sudoku:** * Zero-shot: Approximately 0.18 * Per-Game-RL: Approximately 0.68 * ALL-Game-RL: Approximately 0.96 **Nonogram:** * Zero-shot: Approximately 0.09 * Per-Game-RL: Approximately 0.38 * ALL-Game-RL: Approximately 0.50 **Cryptarithm:** * Zero-shot: Approximately 0.08 * Per-Game-RL: Approximately 0.46 * ALL-Game-RL: Approximately 0.13 **Magic Square:** * Zero-shot: Approximately 0.11 * Per-Game-RL: Approximately 0.78 * ALL-Game-RL: Approximately 0.50 **Zebra Puzzle:** * Zero-shot: Approximately 0.27 * Per-Game-RL: Approximately 0.50 * ALL-Game-RL: Approximately 0.95 **Graph:** * Zero-shot: Approximately 0.74 * Per-Game-RL: Approximately 0.87 * ALL-Game-RL: Approximately 0.99 **Knight & Knaves:** * Zero-shot: Approximately 0.34 * Per-Game-RL: Approximately 0.74 * ALL-Game-RL: Approximately 0.93 ### Key Observations * **General Trend:** Across all games, the ALL-Game-RL consistently achieves the highest accuracy, followed by Per-Game-RL, and then Zero-shot. * **Significant Improvement:** RL fine-tuning (both Per-Game and ALL-Game) significantly improves accuracy compared to the Zero-shot baseline for most games. * **Cryptarithm Anomaly:** ALL-Game-RL performs *worse* on Cryptarithm than Zero-shot. * **High Performance:** Sudoku, Graph, and Knight & Knaves show very high accuracy with ALL-Game-RL, approaching 1.0. * **Low Performance:** Nonogram and Cryptarithm consistently have the lowest accuracy scores across all training methods. ### Interpretation The data strongly suggests that Reinforcement Learning fine-tuning is highly effective in improving the performance of the model on these logic games. The ALL-Game-RL strategy, where the model is trained on all games simultaneously, generally outperforms the Per-Game-RL strategy, indicating a benefit from transfer learning between games. The anomaly with Cryptarithm is interesting. It could indicate that the ALL-Game-RL training process negatively interferes with the model's ability to solve Cryptarithm problems, potentially due to conflicting learned patterns. Alternatively, it could be a statistical fluctuation or a limitation of the model's architecture. The varying levels of performance across different games suggest that some games are inherently easier for the model to learn than others. Sudoku, Graph, and Knight & Knaves appear to be relatively straightforward, while Nonogram and Cryptarithm pose greater challenges. The high accuracy achieved on these games with ALL-Game-RL suggests that the model is capable of learning complex reasoning patterns when provided with sufficient training data and a suitable learning strategy.

## Grouped Bar Chart: Effect of RL Fine-Tuning on Game-Specific Performance ### Overview The image is a grouped bar chart comparing the accuracy of three different methods (Zero-shot, Per-Game-RL, and ALL-Game-RL) across seven distinct logic games. The chart demonstrates the impact of reinforcement learning (RL) fine-tuning on performance for each specific game. ### Components/Axes * **Chart Title:** "Effect of RL Fine-Tuning on Game-Specific Performance" (centered at the top). * **Y-Axis:** Labeled "Accuracy". The scale runs from 0.0 to 1.0, with major gridlines at intervals of 0.2 (0.0, 0.2, 0.4, 0.6, 0.8, 1.0). * **X-Axis:** Labeled "Logic Game". It lists seven categories: Sudoku, Nonogram, Cryptarithm, Magic Square, Zebra Puzzle, Graph, and Knight & Knaves. * **Legend:** Positioned at the bottom center of the chart. It defines three data series: * **Gray Bar:** "Zero-shot" * **Orange Bar:** "Per-Game-RL" * **Blue Bar:** "ALL-Game-RL" * **Data Labels:** Each bar has a numerical value displayed directly above it, indicating the precise accuracy score. ### Detailed Analysis The following data is extracted for each game category, following the order of bars from left (Zero-shot) to right (ALL-Game-RL). 1. **Sudoku** * **Zero-shot (Gray):** 0.18 * **Per-Game-RL (Orange):** 0.68 * **ALL-Game-RL (Blue):** 0.96 * **Trend:** A strong, consistent upward trend from Zero-shot to Per-Game-RL to ALL-Game-RL. 2. **Nonogram** * **Zero-shot (Gray):** 0.09 * **Per-Game-RL (Orange):** 0.50 * **ALL-Game-RL (Blue):** 0.38 * **Trend:** Performance improves significantly from Zero-shot to Per-Game-RL, but then decreases for ALL-Game-RL. 3. **Cryptarithm** * **Zero-shot (Gray):** 0.08 * **Per-Game-RL (Orange):** 0.46 * **ALL-Game-RL (Blue):** 0.13 * **Trend:** Similar to Nonogram, a large jump from Zero-shot to Per-Game-RL, followed by a substantial drop for ALL-Game-RL. 4. **Magic Square** * **Zero-shot (Gray):** 0.11 * **Per-Game-RL (Orange):** 0.78 * **ALL-Game-RL (Blue):** 0.50 * **Trend:** A very large increase from Zero-shot to Per-Game-RL, followed by a moderate decrease for ALL-Game-RL. 5. **Zebra Puzzle** * **Zero-shot (Gray):** 0.27 * **Per-Game-RL (Orange):** 0.95 * **ALL-Game-RL (Blue):** 0.96 * **Trend:** A dramatic increase from Zero-shot to Per-Game-RL, with ALL-Game-RL achieving a nearly identical, very high score. 6. **Graph** * **Zero-shot (Gray):** 0.74 * **Per-Game-RL (Orange):** 0.87 * **ALL-Game-RL (Blue):** 0.99 * **Trend:** A steady, consistent upward trend across all three methods, with ALL-Game-RL achieving near-perfect accuracy. 7. **Knight & Knaves** * **Zero-shot (Gray):** 0.34 * **Per-Game-RL (Orange):** 0.93 * **ALL-Game-RL (Blue):** 0.74 * **Trend:** A very large increase from Zero-shot to Per-Game-RL, followed by a notable decrease for ALL-Game-RL. ### Key Observations * **Universal Zero-shot Baseline:** The "Zero-shot" method (gray bars) consistently yields the lowest accuracy across all seven games, ranging from 0.08 (Cryptarithm) to 0.74 (Graph). * **Per-Game-RL is Highly Effective:** The "Per-Game-RL" method (orange bars) provides a massive performance boost over Zero-shot in every single game. It is the top-performing method for three games: Nonogram (0.50), Cryptarithm (0.46), and Magic Square (0.78). * **ALL-Game-RL Performance is Mixed:** The "ALL-Game-RL" method (blue bars) shows variable results. It is the best-performing method for four games: Sudoku (0.96), Zebra Puzzle (0.96), Graph (0.99), and Knight & Knaves (0.74). However, for Nonogram, Cryptarithm, and Magic Square, its performance is lower than the Per-Game-RL method. * **Highest and Lowest Scores:** The highest accuracy on the chart is 0.99 for ALL-Game-RL on the Graph game. The lowest accuracy is 0.08 for Zero-shot on Cryptarithm. * **Notable Outlier - Graph Game:** The "Graph" game has a much higher Zero-shot baseline (0.74) compared to all other games, suggesting it may be inherently easier for the base model to solve without fine-tuning. ### Interpretation The data suggests that reinforcement learning fine-tuning is a powerful technique for improving performance on logic games, as both RL methods dramatically outperform the Zero-shot baseline in all cases. The key insight lies in the comparison between **Per-Game-RL** (specialized training) and **ALL-Game-RL** (generalized training). The results indicate a trade-off: * **Specialization Wins for Certain Games:** For games like Nonogram, Cryptarithm, and Magic Square, specialized training (Per-Game-RL) yields better results. This implies these games may have unique structures or strategies that benefit from focused training, and generalized training might dilute this specificity. * **Generalization Wins for Others:** For Sudoku, Zebra Puzzle, Graph, and Knight & Knaves, the generalized ALL-Game-RL model performs as well or better. This suggests these games may share underlying logical patterns or reasoning skills that transfer well when trained together, allowing the model to leverage a broader knowledge base. The chart effectively demonstrates that there is no one-size-fits-all approach to RL fine-tuning for logic games. The optimal strategy—specialized versus generalized training—depends on the specific characteristics of the game domain. The high performance of Per-Game-RL across the board, however, underscores the critical importance of any form of task-specific fine-tuning over a zero-shot approach.

## Bar Chart: Effect of RL Fine-Tuning on Game-Specific Performance ### Overview The chart compares the accuracy of three RL fine-tuning approaches (Zero-shot, Per-Game-RL, ALL-Game-RL) across seven logic games. Accuracy values range from 0.0 to 1.0, with distinct color-coded bars for each method. ### Components/Axes - **X-axis (Logic Game)**: Sudoku, Nonogram, Cryptarithm, Magic Square, Zebra Puzzle, Graph, Knight & Knaves - **Y-axis (Accuracy)**: 0.0 to 1.0 in increments of 0.2 - **Legend**: - Gray: Zero-shot - Orange: Per-Game-RL - Blue: ALL-Game-RL - **Title**: Positioned at the top center ### Detailed Analysis 1. **Sudoku** - Zero-shot: 0.18 (gray) - Per-Game-RL: 0.68 (orange) - ALL-Game-RL: 0.96 (blue) 2. **Nonogram** - Zero-shot: 0.09 (gray) - Per-Game-RL: 0.50 (orange) - ALL-Game-RL: 0.38 (blue) 3. **Cryptarithm** - Zero-shot: 0.08 (gray) - Per-Game-RL: 0.46 (orange) - ALL-Game-RL: 0.13 (blue) 4. **Magic Square** - Zero-shot: 0.11 (gray) - Per-Game-RL: 0.78 (orange) - ALL-Game-RL: 0.50 (blue) 5. **Zebra Puzzle** - Zero-shot: 0.27 (gray) - Per-Game-RL: 0.95 (orange) - ALL-Game-RL: 0.96 (blue) 6. **Graph** - Zero-shot: 0.74 (gray) - Per-Game-RL: 0.87 (orange) - ALL-Game-RL: 0.99 (blue) 7. **Knight & Knaves** - Zero-shot: 0.34 (gray) - Per-Game-RL: 0.93 (orange) - ALL-Game-RL: 0.74 (blue) ### Key Observations - **ALL-Game-RL** consistently achieves the highest accuracy across all games, with **Graph** (0.99) and **Zebra Puzzle** (0.96) showing near-perfect performance. - **Zero-shot** performs poorly overall, with **Cryptarithm** (0.08) and **Nonogram** (0.09) having the lowest values. - **Per-Game-RL** outperforms Zero-shot in all cases but lags behind ALL-Game-RL in most games (e.g., Sudoku: 0.68 vs. 0.96). - **Zebra Puzzle** and **Graph** show the smallest performance gap between Per-Game-RL and ALL-Game-RL (0.01 and 0.02, respectively). ### Interpretation The data demonstrates that **ALL-Game-RL** significantly outperforms both Zero-shot and Per-Game-RL across all logic games, suggesting that a generalized fine-tuning approach (ALL-Game-RL) is more effective than game-specific tuning (Per-Game-RL) or no tuning (Zero-shot). Notably, **Graph** and **Zebra Puzzle** achieve near-perfect accuracy with ALL-Game-RL, indicating these games may have simpler patterns or more structured data. The stark contrast between Zero-shot and fine-tuned methods highlights the critical role of RL adaptation in improving performance. However, the superior performance of ALL-Game-RL raises questions about whether it overfits to specific game structures or benefits from a more robust training paradigm.