## Line Chart: 10x10 Maze: Grid Ablation ### Overview The chart visualizes the success rates of different maze-solving strategies across varying numbers of training examples. It compares two baseline methods ("Best Baseline") and two L-ICL variants, each tested with and without a grid structure. Success rates are plotted against training examples (0–240), with shaded regions indicating variability. --- ### Components/Axes - **X-axis**: Training Examples (0, 30, 60, 90, 120, 150, 180, 210, 240) - **Y-axis**: Success Rate (%) (0–50) - **Legend**: - Dashed blue: Best Baseline (With Grid) - Dashed orange: Best Baseline (No Grid) - Solid blue: L-ICL (With Grid) - Solid orange: L-ICL (No Grid) --- ### Detailed Analysis 1. **Best Baseline (With Grid)** - Starts at ~5% success rate at 0 training examples. - Increases steadily to ~45% at 240 examples. - Shaded region (confidence interval) narrows slightly as training progresses. 2. **Best Baseline (No Grid)** - Starts at ~5% and rises to ~35% at 240 examples. - Shaded region widens at lower training examples but stabilizes. 3. **L-ICL (With Grid)** - Begins at ~15% and peaks at ~40% at 240 examples. - Shaded region is the widest, indicating high variability. 4. **L-ICL (No Grid)** - Starts at ~5% and reaches ~35% at 240 examples. - Shaded region remains relatively consistent. --- ### Key Observations - **Grid Impact**: All methods perform significantly better with a grid. For example, Best Baseline (With Grid) achieves 45% vs. 35% without a grid. - **L-ICL Performance**: L-ICL (With Grid) underperforms Best Baseline (With Grid) at 240 examples (40% vs. 45%), suggesting the grid amplifies the effectiveness of simpler baselines. - **Variability**: L-ICL (With Grid) shows the highest uncertainty (widest shaded region), while Best Baseline (With Grid) has the most stable results. - **Convergence**: All methods plateau near 35–45% success rates at 240 examples, indicating diminishing returns with more training. --- ### Interpretation 1. **Grid Ablation Insights**: - The grid structure is critical for success, as all methods show substantial improvements when grids are included. - Best Baseline (With Grid) outperforms L-ICL (With Grid) at scale, implying that simpler heuristics may leverage grid structures more effectively than complex L-ICL models. 2. **L-ICL Limitations**: - L-ICL (With Grid) exhibits higher variability, possibly due to overfitting or sensitivity to grid-specific patterns. - Without a grid, L-ICL performs similarly to Best Baseline (No Grid), suggesting its advantages are grid-dependent. 3. **Practical Implications**: - For grid-based mazes, prioritizing simpler baselines (e.g., Best Baseline) may yield more reliable results than complex L-ICL models. - The grid’s role in structuring the problem space likely reduces the need for advanced reasoning in this context. 4. **Anomalies**: - L-ICL (With Grid) underperforms Best Baseline (With Grid) despite its complexity, highlighting potential inefficiencies in the L-ICL approach for this task. - The shaded regions for L-ICL (With Grid) suggest inconsistent training outcomes, warranting further investigation into model stability.