## Bar Chart: MetaQA 2-Hop Hit@1 Scores (Mean ± Std) for Different N and K ### Overview The chart compares the performance of a retrieval system (MetaQA) across three configurations of candidate retrieval hops (N=1, 2, 3) and three values of K (10, 20, 30). Performance is measured as Hit@1 scores (mean ± standard deviation), with higher scores indicating better performance. ### Components/Axes - **X-axis**: "Number of Hops for Candidate Retrieval (N)" with categories: 1, 2, 3. - **Y-axis**: "Hit@1 Score" scaled from 0.0 to 1.0. - **Legend**: Located in the bottom-right corner, mapping colors to K values: - Light blue: K=10 - Medium blue: K=20 - Dark blue: K=30 - **Error bars**: Vertical lines on top of each bar representing standard deviation. ### Detailed Analysis 1. **N=1 (Single Hop)**: - All K values (10, 20, 30) show nearly identical performance (~0.05–0.07). - Error bars are small (~±0.01), indicating low variability. 2. **N=2 (Two Hops)**: - Scores increase with K: - K=10: ~0.85 (±0.02) - K=20: ~0.88 (±0.01) - K=30: ~0.90 (±0.01) - Highest performance across all configurations. 3. **N=3 (Three Hops)**: - Scores decrease slightly compared to N=2 but remain higher than N=1: - K=10: ~0.75 (±0.02) - K=20: ~0.78 (±0.01) - K=30: ~0.80 (±0.01) - Error bars remain consistent with N=2. ### Key Observations - **K dependency**: Higher K values consistently improve performance across all N. - **Non-linear N effect**: N=2 outperforms both N=1 and N=3, suggesting diminishing returns or overfitting at N=3. - **Error consistency**: Standard deviations are smallest for N=2 and K=30, indicating stable results. ### Interpretation The data demonstrates that increasing K (number of candidates considered) improves retrieval accuracy, but the number of hops (N) has a non-linear relationship with performance. N=2 achieves the optimal balance, likely because it expands candidate diversity without introducing excessive noise. N=1’s low scores suggest insufficient candidate exploration, while N=3’s decline may reflect redundant or conflicting information from additional hops. The minimal error bars across all configurations indicate reliable measurements. This implies that tuning K and N is critical for optimizing 2-hop retrieval systems, with N=2 and K≥20 being the most effective configuration.