## Line Graph: Separation between true and false statements across layers ### Overview The graph illustrates the relationship between between-class variance and within-class variance across 26 layers (0-25) for four categories: cities, neg_cities, sp_en_trans, and neg_sp_en_trans. The y-axis represents the ratio of between-class variance to within-class variance, while the x-axis represents layer depth. ### Components/Axes - **X-axis (Layer)**: Integer scale from 0 to 25 - **Y-axis (Between class variance / within-class variance)**: Continuous scale from 0.0 to 0.8 - **Legend**: Located in top-right corner with four color-coded categories: - Blue: cities - Orange: neg_cities - Green: sp_en_trans - Red: neg_sp_en_trans ### Detailed Analysis 1. **neg_cities (orange line)**: - Peaks at approximately 0.8 between-class variance ratio at layer 12 - Sharp decline after layer 12, reaching ~0.15 by layer 25 - Steepest ascent between layers 5-10 2. **neg_sp_en_trans (red line)**: - Peaks at ~0.55 between-class variance at layer 11 - Gradual decline to ~0.1 by layer 25 - Slight plateau between layers 15-20 3. **cities (blue line)**: - Peaks at ~0.3 between-class variance at layer 11 - Gradual decline to ~0.05 by layer 25 - Smoother curve compared to negated categories 4. **sp_en_trans (green line)**: - Peaks at ~0.35 between-class variance at layer 12 - Gradual decline to ~0.02 by layer 25 - Most gradual overall trajectory ### Key Observations - Negated categories (neg_cities, neg_sp_en_trans) consistently show higher between-class variance ratios than their non-negated counterparts - All lines follow a similar "rise-peak-fall" pattern, suggesting diminishing discriminative power in deeper layers - neg_cities demonstrates the most pronounced separation between classes (highest peak) - sp_en_trans shows the most gradual decline after its peak - All categories converge toward similar low values (~0.05-0.1) by layer 25 ### Interpretation The data suggests that negated categories (neg_cities, neg_sp_en_trans) maintain stronger class separation across layers compared to their non-negated counterparts. This could indicate that: 1. False statements (negated categories) are more easily distinguishable by the model's representations 2. The model's discriminative power for true statements (cities, sp_en_trans) diminishes more rapidly in deeper layers 3. Layer 11-12 represents an optimal depth for distinguishing negated categories, while layer 12 is optimal for sp_en_trans The consistent peak patterns across all lines suggest a systematic relationship between layer depth and class separation capability, with negated categories maintaining advantages throughout the network architecture.