## Line Charts: Early Stopping Step and Loss Trends ### Overview The image contains two line charts. The left chart ("Early Stopping Step") plots early stopping steps against a derived metric involving dataset size and loss. The right chart compares training and test loss across training steps for datasets of varying sizes. Both charts use logarithmic scales and color-coded data series. ### Components/Axes #### Left Chart ("Early Stopping Step"): - **X-axis**: "S_c × [L(N,D) − L(N,∞)]^(-1/α_s)" (log scale, 10³ to 10⁵) - **Y-axis**: "S_stop" (log scale, 10³ to 10⁵) - **Legend**: Located on the right, mapping colors to dataset sizes: - Purple: 21M - Dark blue: 43M - Medium blue: 86M - Teal: 172M - Light teal: 344M - Green: 688M - Yellow: 1.4B - **Trend line**: Red dashed line (approximate equation: y = x) #### Right Chart ("Loss Trends"): - **X-axis**: "Step" (log scale, 10³ to 10⁵) - **Y-axis**: "Loss" (log scale, 2 to 6) - **Lines**: - Solid blue: Test Loss - Dashed blue: Train Loss - **Color gradient**: Right axis maps colors to dataset sizes (same as left chart legend). ### Detailed Analysis #### Left Chart: - Data points (dots) align closely with the red dashed trend line, confirming the relationship: **S_stop ∝ S_c × [L(N,D) − L(N,∞)]^(-1/α_s)**. - Larger datasets (e.g., 1.4B, yellow) have higher S_stop values, while smaller datasets (e.g., 21M, purple) cluster at lower S_stop values. #### Right Chart: - **Test Loss** (solid lines) consistently exceeds **Train Loss** (dashed lines) across all dataset sizes. - Losses decrease sharply at early steps (10³–10⁴) and plateau near step 10⁵. - Larger datasets (yellow) achieve lower loss values than smaller datasets (purple), indicating better generalization. ### Key Observations 1. **Early Stopping Correlation**: The red dashed line in the left chart validates the theoretical relationship between S_stop and dataset size. 2. **Loss Convergence**: All datasets converge to similar loss values at later steps, but larger datasets start with lower loss. 3. **Dataset Size Impact**: Larger datasets (1.4B) outperform smaller ones in both metrics (higher S_stop and lower loss). ### Interpretation - The left chart demonstrates that early stopping steps scale with dataset size and the gap between finite and infinite-sample loss, suggesting adaptive stopping criteria for larger datasets. - The right chart reveals that larger datasets achieve faster and more stable convergence, reducing overfitting (Test Loss ≈ Train Loss at later steps). Smaller datasets show higher variance in loss, indicating instability. - The consistent color coding across both charts allows direct comparison: datasets with higher S_stop (left) also achieve lower loss (right), reinforcing the value of larger datasets in training efficiency.