Investigating whether function composition creates optimization barriers that separate learning epochs for component vs. composed functions.
| Function Family | Mean f MSE | Mean g MSE | Mean Comp MSE | MSE Gap | Sep. Ratio |
|---|---|---|---|---|---|
| Polynomial deg2 | 0.0784 | 0.0871 | 0.0950 | 21.3% | 1.000 |
| Polynomial deg3 | 0.1576 | 0.1723 | 0.1825 | 15.9% | 1.000 |
| ReLU 2-layer | 0.0940 | 0.0966 | 0.1874 | 99.3% | 1.000 |
| ReLU 3-layer | 0.1461 | 0.1398 | 0.2420 | 65.6% | 1.000 |
| Piecewise linear | 0.6739 | 0.6258 | 0.8694 | 29.0% | 1.000 |
| Strategy | poly_deg2 MSE | relu_2layer MSE | poly_deg2 Epochs | relu_2layer Epochs |
|---|---|---|---|---|
| Direct | 0.0988 | 0.1691 | 60.0 | 60.0 |
| Sequential | 0.1465 | 0.2590 | 60.0 | 60.0 |
| Warmstart | 0.0707 | 0.1341 | 57.6 | 60.0 |
| Progressive | 0.1188 | 0.1889 | 60.0 | 60.0 |