Salvato in:
| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2502.03792 |
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Sommario:
- We demonstrate that applying an eventual decay to the learning rate (LR) in empirical risk minimization (ERM), where the mean-squared-error loss is minimized using standard gradient descent (GD) for training a two-layer neural network with Lipschitz activation functions, ensures that the resulting network exhibits a high degree of Lipschitz regularity, that is, a small Lipschitz constant. Moreover, we show that this decay does not hinder the convergence rate of the empirical risk, now measured with the Huber loss, toward a critical point of the non-convex empirical risk. From these findings, we derive generalization bounds for two-layer neural networks trained with GD and a decaying LR with a sub-linear dependence on its number of trainable parameters, suggesting that the statistical behaviour of these networks is independent of overparameterization. We validate our theoretical results with a series of toy numerical experiments, where surprisingly, we observe that networks trained with constant step size GD exhibit similar learning and regularity properties to those trained with a decaying LR. This suggests that neural networks trained with standard GD may already be highly regular learners.