Dynamical Decoupling of Generalization and Overfitting in Large Two-Layer Networks

• URL: http://arxiv.org/abs/2502.21269v3
• Date: Wed, 29 Oct 2025 17:46:23 GMT
• Title: Dynamical Decoupling of Generalization and Overfitting in Large Two-Layer Networks
• Authors: Andrea Montanari, Pierfrancesco Urbani,
• Abstract summary: We study the learning dynamics of large two-layer neural networks via dynamical mean field theory.<n>For large network width $m$, and large number of samples per input dimension $n/d$, the training dynamics exhibits a separation of timescales.
• Score: 10.591718074748895
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Understanding the inductive bias and generalization properties of large overparametrized machine learning models requires to characterize the dynamics of the training algorithm. We study the learning dynamics of large two-layer neural networks via dynamical mean field theory, a well established technique of non-equilibrium statistical physics. We show that, for large network width $m$, and large number of samples per input dimension $n/d$, the training dynamics exhibits a separation of timescales which implies: $(i)$~The emergence of a slow time scale associated with the growth in Gaussian/Rademacher complexity of the network; $(ii)$~Inductive bias towards small complexity if the initialization has small enough complexity; $(iii)$~A dynamical decoupling between feature learning and overfitting regimes; $(iv)$~A non-monotone behavior of the test error, associated `feature unlearning' regime at large times.

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