The coupling effect of Lipschitz regularization in neural networks

Nicolas Couellan (1, 2)

1 ENAC - Ecole Nationale de l'Aviation Civile
2 IMT - Institut de Mathématiques de Toulouse UMR5219

We investigate the robustness of feed-forward neural networks when input data are subject to random uncertainties. More specifically, we consider regularization of the network by its Lipschitz constant and emphasize its role. We highlight the fact that this regularization is not only a way to control the magnitude of the weights but has also a coupling effect on the network weights across the layers. We claim and show evidence on regression and classification datasets that this coupling effect brings a trade-of between robustness and expressiveness of the network. This suggests that Lipschitz regularization should be carefully implemented so as to maintain coupling across layers.

Domaines: Optimisation et contrôle [math.OC]; Apprentissage [cs.LG]

Nicolas Couellan. The coupling effect of Lipschitz regularization in neural networks. SN Computer Science, 2021, 2 (2), pp.113. ⟨10.1007/s42979-021-00514-x⟩. ⟨hal-02090498⟩