Efficient Proximal Mapping of the 1-path-norm of Shallow Networks

Autor:	Latorre, Fabian, Rolland, Paul, Hallak, Nadav, Cevher, Volkan
Rok vydání:	2020
Předmět:	Computer Science - Machine Learning Mathematics - Optimization and Control Statistics - Machine Learning
Druh dokumentu:	Working Paper
Popis:	We demonstrate two new important properties of the 1-path-norm of shallow neural networks. First, despite its non-smoothness and non-convexity it allows a closed form proximal operator which can be efficiently computed, allowing the use of stochastic proximal-gradient-type methods for regularized empirical risk minimization. Second, when the activation functions is differentiable, it provides an upper bound on the Lipschitz constant of the network. Such bound is tighter than the trivial layer-wise product of Lipschitz constants, motivating its use for training networks robust to adversarial perturbations. In practical experiments we illustrate the advantages of using the proximal mapping and we compare the robustness-accuracy trade-off induced by the 1-path-norm, L1-norm and layer-wise constraints on the Lipschitz constant (Parseval networks). Comment: ICML 2020. Fabian Latorre, Paul Rolland and Nadav Hallak have contributed equally
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2007.01003 Zobrazit plný text záznamu View this record from Arxiv