Efficient Proximal Mapping of the 1-path-norm of Shallow Networks
| Autor: | Latorre, F., Rolland, P., Nadav Hallak, Cevher, V. |
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| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
FOS: Computer and information sciences
nonconvex Computer Science - Machine Learning projection Machine Learning (stat.ML) algorithms Machine Learning (cs.LG) ml-ai Optimization and Control (math.OC) Statistics - Machine Learning FOS: Mathematics minimization optimization Mathematics - Optimization and Control |
| Zdroj: | Scopus-Elsevier |
| 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). ICML 2020. Fabian Latorre, Paul Rolland and Nadav Hallak have contributed equally |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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