Efficient proximal mapping of the 1-path-norm of shallow networks

Jul 12, 2020

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We demonstrate two new important properties of the path-norm regularizer for 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, it provides an upper bound on the Lipschitz constant of the network, which is tighter than the trivial layer-wise product of Lipschitz constants, motivating its use for training networks robust to adversarial perturbations. Finally, in practical experiments we show that it provides a better robustness-accuracy trade-off when compared to ℓ_1-norm regularization or training with a layer-wise constrain of the Lipschitz constant.

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The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. ICML is globally renowned for presenting and publishing cutting-edge research on all aspects of machine learning used in closely related areas like artificial intelligence, statistics and data science, as well as important application areas such as machine vision, computational biology, speech recognition, and robotics. ICML is one of the fastest growing artificial intelligence conferences in the world. Participants at ICML span a wide range of backgrounds, from academic and industrial researchers, to entrepreneurs and engineers, to graduate students and postdocs.

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