Manifold Regularization for Locally Stable Deep Neural Networks

Authors: Charles Jin, Martin Rinard
Published: 2020-03-09 | Updated: 2020-09-22

Source: https://arxiv.org/abs/2003.04286

PDF: https://arxiv.org/pdf/2003.04286

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Abstract

We apply concepts from manifold regularization to develop new regularization techniques for training locally stable deep neural networks. Our regularizers are based on a sparsification of the graph Laplacian which holds with high probability when the data is sparse in high dimensions, as is common in deep learning. Empirically, our networks exhibit stability in a diverse set of perturbation models, including ℓ₂, ℓ_∞, and Wasserstein-based perturbations; in particular, we achieve 40 against an adaptive PGD attack using ℓ_∞ perturbations of size ϵ = 8/255, and state-of-the-art verified accuracy of 21 perturbation model. Furthermore, our techniques are efficient, incurring overhead on par with two additional parallel forward passes through the network.