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Lipschitz Bounds and Provably Robust Training by Laplacian Smoothing by Krishnan, Vishaal; Makdah, Abed AlRahman Al; Pasqualetti, Fabio is a scholarly article available to read on EtoBox.

What is Lipschitz Bounds and Provably Robust Training by Laplacian Smoothing about?

In this work we propose a graph-based learning framework to train models with provable robustness to adversarial perturbations. In contrast to regularization-based approaches, we formulate the adversarially robust learning problem as one of loss minimization with a Lipschitz constraint, and show that the saddle point of the associated Lagrangian is characterized by a Poisson equation with weighted Laplace operator. Further, the weighting for the Laplace operator is given by the Lagrange multiplier for the Lipschitz constraint, which modulates the sensitivity of the minimizer to perturbations. We then design a provably robust training scheme using graph-based discretization of the input space and a primal-dual algorithm to converge to the Lagrangian's saddle point. Our analysis establishes a novel connection between elliptic operators with constraint-enforced weighting and adversarial learning. We also study the complementary problem of improving the robustness of minimizers with a margin on their loss, formulated as a loss-constrained minimization problem of the Lipschitz constant. We propose a technique to obtain robustified minimizers, and evaluate fundamental Lipschitz lower bou

Author

Krishnan, Vishaal; Makdah, Abed AlRahman Al; Pasqualetti, Fabio

Published

2020

Language

EN