Verification of Geometric Robustness of Neural Networks via Piecewise Linear Approximation and Lipschitz Optimisation

TL;DR

This paper introduces a novel verification method for neural networks that uses piecewise linear approximation and Lipschitz optimisation to effectively verify robustness against geometric input transformations, outperforming current methods.

Contribution

The paper presents a new verification approach combining sampling, linear approximation, and branch-and-bound Lipschitz optimisation for tighter bounds on geometric transformations.

Findings

Resolves up to 32% more verification cases than existing methods.

Provides tighter over-approximations of input perturbations.

Effective on MNIST and CIFAR10 benchmarks.

Abstract

We address the problem of verifying neural networks against geometric transformations of the input image, including rotation, scaling, shearing, and translation. The proposed method computes provably sound piecewise linear constraints for the pixel values by using sampling and linear approximations in combination with branch-and-bound Lipschitz optimisation. The method obtains provably tighter over-approximations of the perturbation region than the present state-of-the-art. We report results from experiments on a comprehensive set of verification benchmarks on MNIST and CIFAR10. We show that our proposed implementation resolves up to 32% more verification cases than present approaches.