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

2024/08/23 by Ben Batten, Batten, Ben, Yang Zheng +7
Biochemistry, Genetics and Molecular Biology · Computer Science · #Adversarial Robustness in Machine Learning #Artificial Intelligence (cs.AI) #Cell Image Analysis Techniques #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #Machine Learning (cs.LG)

paper · pdf · doi:10.48550/arxiv.2408.13140

openalex publication_date 2024/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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.

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