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

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. A feature of the method is that it obtains tighter over-approximations of the perturbation region than the present state-of-the-art. We report results from experiments on a comprehensive set of benchmarks. We show that our proposed implementation resolves more verification cases than present approaches while being more computationally efficient.