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.

Formal Verification of CNN-based Perception Systems

We address the problem of verifying neural-based perception systems implemented by convolutional neural networks. We define a notion of local robustness based on affine and photometric transformations. We show the notion cannot be captured by previously employed notions of robustness. The method proposed is based on reachability analysis for feed-forward neural networks and relies on MILP encodings of both the CNNs and transformations under question. We present an implementation and discuss the experimental results obtained for a CNN trained from the MNIST data set.