### Fast And Effective Robustness Certification

 Authors: Gagandeep Singh ETH Zurich Timon Gehr ETH Zurich Matthew Mirman ETH Zurich Markus Püschel ETH Zurich Martin Vechev DeepCode and ETH Zurich, Switzerland

Introduction:

The authors present a new method and system, called DeepZ, for certifying neural networkrobustness based on abstract interpretation.

Abstract:

We present a new method and system, called DeepZ, for certifying neural networkrobustness based on abstract interpretation. Compared to state-of-the-art automatedverifiers for neural networks, DeepZ: (i) handles ReLU, Tanh and Sigmoid activation functions, (ii) supports feedforward and convolutional architectures, (iii)is significantly more scalable and precise, and (iv) and is sound with respect tofloating point arithmetic. These benefits are due to carefully designed approximations tailored to the setting of neural networks. As an example, DeepZ achieves averification accuracy of 97% on a large network with 88,500 hidden units under$L_{\infty}$ attack with $\epsilon = 0.1$ with an average runtime of 133 seconds.