Formal verification of neural networks is critical for their safe and secure adoption in real-world applications. However, designing a precise and scalable verifier which can handle different activation functions, realistic network architectures and relevant specifications remains an open and difficult challenge. In this paper, we take a major step in addressing this challenge and present a new verification framework, called PRIMA. PRIMA is both (i) general: it handles any non-linear activation function, and (ii) precise: it computes precise convex approximations involving multiple neurons via novel convex hull approximation algorithms that leverage concepts from computational geometry. The algorithms have polynomial complexity, yield fewer constraints, and minimize precision loss. We evaluate the effectiveness of PRIMA on a variety of challenging image classifiers from prior work. Our results show that PRIMA is significantly more precise than state-of-the-art, verifying robustness for up to 14%, 30%, and 34% more images than existing work on ReLU-, Sigmoid-, and Tanh-based networks, respectively. Further, PRIMA enables, for the first time, precise verification of a realistic neural network for autonomous driving within a few minutes.

@misc{müller2021precise, title={PRIMA: Precise and General Neural Network Certification via Multi-Neuron Convex Relaxations}, author={Mark Niklas Müller and Gleb Makarchuk and Gagandeep Singh and Markus Püschel and Martin Vechev}, year={2021}, eprint={2103.03638}, archivePrefix={arXiv}, primaryClass={cs.AI}}