A Convex Relaxation Barrier to Tight Robustness Verification of Neural Networks
This work addresses the challenge of efficiently verifying neural network robustness for security-critical applications, but it is incremental as it builds on existing convex relaxation methods without achieving major breakthroughs.
The paper tackles the problem of verifying neural network robustness against adversarial attacks by unifying existing LP-relaxed verifiers under a general convex relaxation framework and proving strong duality under mild conditions. Through large-scale experiments (over 22 CPU-years), it finds that the exact solution within this framework does not significantly improve verification tightness for networks trained on MNIST and CIFAR, suggesting an inherent barrier to tight verification for this class of methods.
Verification of neural networks enables us to gauge their robustness against adversarial attacks. Verification algorithms fall into two categories: exact verifiers that run in exponential time and relaxed verifiers that are efficient but incomplete. In this paper, we unify all existing LP-relaxed verifiers, to the best of our knowledge, under a general convex relaxation framework. This framework works for neural networks with diverse architectures and nonlinearities and covers both primal and dual views of robustness verification. We further prove strong duality between the primal and dual problems under very mild conditions. Next, we perform large-scale experiments, amounting to more than 22 CPU-years, to obtain exact solution to the convex-relaxed problem that is optimal within our framework for ReLU networks. We find the exact solution does not significantly improve upon the gap between PGD and existing relaxed verifiers for various networks trained normally or robustly on MNIST and CIFAR datasets. Our results suggest there is an inherent barrier to tight verification for the large class of methods captured by our framework. We discuss possible causes of this barrier and potential future directions for bypassing it. Our code and trained models are available at http://github.com/Hadisalman/robust-verify-benchmark .