Mini-Batch Robustness Verification of Deep Neural Networks

Neural network image classifiers are ubiquitous in many safety-critical applications. However, they are susceptible to adversarial attacks. To understand their robustness to attacks, many local robustness verifiers have been proposed to analyze ε-balls of inputs. Yet, existing verifiers introduce a long analysis time or lose too much precision, making them less effective for a large set of inputs. In this work, we propose a new approach to local robustness: group local robustness verification. The key idea is to leverage the similarity of the network computations of certain ε-balls to reduce the overall analysis time. We propose BaVerLy, a sound and complete verifier that boosts the local robustness verification of a set of ε-balls by dynamically constructing and verifying mini-batches. BaVerLy adaptively identifies successful mini-batch sizes, accordingly constructs mini-batches of ε-balls that have similar network computations, and verifies them jointly. If a mini-batch is verified, all its ε-balls are proven robust. Otherwise, one ε-ball is suspected as not being robust, guiding the refinement. BaVerLy leverages the analysis results to expedite the analysis of that ε-ball as well as the analysis of the mini-batch with the other ε-balls. We evaluate BaVerLy on fully connected and convolutional networks for MNIST and CIFAR-10. Results show that BaVerLy scales the common one by one verification by 2.3x on average and up to 4.1x, in which case it reduces the total analysis time from 24 hours to 6 hours.