An Abstraction-Based Framework for Neural Network Verification

Deep neural networks are increasingly being used as controllers for safety-critical systems. Because neural networks are opaque, certifying their correctness is a significant challenge. To address this issue, several approaches have recently been proposed to formally verify them. However, network size is often a bottleneck for such approaches and it can be difficult to apply them to large networks. In this paper, we propose a framework that can enhance neural network verification techniques by using over-approximation to reduce the size of the network - thus making it more amenable to verification. We perform the approximation such that if the property holds for the smaller (abstract) network, it holds for the original as well. The over-approximation may be too coarse, in which case the underlying verification tool might return a spurious counterexample. Under such conditions, we perform counterexample-guided refinement to adjust the approximation, and then repeat the process. Our approach is orthogonal to, and can be integrated with, many existing verification techniques. For evaluation purposes, we integrate it with the recently proposed Marabou framework, and observe a significant improvement in Marabou's performance. Our experiments demonstrate the great potential of our approach for verifying larger neural networks.