Optimized Symbolic Interval Propagation for Neural Network Verification

Abstract: Neural networks are increasingly applied in safety critical domains, their verification thus is gaining importance. A large class of recent algorithms for proving input-output relations of feed-forward neural networks are based on linear relaxations and symbolic interval propagation. However, due to variable dependencies, the approximations deteriorate with increasing depth of the network. In this paper we present DPNeurifyFV, a novel branch-and-bound solver for ReLU networks with low dimensional input-space that is based on symbolic interval propagation with fresh variables and input-splitting. A new heuristic for choosing the fresh variables allows to ameliorate the dependency problem, while our novel splitting heuristic, in combination with several other improvements, speeds up the branch-and-bound procedure. We evaluate our approach on the airborne collision avoidance networks ACAS Xu and demonstrate runtime improvements compared to state-of-the-art tools.