Dynamic Back-Substitution in Bound-Propagation-Based Neural Network Verification

Abstract We improve the efficacy of bound-propagation-based neural network verification by reducing the computational effort required by state-of-the-art propagation methods without incurring any loss in precision. We propose a method that infers the stability of ReLU nodes at every step of the back-substitution process, thereby dynamically simplifying the coefficient matrix of the symbolic bounding equations. We develop a heuristic for the effective application of the method and discuss its evaluation on common benchmarks where we show significant improvements in bound propagation times.