Safety Verification for Neural Networks Based on Set-Boundary Analysis

Neural networks (NNs) are increasingly applied in safety-critical systems such as autonomous vehicles. However, they fragile and often ill-behaved. Consequently, their behaviors should undergo rigorous guarantees before deployment practice. In this paper, we propose a set-boundary reachability method to investigate the safety verification problem of NNs from topological perspective. Given an NN with input set safe set, is determine whether all outputs resulting fall within set. our method, homeomorphism property mainly exploited, which establishes relationship mapping boundaries boundaries. The exploitation facilitates computations via extracting subsets rather than entire thus controlling wrapping effect analysis facilitating reduction computation burdens for verification. exists some widely used invertible NNs. Notable representations residual (i-ResNets) ordinary differential equations (Neural ODEs). For these NNs, only needs perform on boundary that do not feature respect explore establishing local then abandon computations. Finally, examples demonstrate performance proposed method.