Efficient Bi-Directional Verification of ReLU Networks via Quadratic Programming

Neural networks are known to be sensitive to adversarial perturbations. To investigate this undesired behavior we consider the problem of computing the distance to the decision boundary (DtDB) from a given sample for a deep NN classifier. In this work we present an iterative procedure where in each step we solve a convex quadratic programming (QP) task. Solving the single initial QP already results in a lower bound on the DtDB and can be used as a robustness certificate of the classifier around a given sample. In contrast to currently known approaches our method also provides upper bounds used as a measure of quality for the certificate. We show that our approach provides better or competitive results in comparison with a wide range of existing techniques.