Formal Verification of PieceWise Linear FeedForward Neural Networks
Abstract
We present an approach for the verification of feedforward neural networks in which all nodes have a piecewise linear activation function. Such networks are often used in deep learning and have been shown to be hard to verify for modern satisfiability modulo theory (SMT) and integer linear programming (ILP) solvers. The starting point of our approach is the addition of a global linear approximation of the overall network behavior to the verification problem that helps with SMTlike reasoning over the network behavior. We present a specialized verification algorithm that employs this approximation in a search process in which it infers additional node phases for the nonlinear nodes in the network from partial node phase assignments, similar to unit propagation in classical SAT solving. We also show how to infer additional conflict clauses and safe node fixtures from the results of the analysis steps performed during the search. The resulting approach is evaluated on collision avoidance and handwritten digit recognition case studies.
 Publication:

arXiv eprints
 Pub Date:
 May 2017
 DOI:
 10.48550/arXiv.1705.01320
 arXiv:
 arXiv:1705.01320
 Bibcode:
 2017arXiv170501320E
 Keywords:

 Computer Science  Logic in Computer Science;
 Computer Science  Artificial Intelligence;
 Computer Science  Machine Learning;
 D.2.4;
 I.2.6