Formal Verification of Piece-Wise Linear Feed-Forward Neural Networks
This work addresses the verification problem for neural networks in safety-critical domains, but it is incremental as it builds on existing SMT and ILP methods.
The paper tackles the challenge of verifying feed-forward neural networks with piece-wise linear activation functions, which are difficult for existing SMT and ILP solvers, by introducing a global linear approximation and a specialized verification algorithm; it demonstrates effectiveness on collision avoidance and handwritten digit recognition case studies, though no concrete performance numbers are provided.
We present an approach for the verification of feed-forward neural networks in which all nodes have a piece-wise 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 SMT-like 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 non-linear 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.