Concerned with the reliability of neural networks, researchers have developed verification techniques to prove their robustness.

We thank the reviewers for providing those helpful comments, especially during the challenging time this year. All the empirical results are for small examples (CIF AR-10) raising the question of scalability. We cite previous work on SA T solver support for cardinality constraints (Liffiton et al. [35]) and are happy There are more compact and efficient encodings for encoding cardinality constraints compared to sequential counters. We use sequential counters only for comparison with other BNN verification research (e.g. The main contribution of the paper is the extension of an existing SAT solver (i.e., MiniSAT) to a SAT solver that can Icarte et al. 2019 focuses on generalizability in few-shot learning, which is a different setting than ours.

The paper was assessed as a high quality work by most of the reviewers, contributing fast methods for robustness verification of binary neural networks and training robust binary networks. The points of strong criticism were positioning of the contribution wrt to the constraint programming methods. Since one of the main claimed contributions is the speed-up, it was questioned whether such a speed-up can be obtained by just existing methods / solvers. In particular, L168: "We present the first extension to handle the reified cardinality constraints" was criticized. The arguments of the discussion clarified that in modern pseudo-Boolean solvers the same (resp. Cardinality constraints and more generally linear inequality constraints can be handled natively.