  State-of-the-art neural network verifiers are fundamentally based on one of
two paradigms: either encoding the whole verification problem via tight
multi-neuron convex relaxations or applying a Branch-and-Bound (BaB) procedure
leveraging imprecise but fast bounding methods on a large number of easier
subproblems. The former can capture complex multi-neuron dependencies but
sacrifices completeness due to the inherent limitations of convex relaxations.
The latter enables complete verification but becomes increasingly ineffective
on larger and more challenging networks. In this work, we present a novel
complete verifier which combines the strengths of both paradigms: it leverages
multi-neuron relaxations to drastically reduce the number of subproblems
generated during the BaB process and an efficient GPU-based dual optimizer to
solve the remaining ones. An extensive evaluation demonstrates that our
verifier achieves a new state-of-the-art on both established benchmarks as well
as networks with significantly higher accuracy than previously considered. The
latter result (up to 28% certification gains) indicates meaningful progress
towards creating verifiers that can handle practically relevant networks.
