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Recent works have tried to increase the verifiability of adversariallytrained networks by running the attacks over domains larger than the originalperturbations and adding various regularization terms to the objective.However, these algorithms either underperform or require complex and expensivestage-wise training procedures, hindering their practical applicability. Wepresent IBP-R, a novel verified training algorithm that is both simple andeffective. IBP-R induces network verifiability by coupling adversarial attackson enlarged domains with a regularization term, based on inexpensive intervalbound propagation, that minimizes the gap between the non-convex verificationproblem and its approximations. By leveraging recent branch-and-boundframeworks, we show that IBP-R obtains state-of-the-art verifiedrobustness-accuracy trade-offs for small perturbations on CIFAR-10 whiletraining significantly faster than relevant previous work. Additionally, wepresent UPB, a novel branching strategy that, relying on a simple heuristicbased on $\beta$-CROWN, reduces the cost of state-of-the-art branchingalgorithms while yielding splits of comparable quality.

IBP Regularization for Verified Adversarial Robustness via Branch-and-Bound