mlsanityData to 14 Oct 2026

Provable defenses against adversarial examples via the convex outer adversarial polytope

arXiv 1711.00851 ↗First posted 2 Nov 2017cs.LG cs.AI math.OCcited by 567

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Abstract (arXiv)

We propose a method to learn deep ReLU-based classifiers that are provably robust against norm-bounded adversarial perturbations on the training data. For previously unseen examples, the approach is guaranteed to detect all adversarial examples, though it may flag some non-adversarial examples as well. The basic idea is to consider a convex outer approximation of the set of activations reachable through a norm-bounded perturbation, and we develop a robust optimization procedure that minimizes the worst case loss over this outer region (via a linear program). Crucially, we show that the dual problem to this linear program can be represented itself as a deep network similar to the backpropagation network, leading to very efficient optimization approaches that produce guaranteed bounds on the robust loss. The end result is that by executing a few more forward and backward passes through a slightly modified version of the original network (though possibly with much larger batch sizes), we can learn a classifier that is provably robust to any norm-bounded adversarial attack. We illustrate the approach on a number of tasks to train classifiers with robust adversarial guarantees (e.g. for MNIST, we produce a convolutional classifier that provably has less than 5.8% test error for any adversarial attack with bounded ℓ_∞ norm less than ε = 0.1), and code for all experiments in the paper is available at https://github.com/locuslab/convexadversarial.

Key facts. Cited by 567 papers in the map (data through 14 Oct 2026). First posted on arXiv 2 Nov 2017.

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Citing papers per year: 2021: 172; 2022: 133; 2023: 107; 2024: 74; 2025: 37; 2026: 44.

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