Research
Duality for the Adversarial Total Variation
arXiv:2604.18540v1 Announce Type: cross Abstract: Adversarial training of binary classifiers can be reformulated as regularized risk minimization involving a nonlocal total variation. Building on this
arXiv:2604.18540v1 Announce Type: cross Abstract: Adversarial training of binary classifiers can be reformulated as regularized risk minimization involving a nonlocal total variation. Building on this perspective, we establish a characterization of the subdifferential of this total variation using duality techniques. To achieve this, we derive a dual representation of the nonlocal total variation and a related integration of parts formula, involving a nonlocal gradient and divergence. We provide such duality statements both in the space of continuous functions vanishing at infinity on proper metric spaces and for the space of essentially bounded functions on Euclidean domains. Furthermore, under some additional conditions we provide characterizations of the subdifferential in these settings.
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Source: arXiv cs.LG | 2026-04-21