← 研踪 PaperTrailarXiv:2604.18540 · v2
Duality for the Adversarial Total Variation
首次提交 2026-04-21 01:34
版本更新 2026-11-06 21:40
雷达观测 2026-11-09 11:19
摘要
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-by-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 separable metric spaces. Furthermore, under some additional conditions we provide characterizations of the subdifferential in these settings.
作者备注：34 pages
观测到的版本
相邻记录可能跳过中间版本；首次发现 v2 及以上也会标为版本更新。
v2 · 2026-11-06 21:40 · 最新观测版本
Duality for the Adversarial Total Variation
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-by-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 separable metric spaces. Furthermore, under some additional conditions we provide characterizations of the subdifferential in these settings.
查看此版本解读 →查看此版本原文 ↗