Duality for the Adversarial Total Variation
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914492539994112 |
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| author | Bungert, Leon Schmitt, Lucas |
| author_facet | Bungert, Leon Schmitt, Lucas |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_18540 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Duality for the Adversarial Total Variation Bungert, Leon Schmitt, Lucas Analysis of PDEs Machine Learning Functional Analysis Optimization and Control 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. |
| title | Duality for the Adversarial Total Variation |
| topic | Analysis of PDEs Machine Learning Functional Analysis Optimization and Control |
| url | https://arxiv.org/abs/2604.18540 |