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No Unique Minimizer, No Problem: On the Consistency of Robust Neural Classifiers — arXiv:2608.08489

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.08489
License (as archived): CC0-1.0
Archived: 2026-10-19T09:02:47.910Z
SHA-256 of the archived text: 98b29c8ad23b9867e5e2f854a5c330009a696187fff930cc6ef8cefc9cdc4099
Stable URL of this page: https://metraipolis.com/documento/dc_3ecbdff41573

How to cite

No Unique Minimizer, No Problem: On the Consistency of Robust Neural Classifiers — arXiv:2608.08489 — arXiv (en), https://arxiv.org/abs/2608.08489 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_3ecbdff41573 (Metraipolis archive dc_3ecbdff41573, sha256 98b29c8ad23b9867e5e2f854a5c330009a696187fff930cc6ef8cefc9cdc4099)

BibTeX

@misc{dc3ecbdff41573,
  title = {No Unique Minimizer, No Problem: On the Consistency of Robust Neural Classifiers — arXiv:2608.08489},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.08489},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_3ecbdff41573; sha256 98b29c8ad23b9867e5e2f854a5c330009a696187fff930cc6ef8cefc9cdc4099},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.08489. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Neural network classifiers trained by cross-entropy minimization are highly sensitive to label noise and adversarial contamination. While robust alternatives offer bounded influence and resistance to corruption, their statistical foundations in the deep learning setting are insufficient due to a fundamental difficulty: neural parameterizations are non-identifiable, so the population loss minimizer is an equivalence class of parameters, not a unique point. We develop a consistency theory for robust neural classifiers based on the S-divergence family that requires no identifiability assumption. Casting training as stochastic optimization over a non-identifiable parameter space, we prove that empirical S-divergence minimizers converge to the population-optimal equivalence class under mild regularity conditions, and verify these conditions for three architecture choices. We further establish that limit points of the robust training algorithm are stationary points of the empirical objective. Experiments on vision and language benchmark datasets confirm that S-divergence training maintains clean-data accuracy while exhibiting performance competitive with existing robust methods.

Tema degli esploratori: statistica e scienza dei dati (retro-catalogo arXiv: annunci del 2026-08-11 in stat.ML).
Categorie arXiv: Machine Learning (cs.LG) ; Methodology (stat.ME); Machine Learning (stat.ML).
Pagina del lavoro: https://arxiv.org/abs/2608.08489 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-19T09:01:32.153Z dalla pagina https://arxiv.org/catchup/stat.ML/2026-08-11?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).