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The Geometry of Randomized Smoothing on Feasible Sets — arXiv:2609.39497

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.39497
License (as archived): CC0-1.0
Archived: 2026-10-07T13:46:18.256Z
SHA-256 of the archived text: 26d3066f95f44261df21b79f135303e6ac8f5e2e96946e863f77452dd45439d3
Stable URL of this page: https://metraipolis.com/documento/dc_708cccce48cf

How to cite

The Geometry of Randomized Smoothing on Feasible Sets — arXiv:2609.39497 — arXiv (en), https://arxiv.org/abs/2609.39497 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_708cccce48cf (Metraipolis archive dc_708cccce48cf, sha256 26d3066f95f44261df21b79f135303e6ac8f5e2e96946e863f77452dd45439d3)

BibTeX

@misc{dc708cccce48cf,
  title = {The Geometry of Randomized Smoothing on Feasible Sets — arXiv:2609.39497},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.39497},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_708cccce48cf; sha256 26d3066f95f44261df21b79f135303e6ac8f5e2e96946e863f77452dd45439d3},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.39497. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Randomized smoothing certifies the probability of a fixed output event as the center of Gaussian noise moves. Feasibility or confidence filtering reports label probabilities only among retained proposals, producing a ratio. Its numerator is a fixed Gaussian event mass, while its denominator is the probability of retention and can change with the center. Substituting this ratio into the ordinary smoothing formula can therefore certify a ball that contains a decision boundary. We separate the problem into a geometric question and a certification question. Geometry determines when conditioning preserves Gaussian comparisons. Convex retained sets preserve the full comparison, while general sets require geometric control of the retained law as the center moves. Without such control, conditional probabilities imply no positive universal radius. Joint retention-and-label probabilities always yield a valid certificate for the same filtered predictor. A uniform covariance bound transfers divergence certificates to the retained law and can yield larger radii even when the Gaussian event comparison fails. Both methods admit finite-sample bounds. For a learned image classifier with a training-selected nonconvex filter, conditional Rényi bounds certify more images than joint-mass bounds without additional model evaluations. A released confidence filter exhibits verified label changes inside radii obtained by conditional substitution. An application of adaptive Gaussian composition covers causal finite-horizon executions with history-dependent center shifts under a pathwise energy bound.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-10-01 in cs.LG).
Categorie arXiv: Machine Learning (cs.LG) ; Machine Learning (stat.ML).
Pagina del lavoro: https://arxiv.org/abs/2609.39497 — 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 2026-10-07T13:18:10.400Z dalla pagina https://arxiv.org/catchup/cs.LG/2026-10-01?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).