{
  "abstract": "This paper develops a foundational measure-geometric theory of robustness in machine learning. Robustness is formulated as escape from a retained task state relative to a reference measure on a data-bearing manifold, a perturbation gauge, and an admissible realization mechanism. The theory distinguishes the structural possibility of escape on the reference manifold from its ambient realization under mechanism-dependent observable readouts, while placing both within a unified geometric account. It introduces a mesoscopic organization of escape geometry, through which vulnerable mass, finite-scale morphology, delivered progress, and branch coherence are characterized by explicit laws as linked but non-identical robustness phenomena. By recasting robustness as the geometric formation, organization, realization, and persistence of escape, the theory provides a structural basis for analysis beyond scalar criteria.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33123",
  "author_total": 1,
  "authors": [
    {
      "name": "Cheng-Chao Huang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9zxcm37va1b3j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33123",
  "fulltext_url": null,
  "id": "9zxcm37va1b3j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33123",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Adversarial Robustness in Machine Learning"
    ]
  ],
  "openalex": "W7223920059",
  "pdf_url": "https://arxiv.org/pdf/2610.33123",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9zxcm37va1b3j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:49Z",
      "native_id": "2610.33123",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33123"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "A Measure-Geometric Theory of Robustness in Machine Learning",
  "title_text": "A Measure-Geometric Theory of Robustness in Machine Learning",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:49Z",
  "url": "https://research.draconitic.com/paper/9zxcm37va1b3j",
  "venue": "arXiv",
  "versions": []
}