A Measure-Geometric Theory of Robustness in Machine Learning
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.
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BibTeX
@misc{huang2026measuregeometric,
title = {{A Measure-Geometric Theory of Robustness in Machine Learning}},
author = {Cheng-Chao Huang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33123},
eprint = {2610.33123},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33123},
}
RIS
TY - UNPB
TI - A Measure-Geometric Theory of Robustness in Machine Learning
AU - Cheng-Chao Huang
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.33123
UR - https://arxiv.org/abs/2610.33123
AB - 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.
ER -