Year: 2025
Type: article
Abstract: In recent years, there has been significant interest in the effect of different types of adversarial perturbations in data classification problems. Many of these models incorporate the adversarial power, which is an important parameter with an associated trade-off between accuracy and robustness. This work considers a general framework for adversarially perturbed classification problems, in a large data or population-level limit. In such a regime, we demonstrate that as adversarial strength goes to zero that optimal classifiers converge to the Bayes classifier in the Hausdorff distance. This significantly strengthens previous results, which generally focus on $L^1$ -type convergence. The main argument relies upon direct geometric comparisons and is inspired by techniques from geometric measure theory.
Authors: Rachel Morris, Ryan Murray
Institution: North Carolina State University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,550
Funder: National Science Foundation
OpenAlex ID: W4416598291