Contradiction Graphs Determine VC Dimension
机器学习
2026-05-21 v1 离散数学
机器学习
摘要
We study the contradiction graphs associated with binary concept classes. For a class , the order- contradiction graph has as vertices the -realizable labeled sequences of length , with two vertices adjacent when the two sequences assign opposite labels to some common domain point. Our main result is that the single graph determines the threshold predicate . Consequently, the full sequence determines the exact VC dimension and, in particular, detects finite versus infinite VC dimension, answering a question posed by Alon et al. (2024).
引用
@article{arxiv.2605.20434,
title = {Contradiction Graphs Determine VC Dimension},
author = {Jesse Campbell and Daniel Ibaibarriaga and Lev Reyzin},
journal= {arXiv preprint arXiv:2605.20434},
year = {2026}
}