Research
Contradiction Graphs Determine VC Dimension
arXiv:2605.20434v1 Announce Type: cross Abstract: We study the contradiction graphs associated with binary concept classes. For a class H subseteq {0,1}^X, the order-m contradiction graph G_m(H) has a
arXiv:2605.20434v1 Announce Type: cross Abstract: We study the contradiction graphs associated with binary concept classes. For a class H subseteq {0,1}^X, the order-m contradiction graph G_m(H) has as vertices the H-realizable labeled sequences of length m, with two vertices adjacent when the two sequences assign opposite labels to some common domain point. Our main result is that the single graph G_m(H) determines the threshold predicate VCdim(H)ge m. Consequently, the full sequence (G_m(H))_{m ge 1} determines the exact VC dimension and, in particular, detects finite versus infinite VC dimension, answering a question posed by Alon et al. (2024).
Source: arXiv cs.LG | 2026-05-21