Contradiction Graphs Determine VC Dimension
Authors: Jesse Campbell, Daniel Ibaibarriaga, Lev Reyzin
Summary
arXiv:2605. 20434v1 Announce Type: new Abstract: We study the contradiction graphs associated with binary concept classes.
Relevance
Read next because Contradiction Graphs Determine VC Dimension overlaps with clean result "Leakage rate is a usable signal for recovering trigger-shaped phrases on Gaperon-1125-1B without knowing the hidden trigger itself (MODERATE confidence)", clean result "Language-mismatch LoRA SFT on Qwen2.5-7B leaks the trained completion language into bystander directives the model was never trained on, absent under same-language SFT (LOW confidence)", clean result "A pretraining-data-poisoned Qwen3-4B backdoor only fires on the exact trigger tokens — paraphrases don't activate it, and base-model similarity to the trigger doesn't predict which inputs fire (MODERATE confidence)". Matching terms: class, full, length. Source: arxiv stat.ML (Machine Learning).
Abstract
arXiv:2605.20434v1 Announce Type: new 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 $\mathrm{VCdim}(H)\ge m$. 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).