A Reverse-Gold Theorem: Positive-Data Identification by Substrate-Bounded Contrastive Learners
Read the original on arXiv Machine Learning →The paper presents a positive result contrasting Gold’s theorem by showing that a learner equipped with a recursive contrast operator and a bounded-capacity InfoNCE-style scorer can achieve PAC conditional identification from positive data alone. Under a faithfulness condition, the trained scorer ranks almost all positives above any out-of-language perturbation within their orbit, with polynomial sample complexity in the operator’s capacity, orbit size, score bound, and error tolerance. The method constructs negatives internally, avoids global normalization, and extends to a membership classifier and a normalization-free Metropolis–Hastings generator, with instantiations for substitutable context‑free and subregular languages. whyItMatters":"The work demonstrates that contrastive learning can overcome classical limits on language identification by positive data, offering a concrete, sample‑efficient framework for learning structured language classes without external negative examples."
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