arXiv:2607. 11606v1 Announce Type: cross Abstract: We study how little extra information is needed to make adversarial language learning possible.
arXiv:2607. 12443v1 Announce Type: cross Abstract: Motivated by the power of large language models, there has been renewed interest in the Gold-Angluin model of language identification in the limit, with an eye toward variants of the model that might overcome the negative results for its original formulation.
arXiv:2607. 23361v1 Announce Type: cross Abstract: Language generation in the limit is an elegant model introduced by Kleinberg and Mullainathan [KM24] to formally study language generation by an algorithm that learns solely based on example strings.
arXiv:2608. 01320v1 Announce Type: cross Abstract: Language generation in the limit is a theoretical framework for studying how a generator can learn to produce new valid strings from a stream of positive examples.
arXiv:2606. 14688v1 Announce Type: cross Abstract: AI systems coupled to proof assistants now generate formal mathematics at scale, and the gap between what a checker can verify and what a mathematician would value has become the binding constraint.
arXiv:2606. 25777v1 Announce Type: cross Abstract: We initiate a resource-aware theory of \textit{language generation in the limit} under the minimal constraint of space efficiency.
arXiv:2605. 11644v3 Announce Type: replace-cross Abstract: Positive data can show that two tuple occurrences share a successful sentence context without certifying that they are safely interchangeable.
arXiv:2601. 21237v2 Announce Type: replace-cross Abstract: Kleinberg and Mullainathan recently proposed a formal framework for studying the phenomenon of language generation, called language generation in the limit.
The paper studies the problem of language generation in the limit, where a learner must produce valid unseen elements from any exhaustive positive presentation of an unknown infinite language. It establishes that generation is possible precisely when each target language admits a finite positive witness such that all targets activated by any finite sample share an infinite common intersection. The authors introduce a separation-width hierarchy to measure the size of compatible witnesses, showing that every level of the hierarchy occurs and that countable families admit singleton witnesses while more complex families require unbounded finite witnesses. The results are formalized and verified in Lean, with the development available on GitHub.
arXiv:2608. 13433v1 Announce Type: cross Abstract: Transformer-based language models are known to sometimes generalize to sequences longer than seen during training, but we lack a precise characterization of which tasks admit length generalization.
arXiv:2604. 25800v2 Announce Type: replace Abstract: Chain-of-Thought (CoT) has been shown to empirically improve Transformers' performance, and theoretically increase their expressivity to Turing completeness.
arXiv:2601. 08648v2 Announce Type: replace-cross Abstract: Recent results in learning a language in the limit have shown that, although language identification is impossible, language generation is tractable.
arXiv:2511. 02644v2 Announce Type: replace Abstract: We study computable probably approximately correct (CPAC) learning, where learners are required to be computable functions.