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:2605. 11644v2 Announce Type: replace-cross Abstract: We study positive-data learning of languages admitting reduced working binary linear nondeleting multiple context-free grammar presentations of bounded fan-out.
arXiv:2608. 14004v1 Announce Type: new Abstract: In-context learning is commonly formalized as inference from examples of a function.
Gold's theorem shows that no learner can identify an arbitrary language in a superfinite class from positive presentations alone. We prove a positive result of a different shape. Fix an innate \emph{r...
The paper investigates exact factorization and canonical presentations of languages relative to a fixed finite‑monoid observation. It shows that unique factorization does not guarantee a finite relative presentation property (FRP) by presenting a 36‑element quotient with infinite valid prime‑return rules, and introduces the stronger finite‑state relative presentation property (FSRP). The authors further define prime‑target left‑division determinism (PTLD), prove its implications for factorization and rule bounds, and provide efficient learning algorithms for the canonical PTLD presentation and FSRP controller.
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."
The paper argues that Large Language Models (LLMs) do not function as Solomonoff induction estimators because their training objectives—cross‑entropy, negative log‑likelihood, and next‑token prediction—optimize fit to a supplied conditional distribution rather than a program‑weighted universal mixture. It further contends that additional computation alone does not transform these models into optimal predictors without external hyper‑parameter or architectural changes. The authors suggest that neurosymbolic machine learning, exemplified by models such as Fable and Astra, represents a shift toward symbolic model synthesis, moving beyond purely statistical LLMs.
arXiv:2601.05280v4 Announce Type: replace-cross Abstract: On the one hand, the question of whether Large Language Models (LLMs) are Solomonoff induction estimators has become an explicit question at...
arXiv:2606. 07623v1 Announce Type: new Abstract: This paper develops a model-theoretic framework for verifying context-conditioned language-model behavior by replacing benchmark labels with finite semantic certificates.
arXiv:2606. 16541v1 Announce Type: new Abstract: Autoformalization, translating natural-language mathematics into formal proof assistants, is bottlenecked not by translation fluency but by \emph{faithfulness}: a formal statement can typecheck and be provable, yet still encode a different theorem than the source intended.
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:2607. 18305v1 Announce Type: cross Abstract: Some limits on what language models know are not gaps in data coverage but structural properties of learning from text.
arXiv:2601. 05280v3 Announce Type: replace-cross Abstract: On the one hand, the question of whether large language models (LLMs) are Solomonoff induction estimators has become an explicit question at the intersection of Algorithmic Information Theory (AIT) and Machine Learning (ML) of great interest.