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.
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: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:2607. 29496v1 Announce Type: new Abstract: We study transcript management for fixed, finite-precision causal Transformers.
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 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 introduces the notion of finitely verifiable segmentation, where a finite automaton accepts exactly the segmentations produced by a given policy. It proves that several key decision problems—such as boundary certification, bounded gaps, mask completable generation, and policy equivalence—become decidable for this class, which lies strictly between online‑scannable and regular‑domain policies. The class is closed under common pipeline operations and supports practical implementations like maximal‑munch lexing and WordPiece, with all results accompanied by executable checks.
arXiv:2607. 26988v1 Announce Type: cross Abstract: What types of decision problems can a causally masked, finite-precision transformer solve for inputs of arbitrary length?
arXiv:2607. 15107v1 Announce Type: new Abstract: This paper develops a categorical framework -- Learning in Infinitesimal Non-Compositional Sketches (LINCS) -- as the repair of non-compositionality: failures of diagrams to factor through quotient sketches lifted to the tangent category setting.
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:2603. 25414v4 Announce Type: replace-cross Abstract: A prevailing assumption in machine learning is that model correctness must be enforced after the fact.
arXiv:2607. 11897v1 Announce Type: new Abstract: Linear attention replaces softmax attention's growing KV cache with a fixed recurrent state, but this compression limits exact state tracking and long-context memory.
arXiv:2608. 10288v1 Announce Type: new Abstract: The Large Language Model from Power Law Decoder Representations (PLDR-LLM) and its attention, Power Law Graph Attention (PLGA), replace the fixed bilinear form of scaled dot-product attention (SDPA) with a learned, input-generated bilinear operator $G_{LM}$, built from a positive tensor $A_{LM}$ by elementwise power laws.