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:2511. 02644v2 Announce Type: replace Abstract: We study computable probably approximately correct (CPAC) learning, where learners are required to be computable functions.
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:2606. 28309v1 Announce Type: cross Abstract: Binary classification from positive-only samples is a variant of PAC learning in which the learner receives i.
arXiv:2608. 14004v1 Announce Type: new Abstract: In-context learning is commonly formalized as inference from examples of a function.
arXiv:2607. 19573v1 Announce Type: cross Abstract: Structural generalization has been measured repeatedly by several benchmarks, yet it has never been formally defined.
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.
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:2607. 07423v1 Announce Type: new Abstract: We prove that, in the realizable PAC setting, the sample complexity of exact-trace learning for full autoregressive Chain-of-Thought traces is upper bounded by the standard multiclass rate of the local next-token class, where this rate is governed by the Daniely--Shalev-Shwartz dimension.
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.
arXiv:2608. 10441v1 Announce Type: new Abstract: Many pipelines can pay a per-example cost to acquire an auxiliary, model-derived observation -- an LLM's structured reasoning, a slow oracle, an expensive measurement -- and then must decide when the acquired signal is worth using.
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.