arXiv:2606. 23715v1 Announce Type: cross Abstract: A Markov Logic Network (MLN) is a probabilistic relational model used in Statistical Relational Artificial Intelligence for defining a probability distribution on the set of possible worlds with domain $D$ for an arbitrary finite domain $D$.
arXiv:2608. 15798v1 Announce Type: new Abstract: Language models are compared by their held-out per-token cross-entropy risk---the quantity scaling laws are fitted to.
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.
The paper introduces a framework called stochastic lexical calculus that determines when probabilities produced by large language models can be used to represent sequential states in scientific systems. It defines typed measurable transformations of contextual language, constructs a minimal closed representation, and provides necessary and sufficient conditions for unique semantic updates. The authors prove bounds on irreducible nonclosure and accumulated error, and show that under average contraction an external random recursion on a probability simplex is stable and unique. Empirical tests on frozen experiments demonstrate that raw prompt-conditioned probabilities fail an invariance gate, but after prompt-specific calibration a common three-state representation satisfies stability gates and covers 28 of 30 eight-step paths, achieving 0.933 coverage at a nominal 0.90 level.
arXiv:2507. 05972v3 Announce Type: replace-cross Abstract: Pseudoentropy characterizations give quantitatively precise formulations of the relationship between computational hardness and computational randomness.
arXiv:2608. 14004v1 Announce Type: new Abstract: In-context learning is commonly formalized as inference from examples of a function.
Knowledge graphs can guide large language models (LLMs) reasoning, but the graph seen by a system is usually a retrieved, linked, temporally scoped, and incomplete evidence state rather than a complete account of truth. We develop a theoretical perspective on grounding observable LLM trajectories under such incomplete graph evidence.
arXiv:2609.24942v1 Announce Type: new Abstract: A model generalizes outside its training distribution only when it computes a representation structurally equivalent to the generating mechanism, not a...
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: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:2601. 18747v2 Announce Type: replace-cross Abstract: Modern AI agents increasingly rely on search infrastructure to execute complex, neuro-symbolic reasoning workflows.
arXiv:2606. 03655v1 Announce Type: new Abstract: Recent work in defeasible reasoning has seen notions of preferential semantics and entailment in the style of Kraus et al.
arXiv:2606. 12471v2 Announce Type: replace-cross Abstract: Klindt, LeCun, and Balestriero (arXiv:2605.