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:2406. 05335v3 Announce Type: replace-cross Abstract: Generation of text and speech in natural languages can be modeled as a stochastic process.
arXiv:2608. 03588v1 Announce Type: cross Abstract: AI coding agents are stochastic workflows: prompts are interpreted, artifacts are sampled, validators produce observations, and orchestrators commit or repair.
The paper addresses the challenge of extracting reliable posterior uncertainty from probabilistic text generators, such as large language models, which provide phrase-level probabilities that are prompt-dependent and incomplete. It formulates the recovery of the target posterior as a semiparametric inverse problem and introduces honest recovery guarantees that jointly consider calibration error, measurement noise, incomplete probabilities, and weak identification. Simulations and studies on frozen language models validate the method’s coverage and stability, showing how to determine when a semantic measurement can be trusted for inference or when recalibration or abstention is needed.
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: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.
Recent advancements in Large Language Models (LLMs) have enabled sophisticated reasoning and content generation, yet their inherent stochasticity poses significant challenges for ensuring predictive credibility. While traditional uncertainty taxonomy paradigms, such as the dichotomy of aleatoric and epistemic uncertainties, provide conceptual foundations, they often fail to capture the multi-component and multi-stage nature of LLM generation and struggle to evaluate the effectiveness of various Uncertainty Quantification (UQ) methods.
arXiv:2609.16854v1 Announce Type: new Abstract: Probability is fundamental to theories of language comprehension, production, acquisition, and evolution, as well as to large language models. Existing...
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: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. 15448v1 Announce Type: cross Abstract: Large language models increasingly rely on sampling as a driver of their own improvement, making the fidelity of their learned distributions more critical than ever.
arXiv:2607. 20483v1 Announce Type: new Abstract: Constraining the generation of autoregressive large language models (LLMs) is an important component of integrating language models into formal systems.
arXiv:2609.23567v1 Announce Type: cross Abstract: We reconsider the theory of probabilistic formal languages generated by n-gram models and by probabilistic context-free grammars (PCFGs). The expecte...