← Back to all news
arXiv Computation and Language By Matthew F Dixon

Foundations of Stochastic Lexical Calculus: Semantic Descent and Random Dynamics on Probability Simplices

Read the original on arXiv Computation and Language →

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.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Computation and Language.

Related stories

arXiv Statistics ML
Aug 24

Identification and Honest Recovery from Semantic Observation Kernels: Operator Error, Coarsening, and Stability

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.

By Matthew Francis Dixon
llms
More like this →
Hugging Face Trending Papers
Jun 22

The Origins of Stochasticity: Comprehensive Investigations on Uncertainty Quantification for Large Language Models

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.

llmsbenchmarks
More like this →