Foundations of Stochastic Lexical Calculus: Semantic Descent and Random Dynamics on Probability Simplices
Large language models produce prompt-dependent probabilities over words, whereas scientific systems require uncertainty over meaningful states that can be updated as evidence arrives. We develop an observable framework for determining when language-derived probabilities support such a sequential state representation. Theoretically, we define typed measurable transformations of contextual language, construct a minimal closed representation, and give necessary and sufficient conditions for semantic updates to exist uniquely. We bound irreducible nonclosure and accumulated error, and under average contraction prove existence, uniqueness and stability of an external random recursion on a prob...
| Authors | Matthew F Dixon |
|---|---|
| Primary category | cs.CL |
| Published | 25 July 2026 |
| Last updated at source | 25 July 2026 |
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