发表机构
Artificial Intelligence Finance Institute (AIFI)（人工智能金融研究所（AIFI））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出随机词汇演算框架，通过可测变换和随机递归，证明语言模型概率在特定条件下可支持顺序状态更新，并经实验验证其稳定性与覆盖性。
AI 中文摘要
大型语言模型产生依赖于提示词的概率分布，而科学系统则需要能够随着证据到来而更新的有意义状态的不确定性。我们开发了一个可观测框架，用于确定语言衍生的概率何时支持这种顺序状态表示。在理论上，我们定义了上下文语言的类型化可测变换，构建了最小闭包表示，并给出了语义更新唯一存在的充分必要条件。我们界定了不可约非闭包性和累积误差，并在平均压缩条件下证明了概率单纯形上外部随机递归的存在性、唯一性和稳定性。这些结果定义了一种随机词汇演算，而不将内部演算归因于语言模型。在实证上，冻结实验测试了可观测的含义。原始提示条件概率未能通过预设的不变性门控；经过提示特定校准后，一个共同的三状态表示通过了稳定性门控，并覆盖了30条未触及的八步路径中的28条，即名义水平0.90下的0.933。因此，语言概率仅在声明的操作域内验证了闭包性、稳定性和覆盖性后，才支持随机状态。
英文摘要
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 probability simplex. These results define a stochastic lexical calculus without attributing an internal calculus to the language model. Empirically, frozen experiments test the observable implications. Raw prompt-conditioned probabilities fail the prespecified invariance gate; after prompt-specific calibration, a common three-state representation passes the stability gates and covers 28 of 30 untouched eight-step paths, or 0.933 at nominal level 0.90. Accordingly, language probabilities support a stochastic state only conditionally on verified closure, stability and coverage within a declared operating domain.
