AI 中文总结
探讨可观察语言法则何时支持状态可重现后验概率，提出语义映射方法，保持语言法则非参数性且不使用隐藏模型量。理论上推导多项条件和率等，实证上通过模拟和研究验证相关指标，明确语言概率提供可审计状态测量的条件。
AI 中文摘要
概率文本生成器提供令牌上的条件分布和完整的语言延续，而科学应用通常需要有限状态上的后验概率。大型语言模型就是主要例子：短语概率取决于提示措辞，模型输出的百分比是生成的文本而非状态后验概率。更一般地，我们探讨可观察语言法则何时能支持关于声明状态的可重现后验概率。语义映射对意义等价的延续进行分组；具有参考后验概率的留出案例识别从分组语言概率到状态概率的半参数逆。语言法则保持非参数性且不使用隐藏模型量。本文主要是理论和方法论文并做出多项贡献。理论上，推导了存在性、识别、稳定恢复和顺序更新的条件、集中、渐近和非参数率、截断概率下的识别集以及一致稳定性的极小极大边界。实证方面，定理导向的模拟验证了恢复率、兼容集覆盖率和稳定性门限，两项冻结语言模型研究说明了留出恢复和共形覆盖。结果明确了可观察语言概率何时能提供可审计的状态测量而无需被解释为内部信念。
英文摘要
Probabilistic text generators, such as large language models, assign probabilities to phrases, but consequential decisions require posterior uncertainty over meaningful states. These are not interchangeable: language probabilities depend on the prompt, may be incomplete and need not reliably identify state uncertainty. Without a statistical bridge, fluent responses and numerical confidence are insufficient for inference or governance. We formulate recovery of the target posterior as a semiparametric inverse problem and develop honest recovery guarantees that account jointly for calibration error, measurement noise, incomplete probabilities and weak identification. Simulations demonstrate the predicted coverage and stability behaviour, while two frozen language-model studies demonstrate held-out recovery. The resulting method determines when a semantic measurement can be trusted for inference and when use, review, recalibration or abstention is warranted, providing a statistical foundation for runtime AI governance.
