用几何方法防止高风险领域中的虚假承诺。
Semantic Geometry for policy-constrained interpretation
- 语义用单位球上的方向表示，证据为观测向量集合，可接受解释为球面凸区域。
- 在多个政策下对金融数据验证，零虚假批准，首次实现大规模验证。
- 适合需要严格合规的AI系统，如金融、医疗决策支持。
我们提出一种政策约束下的语义解释几何框架，可证明杜绝高风险领域中的幻觉承诺。语义意义被表示为单位球上的方向，证据建模为一组见证向量，可接受的解释对应于球面凸区域。政策约束作为定义在同一流形上的显式先验引入，与证据几何分离。解释过程转化为对可接受区域的约束优化，当出现矛盾或违反政策时，拒绝成为拓扑上必然结果。该框架与信息论、贝叶斯推理及层论语义相连，证明其复杂度界为信息论最优。在大规模受监管金融数据上的实证验证表明，在多个政策制度下均实现零幻觉批准，这是首次在规模上达成此类结果。
原文摘要 · Abstract (English)
We present a geometric framework for policy-constrained semantic interpretation that provably prevents hallucinated commitments in high-stakes domains. Semantic meaning is represented as direction on a unit sphere, evidence is modeled as sets of witness vectors, and admissible interpretations correspond to spherical convex regions. Policy constraints are introduced as explicit priors defined over the same manifold, separated from evidence geometry. Interpretation reduces to constrained optimization over admissible regions, with refusal emerging as a topologically necessary outcome under contradiction or policy exclusion. We connect this framework to information theory, Bayesian inference, and sheaf-theoretic semantics, proving that our complexity bounds are information-theoretically optimal. Empirical validation on large scale regulated financial data demonstrates zero hallucinated approvals across multiple policy regimes-the first such result at scale.
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