# Semantic Geometry for policy-constrained interpretation

arXiv: https://arxiv.org/abs/2512.14731 · HTML: https://mlsanity.com/paper/2512.14731/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 22 references that are in the map.
- First posted on arXiv 10 Dec 2025.

## Builds on (most cited first, 10 of 10)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [Deep Variational Information Bottleneck](https://mlsanity.com/paper/1612.00410/) (2016)
- [Plug and Play Language Models: A Simple Approach to Controlled Text Generation](https://mlsanity.com/paper/1912.02164/) (2019)
- [CTRL: A Conditional Transformer Language Model for Controllable Generation](https://mlsanity.com/paper/1909.05858/) (2019)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [Recent Advances in Autoencoder-Based Representation Learning](https://mlsanity.com/paper/1812.05069/) (2018)

## Abstract (arXiv)

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.