# Conflict-Free Policy Languages for Probabilistic ML Predicates: A Framework and Case Study with the Semantic Router DSL

arXiv: https://arxiv.org/abs/2603.18174 · HTML: https://mlsanity.com/paper/2603.18174/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 20 references that are in the map.
- First posted on arXiv 18 Mar 2026.

## Builds on (most cited first, 5 of 5)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [RouteLLM: Learning to Route LLMs with Preference Data](https://mlsanity.com/paper/2406.18665/) (2024)
- [Hybrid LLM: Cost-Efficient and Quality-Aware Query Routing](https://mlsanity.com/paper/2404.14618/) (2024)
- [Efficient Few-Shot Learning Without Prompts](https://mlsanity.com/paper/2209.11055/) (2022)
- [Coherent Hierarchical Multi-Label Classification Networks](https://mlsanity.com/paper/2010.10151/) (2020)

## Built on by (most cited first, 2 of 2)

- [From Inference Routing to Agent Orchestration: Declarative Policy Compilation with Cross-Layer Verification](https://mlsanity.com/paper/2603.27299/) (2026)
- [The Workload-Router-Pool Architecture for LLM Inference Optimization: A Vision Paper from the vLLM Semantic Router Project](https://mlsanity.com/paper/2603.21354/) (2026)

## Abstract (arXiv)

Conflict detection in policy languages is a solved problem -- as long as every rule condition is a crisp Boolean predicate. BDDs, SMT solvers, and NetKAT all exploit that assumption. But a growing class of routing and access-control systems base their decisions on probabilistic ML signals: embedding similarities, domain classifiers, complexity estimators. Two such signals, declared over categories the author intended to be disjoint, can both clear their thresholds on the same query and silently route it to the wrong model. Nothing in the compiler warns about this. We characterize the problem as a three-level decidability hierarchy -- crisp conflicts are decidable via SAT, embedding conflicts reduce to spherical cap intersection, and classifier conflicts are undecidable without distributional knowledge -- and show that for the embedding case, which dominates in practice, replacing independent thresholding with a temperature-scaled softmax partitions the embedding space into Voronoi regions where co-firing is impossible. No model retraining is needed. We implement the detection and prevention mechanisms in the Semantic Router DSL, a production routing language for LLM inference, and discuss how the same ideas apply to semantic RBAC and API gateway policy.