LLM Routing as Reasoning: A MaxSAT View

Computer Science > Artificial Intelligence [Submitted on 13 Mar 2026] LLM Routing as Reasoning: A MaxSAT View Son Nguyen, Xinyuan Liu, Ransalu Senanayake Routing a query through an appropriate LLM is challenging, particularly when user preferences are expressed in natural language and model attributes are only partially observable. We propose a constraint-based interpretation of language-conditioned LLM routing, formulating it as a weighted MaxSAT/MaxSMT problem in which natural language feedback induces hard and soft constraints over model attributes. Under this view, routing corresponds to selecting models that approximately maximize satisfaction of feedback-conditioned clauses. Empirical analysis on a 25-model benchmark shows that language feedback produces near-feasible recommendation sets, while no-feedback scenarios reveal systematic priors. Our results suggest that LLM routing can be understood as structured constraint optimization under language-conditioned preferences. Subjects: Artificial Intelligence (cs.AI) Cite as: arXiv:2603.13612 [cs.AI]   (or arXiv:2603.13612v1 [cs.AI] for this version)   https://doi.org/10.48550/arXiv.2603.13612 Focus to learn more Submission history From: Son Nguyen [view email] [v1] Fri, 13 Mar 2026 21:39:22 UTC (187 KB) Access Paper: HTML (experimental) view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-03 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)