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arXiv · 2603.13612

LLM Routing as Reasoning: A MaxSAT View

Son Nguyen·Xinyuan Liu·Ransalu Senanayake
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Abstract

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.

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Son Nguyen, Xinyuan Liu, Ransalu Senanayake. 2026-03-13. LLM Routing as Reasoning: A MaxSAT View. https://arxiv.org/abs/2603.13612

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