LLM Routing as Reasoning: A MaxSAT View

TL;DR

This paper presents a novel approach to routing language models using a MaxSAT framework, interpreting natural language feedback as constraints to optimize model selection.

Contribution

It introduces a constraint-based formulation of LLM routing as a MaxSAT/MaxSMT problem, bridging language feedback with structured model selection.

Findings

Language feedback yields near-feasible model recommendations

No-feedback scenarios reveal underlying priors in model selection

The MaxSAT approach effectively captures language-conditioned preferences

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.