LLM Routing as Reasoning: A MaxSAT View

2026-03-13

AI Summary

This study addresses the problem of selecting an appropriate large language model (LLM) for a given query when user preferences are expressed in natural language and model attributes are only partially observable. The work proposes a novel formulation of LLM routing as a weighted MaxSAT/MaxSMT constraint optimization problem grounded in natural language feedback. By translating linguistic feedback into hard and soft logical constraints, the approach leverages formal reasoning to identify the optimal model. Integrating natural language understanding with structured constraint satisfaction, the method is evaluated on a benchmark comprising 25 LLMs. Results demonstrate that, when feedback is available, it yields near-optimal model recommendations; even in the absence of explicit feedback, it effectively uncovers systematic prior preferences.

Technology Category

Planning, Routing, and Scheduling: Planning with Language ModelsNatural Language Processing: (Large) Language ModelsMachine Learning: Large Multimodal Models (LMMs)

Application Category

User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendationSearch and Retrieval-Augmented AI: Large language models for searchSemantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

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.

Problem

• LLM routing
• natural language preferences
• model selection
• constraint optimization
• MaxSAT

Innovation

• LLM routing
• MaxSAT
• constraint-based reasoning
• natural language feedback
• model selection