FlexRouter: Learning Complementary Model Sets for Flexible LLM Routing

Hugging Face Daily Papers Papers
llm-routing mixture-of-experts determinantal-point-processes model-selection inference-efficiency

Summary

FlexRouter proposes a coverage-oriented LLM routing framework that uses Determinantal Point Processes to model complementarity among models, maximizing the probability that at least one selected model answers correctly while avoiding redundant selections and fixed budgets.

Existing Large Language Model (LLM) routing methods score LLMs independently to select top-k models. However, this ignores model correlations and enforces a rigid computational budget. Consequently, routers often select redundant models that share failure modes, limiting the overall probability of success. To address this, we propose FlexRouter, a routing framework that explicitly models model complementarity. FlexRouter optimizes for answer coverage, maximizing the probability that at least one selected model yields a correct response. This objective aligns with practical inference pipelines where multiple candidate outputs are generated and a downstream verifier or user selects the final one. We formulate routing as a coverage-oriented subset selection problem and model the routing policy using Determinantal Point Processes (DPPs), which naturally capture both model competence and redundancy. To directly optimize coverage without requiring a ground-truth target subset, we introduce a training objective based on marginalizing over failure sets. During inference, we employ a greedy strategy based on marginal log-determinant gains, enabling the router to adaptively determine subset sizes without a predefined budget. Extensive experiments on the large-scale RouterEval benchmark demonstrate that our proposed FlexRouter achieves higher coverage with lower redundancy across both in-domain and out-of-domain tasks than strong baselines while maintaining flexible inference cost.
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Source: https://huggingface.co/papers/2609.38585

Abstract

ExistingLargeLanguageModel(LLM)routingmethodsscoreLLMsindependentlytoselecttop-kmodels.However,thisignoresmodelcorrelationsandenforcesarigidcomputationalbudget.Consequently,routersoftenselectredundantmodelsthatsharefailuremodes,limitingtheoverallprobabilityofsuccess.Toaddressthis,weproposeFlexRouter,aroutingframeworkthatexplicitlymodelsmodelcomplementarity.FlexRouteroptimizesforanswercoverage,maximizingtheprobabilitythatatleastoneselectedmodelyieldsacorrectresponse.Thisobjectivealignswithpracticalinferencepipelineswheremultiplecandidateoutputsaregeneratedandadownstreamverifieroruserselectsthefinalone.Weformulateroutingasacoverage-orientedsubsetselectionproblemandmodeltheroutingpolicyusingDeterminantalPointProcesses(DPPs),whichnaturallycapturebothmodelcompetenceandredundancy.Todirectlyoptimizecoveragewithoutrequiringaground-truthtargetsubset,weintroduceatrainingobjectivebasedonmarginalizingoverfailuresets.Duringinference,weemployagreedystrategybasedonmarginallog-determinantgains,enablingtheroutertoadaptivelydeterminesubsetsizeswithoutapredefinedbudget.Extensiveexperimentsonthelarge-scaleRouterEvalbenchmarkdemonstratethatourproposedFlexRouterachieveshighercoveragewithlowerredundancyacrossbothin-domainandout-of-domaintasksthanstrongbaselineswhilemaintainingflexibleinferencecost.

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