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FlexRouter introduces a novel routing framework that utilizes Determinantal Point Processes to explicitly model correlations between Large Language Models, thereby reducing redundancy in selected subsets. By optimizing for answer coverage rather than independent scoring, this approach significantly increases the probability of generating at least one correct response while adaptively managing computational costs without rigid budgets. The method demonstrates superior performance on large-scale benchmarks by effectively balancing model competence with diversity to mitigate shared failure modes.
FlexRouter: Learning Complementary Model Sets for Flexible LLM Routing
arXiv:2609.38585v1 Announce Type: cross Abstract: 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 \textit{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.
Abstract: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 \textit{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.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2609.38585 [cs.LG]
(or arXiv:2609.38585v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.38585 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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