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.
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Publication details
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- Open access
- Green open access
Cite this article
APA 7
Wei, W., Yang, H., Yang, T., Basu, S., Chen, H., Zhao, A., Dernoncourt, F., Rossi, R. A., & Eldardiry, H. (2026). FlexRouter: Learning Complementary Model Sets for Flexible LLM Routing. https://omanscience.com/en/articles/flexrouter-learning-complementary-model-sets-for-flexible-llm-routing
MLA 9
Wei, Wang, et al. "FlexRouter: Learning Complementary Model Sets for Flexible LLM Routing." https://omanscience.com/en/articles/flexrouter-learning-complementary-model-sets-for-flexible-llm-routing.
Chicago (author–date)
Wei, Wang, Harry Yang, Tiankai Yang, Samyadeep Basu, Hongjie Chen, Andy Zhao, Franck Dernoncourt, Ryan A. Rossi, and Hoda Eldardiry. 2026. "FlexRouter: Learning Complementary Model Sets for Flexible LLM Routing." https://omanscience.com/en/articles/flexrouter-learning-complementary-model-sets-for-flexible-llm-routing.
Harvard
Wei, W., Yang, H., Yang, T., Basu, S., Chen, H., Zhao, A., Dernoncourt, F., Rossi, R. A. and Eldardiry, H. (2026) 'FlexRouter: Learning Complementary Model Sets for Flexible LLM Routing', Available at: https://omanscience.com/en/articles/flexrouter-learning-complementary-model-sets-for-flexible-llm-routing.
Vancouver
Wei W, Yang H, Yang T, Basu S, Chen H, Zhao A, et al. FlexRouter: Learning Complementary Model Sets for Flexible LLM Routing. https://omanscience.com/en/articles/flexrouter-learning-complementary-model-sets-for-flexible-llm-routing
IEEE
W. Wei, H. Yang, T. Yang, S. Basu, H. Chen, A. Zhao, F. Dernoncourt, R. A. Rossi, and H. Eldardiry, "FlexRouter: Learning Complementary Model Sets for Flexible LLM Routing," https://omanscience.com/en/articles/flexrouter-learning-complementary-model-sets-for-flexible-llm-routing.