[
    {
        "id": "osp-20358",
        "type": "article-journal",
        "title": "FlexRouter: Learning Complementary Model Sets for Flexible LLM Routing",
        "author": [
            {
                "family": "Wei",
                "given": "Wang"
            },
            {
                "family": "Yang",
                "given": "Harry"
            },
            {
                "family": "Yang",
                "given": "Tiankai"
            },
            {
                "family": "Basu",
                "given": "Samyadeep"
            },
            {
                "family": "Chen",
                "given": "Hongjie"
            },
            {
                "family": "Zhao",
                "given": "Andy"
            },
            {
                "family": "Dernoncourt",
                "given": "Franck"
            },
            {
                "family": "Rossi",
                "given": "Ryan A."
            },
            {
                "family": "Eldardiry",
                "given": "Hoda"
            }
        ],
        "URL": "https://omanscience.com/ar/articles/flexrouter-learning-complementary-model-sets-for-flexible-llm-routing",
        "language": "en",
        "issued": {
            "date-parts": [
                [
                    2026
                ]
            ]
        },
        "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."
    }
]