ODAR: Principled Adaptive Routing for LLM Reasoning via Active Inference

• URL: http://arxiv.org/abs/2602.23681v1
• Date: Fri, 27 Feb 2026 05:22:01 GMT
• Title: ODAR: Principled Adaptive Routing for LLM Reasoning via Active Inference
• Authors: Siyuan Ma, Bo Gao, Xiaojun Jia, Simeng Qin, Tianlin Li, Ke Ma, Xiaoshuang Jia, Wenqi Ren, Yang Liu,
• Abstract summary: ODAR-Expert is an adaptive routing framework that optimize the accuracy-efficiency trade-off via principled resource allocation.<n>We show strong and consistent gains, including 98.2% accuracy on MATH and 54.8% on Humanity's Last Exam.
• Score: 60.958331943869126
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The paradigm of large language model (LLM) reasoning is shifting from parameter scaling to test-time compute scaling, yet many existing approaches still rely on uniform brute-force sampling (for example, fixed best-of-N or self-consistency) that is costly, hard to attribute, and can trigger overthinking with diminishing returns. We propose ODAR-Expert, an adaptive routing framework that optimizes the accuracy-efficiency trade-off via principled resource allocation. ODAR uses a difficulty estimator grounded in amortized active inference to dynamically route queries between a heuristic Fast Agent and a deliberative Slow Agent. We further introduce a free-energy-principled, risk-sensitive fusion mechanism that selects answers by minimizing a variational free energy objective, balancing log-likelihood with epistemic uncertainty (varentropy) as a principled alternative to ad hoc voting over heterogeneous candidates. Extensive evaluation across 23 benchmarks shows strong and consistent gains, including 98.2% accuracy on MATH and 54.8% on Humanity's Last Exam (HLE), while improving the compute-accuracy frontier under compute-matched settings. We also validate reproducibility on a fully open-source stack (Llama 4 + DeepSeek), where ODAR surpasses homogeneous sampling strategies while reducing computational costs by 82%. Overall, our results suggest that thinking-optimal scaling requires adaptive resource allocation with free-energy-based decision-making rather than simply increasing test-time compute.

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