[2602.23681] ODAR: Principled Adaptive Routing for LLM Reasoning via Active Inference

Computer Science > Artificial Intelligence arXiv:2602.23681 (cs) [Submitted on 27 Feb 2026] 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 View a PDF of the paper titled ODAR: Principled Adaptive Routing for LLM Reasoning via Active Inference, by Siyuan Ma and 8 other authors View PDF HTML (experimental) 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...