ODAR: Principled Adaptive Routing for LLM Reasoning via Active Inference

2026-02-27

AI Summary

This work addresses the high computational cost, attribution ambiguity, and overthinking inherent in uniform brute-force sampling during large language model inference. To overcome these limitations, the authors propose ODAR-Expert, an adaptive routing framework that dynamically assesses query difficulty via amortized active inference and routes requests to either fast or slow reasoning agents accordingly. The framework integrates a risk-sensitive free energy minimization mechanism to fuse agent outputs, leveraging varentropy-based uncertainty quantification and heterogeneous agent policies. Evaluated across 23 benchmarks, ODAR-Expert achieves Pareto-optimal trade-offs between accuracy and efficiency—attaining 98.2% on MATH and 54.8% on HLE—while reducing computational costs by 82% under open-source stacks, substantially outperforming homogeneous sampling approaches.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Planning, Routing, and Scheduling: Planning with Language Models
• Machine Learning: Mixture of Experts (MoE)

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

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.

Problem

• LLM reasoning
• test-time compute scaling
• adaptive routing
• resource allocation
• overthinking

Innovation

• adaptive routing
• active inference
• free energy principle
• epistemic uncertainty
• compute-efficient LLM reasoning