Efficient LLM Reasoning via Variational Posterior Guidance with Efficiency Awareness

TL;DR

This paper introduces VPG-EA, a variational inference framework that guides large language models towards more efficient reasoning by distilling posterior patterns into the prior policy, significantly improving inference efficiency.

Contribution

It formalizes efficient reasoning as a variational inference problem and proposes a novel dual-stream architecture to transfer posterior efficiency patterns to the prior policy.

Findings

VPG-EA improves efficiency metric epsilon cubed by 8.73% on 1.5B models.

VPG-EA improves efficiency metric epsilon cubed by 12.37% on 7B models.

Experiments demonstrate significant efficiency gains over strong baselines.

Abstract

Although large language models rely on chain-of-thought for complex reasoning, the overthinking phenomenon severely degrades inference efficiency. Existing reinforcement learning methods compress reasoning chains by designing elaborate reward functions, which renders high-quality samples extremely sparse in the exploration space and creates a sampling bottleneck for the prior policy. Inspired by cognitive science, we theoretically prove that a posterior distribution guided by reference answers achieves higher expected utility than the prior distribution, thus capable of breaking through the sampling bottleneck of high-quality samples. However, the posterior distribution is unavailable during inference. To this end, we formalize efficient reasoning as a variational inference problem and introduce an efficiency-aware evidence lower bound as the theoretical foundation. Based on this, we propose the VPG-EA framework. It adopts a parameter-shared dual-stream architecture to instantiate both the posterior distribution and the prior policy; after filtering out pseudo-efficient paths via cross-view evaluation, it unidirectionally transfers the posterior's efficient patterns to the prior policy through variational distillation. Experiments on DeepSeek-R1-Distill-Qwen-1.5B and 7B scales demonstrate that VPG-EA improves the comprehensive efficiency metric epsilon cubed by 8.73% and 12.37% over the strongest baselines on each model size, respectively.