# Efficient LLM Reasoning via Variational Posterior Guidance with Efficiency Awareness

arXiv: https://arxiv.org/abs/2605.11019 · HTML: https://mlsanity.com/paper/2605.11019/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 10 of its 40 references that are in the map.
- First posted on arXiv 10 May 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 10 of 10)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs](https://mlsanity.com/paper/2412.21187/) (2024)
- [RAVR: Reference-Answer-guided Variational Reasoning for Large Language Models](https://mlsanity.com/paper/2510.25206/) (2025)

## Abstract (arXiv)

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.