Scalable Power Sampling: Unlocking Efficient, Training-Free Reasoning for LLMs via Distribution Sharpening
Reinforcement learning (RL) post-training is a dominant approach for improving the reasoning performance of large language models (LLMs), yet growing evidence suggests that its gains arise primarily from distribution sharpening rather than the acquisition of new capabilities. Recent work has shown that sampling from the power distribution of LLMs using Markov chain Monte Carlo (MCMC) can recover performance comparable to RL post-training without relying on external rewards; however, the high computational cost of MCMC makes such approaches impractical for widespread adoption. In this work, we propose a theoretically grounded alternative that eliminates the need for iterative MCMC. We derive a novel formulation showing that the global power distribution can be approximated by a token-level scaled low-temperature one, where the scaling factor captures future trajectory quality. Leveraging this insight, we introduce a training-free and verifier-free algorithm that sharpens the base model's generative distribution autoregressively. Empirically, we evaluate our method on math, QA, and code tasks across four LLMs, and show that our method matches or surpasses one-shot GRPO without relying on any external rewards, while reducing inference latency by over 10x compared to MCMC-based sampling.
697c85936676f93322706019
Xiaotong Ji
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2026-01-30T13:31:30.083Z
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xiaotong
xtongji
user
xtongji
697c85936676f9332270601a
Rasul Tutunov
697c85936676f9332270601b
Matthieu Zimmer
697c85936676f9332270601c
Haitham Bou Ammar
Scalable Power Sampling: Unlocking Efficient, Training-Free Reasoning for LLMs via Distribution Sharpening
Reinforcement learning (RL) post-training is a dominant approach for improving the reasoning performance of large language models (LLMs), yet growing evidence suggests that its gains arise primarily from distribution sharpening rather than the acquisition of new capabilities. Recent work has shown that sampling from the power distribution of LLMs using Markov chain Monte Carlo (MCMC) can recover performance comparable to RL post-training without relying on external rewards; however, the high computational cost of MCMC makes such approaches impractical for widespread adoption. In this work, we propose a theoretically grounded alternative that eliminates the need for iterative MCMC. We derive a novel formulation showing that the global power distribution can be approximated by a token-level scaled low-temperature one, where the scaling factor captures future trajectory quality. Leveraging this insight, we introduce a training-free and verifier-free algorithm that sharpens the base model's generative distribution autoregressively. Empirically, we evaluate our method on math, QA, and code tasks across four LLMs, and show that our method matches or surpasses one-shot GRPO without relying on any external rewards, while reducing inference latency by over 10x compared to MCMC-based sampling.
A theoretically grounded method for improving large language model reasoning performance through distribution sharpening without iterative sampling or external rewards, achieving comparable results to reinforcement learning post-training with significantly reduced computational costs.
reinforcement learning large language models distribution sharpening Markov chain Monte Carlo power distribution low-temperature sampling autoregressive generation GRPO inference latency