# Reasoning with Sampling: Cutting at Decision Points

arXiv: https://arxiv.org/abs/2605.30327 · HTML: https://mlsanity.com/paper/2605.30327/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 14 of its 86 references that are in the map.
- First posted on arXiv 28 May 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 14 of 14)

- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Accelerating Large Language Model Decoding with Speculative Sampling](https://mlsanity.com/paper/2302.01318/) (2023)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Phi-4 Technical Report](https://mlsanity.com/paper/2412.08905/) (2024)
- [Semantic Entropy Probes: Robust and Cheap Hallucination Detection in LLMs](https://mlsanity.com/paper/2406.15927/) (2024)
- [Spurious Rewards: Rethinking Training Signals in RLVR](https://mlsanity.com/paper/2506.10947/) (2025)
- [Maximizing Confidence Alone Improves Reasoning](https://mlsanity.com/paper/2505.22660/) (2025)
- [Outcome-based Exploration for LLM Reasoning](https://mlsanity.com/paper/2509.06941/) (2025)
- [Rewarding the Unlikely: Lifting GRPO Beyond Distribution Sharpening](https://mlsanity.com/paper/2506.02355/) (2025)
- [Scalable Power Sampling: Unlocking Efficient, Training-Free Reasoning for LLMs via Distribution Sharpening](https://mlsanity.com/paper/2601.21590/) (2026)
- [Power-SMC: Low-Latency Sequence-Level Power Sampling for Training-Free LLM Reasoning](https://mlsanity.com/paper/2602.10273/) (2026)
- [Adaptive Guidance Accelerates Reinforcement Learning of Reasoning Models](https://mlsanity.com/paper/2506.13923/) (2025)

## Built on by (most cited first, 3 of 3)

- [ReSight-SMC: Two-Stage Power Sampling via Island SMC with Visual Scouts](https://mlsanity.com/paper/2609.34905/) (2026)
- [Finetuning with Sampling: SFT Learns Better Than You Think](https://mlsanity.com/paper/2610.02140/) (2026)
- [Adaptive Power Sampling for LLM Reasoning](https://mlsanity.com/paper/2610.08563/) (2026)

## Abstract (arXiv)

Frontier reasoning models are produced by post-training base language models with reinforcement learning. Recent work has challenged this by showing that sampling from a sharpened version of the base model's distribution, a so-called power distribution, elicits comparable reasoning without additional training, curated datasets, or verifiers. However, making this method practical requires efficiently sampling from the power distribution. A sampler needs to "mix" to the power distribution, which necessitates moving between modes of the target distribution; intuitively, e.g., trying different reasoning strategies. The samplers proposed in prior works repeatedly select a "cut" position in the current reasoning trace uniformly at random and resample the suffix from that position onward. However, reasoning traces typically contain a few consequential decisions (e.g., the choice of proof strategy or algorithm), and we observe that a uniformly chosen cut tends to rewrite local details rather than revisit decision points. We introduce an algorithm (Entropy-Cut Metropolis-Hastings) that uses the base model's next-token entropy as a proxy to identify key decision points and resample from those positions. We empirically verify that entropy jumps are a useful proxy for decision points and, in a stylized model of reasoning, prove that our method's mixing time scales with the number of decisions in a trace rather than with the number of tokens, which can be much larger. Across MATH500, HumanEval, GPQA Diamond, and AIME26, our method consistently improves over baselines and RL-trained models, including best-of-N at the same token budget.