# Power-SMC: Low-Latency Sequence-Level Power Sampling for Training-Free LLM Reasoning

arXiv: https://arxiv.org/abs/2602.10273 · HTML: https://mlsanity.com/paper/2602.10273/

## Key facts

- Cited by 21 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 10 of its 16 references that are in the map.
- First posted on arXiv 10 Feb 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, 10 of 10)

- [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)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phone](https://mlsanity.com/paper/2404.14219/) (2024)
- [Scalable Power Sampling: Unlocking Efficient, Training-Free Reasoning for LLMs via Distribution Sharpening](https://mlsanity.com/paper/2601.21590/) (2026)
- [Top-H Decoding: Adapting the Creativity and Coherence with Bounded Entropy in Text Generation](https://mlsanity.com/paper/2509.02510/) (2025)

## Built on by (most cited first, 21 of 21)

- [The Model Knows, the Decoder Finds: Future Value Guided Particle Power Sampling](https://mlsanity.com/paper/2605.02427/) (2026)
- [Sampling for Quality: Training-Free Reward-Guided LLM Decoding via Sequential Monte Carlo](https://mlsanity.com/paper/2604.16453/) (2026)
- [Power Distribution Bridges Sampling, Self-Reward RL, and Self-Distillation](https://mlsanity.com/paper/2605.04542/) (2026)
- [Self-Consistency via Marginal Sharpening](https://mlsanity.com/paper/2605.28142/) (2026)
- [When are likely answers right? On Sequence Probability and Correctness in LLMs](https://mlsanity.com/paper/2606.27359/) (2026)
- [Reasoning with Sampling: Cutting at Decision Points](https://mlsanity.com/paper/2605.30327/) (2026)
- [COFT: Counterfactual-Conformal Decoding for Fair Chain-of-Thought Reasoning in Large Language Models](https://mlsanity.com/paper/2605.30641/) (2026)
- [Sample Where You Struggle: Sharpening Base Model Reasoning via Entropy-Guided Power Sampling](https://mlsanity.com/paper/2606.09926/) (2026)
- [Depth-Entropy Guided Sampling for Training-Free LLM Reasoning](https://mlsanity.com/paper/2607.09693/) (2026)
- [More Correct Mass, Worse Answers: Why Power Sampling Can Fail and How to Fix It](https://mlsanity.com/paper/2608.14420/) (2026)
- [FluxLite: Inference-Time Proposal Control for Discrete Diffusion Models](https://mlsanity.com/paper/2609.35947/) (2026)
- [Faster LLM Inference via Sequential Monte Carlo](https://mlsanity.com/paper/2604.15672/) (2026)
- [MOSAIC: Efficient Mixture-of-Agent Scheduling via Adaptive Aggregation and Inference Concurrency](https://mlsanity.com/paper/2606.03014/) (2026)
- [Chopthin-Consensus Power Sampling: A Diversity-Preserving Approach to LLM Decoding](https://mlsanity.com/paper/2609.12243/) (2026)
- [ReSight-SMC: Two-Stage Power Sampling via Island SMC with Visual Scouts](https://mlsanity.com/paper/2609.34905/) (2026)
- [Explore Broadly, Reason Sharply: Push Small Models toward the Frontier via Sampling](https://mlsanity.com/paper/2609.38104/) (2026)
- [Finetuning with Sampling: SFT Learns Better Than You Think](https://mlsanity.com/paper/2610.02140/) (2026)
- [Sharpen Without Search: On-Policy Distillation of Sequence-Level Power Distribution](https://mlsanity.com/paper/2610.06804/) (2026)
- [Adaptive Power Sampling for LLM Reasoning](https://mlsanity.com/paper/2610.08563/) (2026)
- [A Critical Look at Power Sampling when Test Time Sharpening LLMs](https://mlsanity.com/paper/2610.13653/) (2026)
- [Decoupled Marginal Sharpening for Training-Free Inference-Time Scaling](https://mlsanity.com/paper/2610.20483/) (2026)

## Abstract (arXiv)

Reasoning ability in large language models is often attributed to distribution sharpening: concentrating output probability on high-likelihood sequences. Recent works show that this sharpening effect can be obtained at inference time, without modifying model parameters, and can elicit strong reasoning performance. A natural formalization is the sequence-level power distribution, which is proportional to the model's probability raised to an exponent α>1. Prior work leveraged Metropolis--Hastings (MH) sampling to draw samples from this distribution and achieves strong results, however, at order-of-magnitude inference slowdowns. We introduce Power-SMC, a textit`training-free' sampling method that targets the same power distribution yielding close to standard decoding latency. Power-SMC maintains multiple candidate sequences in parallel. Each candidate sequence is assigned a score, namely the importance weight, that measures how well it matches the power distribution. It then periodically prunes low-scoring candidate sequences in favor of high-scoring ones. We further provide a theoretical justification for the design choices in Power-SMC. Among all next-token sampling strategies that do not rely on future tokens, we prove that sampling temperature τ=1/α uniquely eliminates per-step weight variance. Finally, we characterize the remaining source of weight instability and introduce a gradual sharpening schedule to reduce weight collapse, while targeting the same power distribution. Extensive evaluations on MATH500, GSM8K, GPQA, and HumanEval show that Power-SMC matches or exceeds MH sampling in accuracy, preserves output diversity unlike RL-finetuned models, while accelerating inference speed by up to 17.6×. The code is available at https://github.com/ArminAzizi98/Power-SMC.