# Adaptive Power Sampling for LLM Reasoning

arXiv: https://arxiv.org/abs/2610.08563 · HTML: https://mlsanity.com/paper/2610.08563/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 21 of its 41 references that are in the map.
- First posted on arXiv 6 Oct 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, 21 of 21)

- [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)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [A Survey on Test-Time Scaling in Large Language Models: What, How, Where, and How Well?](https://mlsanity.com/paper/2503.24235/) (2025)
- [Spurious Rewards: Rethinking Training Signals in RLVR](https://mlsanity.com/paper/2506.10947/) (2025)
- [Outcome-based Exploration for LLM Reasoning](https://mlsanity.com/paper/2509.06941/) (2025)
- [Scalable Power Sampling: Unlocking Efficient, Training-Free Reasoning for LLMs via Distribution Sharpening](https://mlsanity.com/paper/2601.21590/) (2026)
- [Contextual Temperature for Language Modeling](https://mlsanity.com/paper/2012.13575/) (2020)
- [Power-SMC: Low-Latency Sequence-Level Power Sampling for Training-Free LLM Reasoning](https://mlsanity.com/paper/2602.10273/) (2026)
- [The Model Knows, the Decoder Finds: Future Value Guided Particle Power Sampling](https://mlsanity.com/paper/2605.02427/) (2026)
- [Test-Time Scaling in Reasoning LLMs: Inference Regimes, Evaluation, and Reproducibility](https://mlsanity.com/paper/2608.04001/) (2026)
- [Power Distribution Bridges Sampling, Self-Reward RL, and Self-Distillation](https://mlsanity.com/paper/2605.04542/) (2026)
- [Reasoning with Sampling: Cutting at Decision Points](https://mlsanity.com/paper/2605.30327/) (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)

## Abstract (arXiv)

Sequence-level power sampling has recently emerged as a training-free approach to reasoning by sampling from a sharpened output distribution of a base large language model (LLM). Nevertheless, existing methods typically sharpen the base model distribution uniformly across queries, overlooking variations in query difficulty and in how well the base model already handles each query. The goal of this work is to equip power sampling with query adaptivity. Theoretically, we show that the benefits of further sharpening are determined by the self-reward gap between correct and incorrect responses. Based on this insight, we propose Adaptive Power Sampling (APS), which adjusts the sharpening exponent on a per-query basis at test time using the relationship between answer agreement and the model's self-reward. Experiments across diverse reasoning tasks, including MATH500, HumanEval, and GPQA, show that APS consistently outperforms power sampling with a fixed sharpening exponent, without additional training.