# Sample Where You Struggle: Sharpening Base Model Reasoning via Entropy-Guided Power Sampling

arXiv: https://arxiv.org/abs/2606.09926 · HTML: https://mlsanity.com/paper/2606.09926/

## Key facts

- Cited by 1 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 15 of its 19 references that are in the map.
- First posted on arXiv 7 Jun 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, 15 of 15)

- [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)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Deep Think with Confidence](https://mlsanity.com/paper/2508.15260/) (2025)
- [Stay on topic with Classifier-Free Guidance](https://mlsanity.com/paper/2306.17806/) (2023)
- [Reasoning with Sampling: Your Base Model is Smarter Than You Think](https://mlsanity.com/paper/2510.14901/) (2025)
- [Critical Tokens Matter: Token-Level Contrastive Estimation Enhances LLM's Reasoning Capability](https://mlsanity.com/paper/2411.19943/) (2024)
- [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)
- [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)
- [Less is More: Improving LLM Reasoning with Minimal Test-Time Intervention](https://mlsanity.com/paper/2510.13940/) (2025)
- [Sampling for Quality: Training-Free Reward-Guided LLM Decoding via Sequential Monte Carlo](https://mlsanity.com/paper/2604.16453/) (2026)

## Built on by (most cited first, 1 of 1)

- [Adaptive Power Sampling for LLM Reasoning](https://mlsanity.com/paper/2610.08563/) (2026)

## Abstract (arXiv)

Sampling from the sequence-level power distribution pα elicits RL-level reasoning from base language models without any parameter updates, but the standard Metropolis--Hastings (MH), a Markov Chain Monte Carlo (MCMC) sampler, is both expensive and slow-mixing. We trace both to a structural mismatch: pα mainly departs from p at a sparse, spatially clustered set of high-entropy decision points, yet MH proposes resampling positions uniformly along the prefix -- wasting compute on near-degenerate conditionals while under-mixing precisely where modes diverge. We propose Entropy-Guided Power Sampling (EGPS), a training-free and verifier-free sampler that re-derives its proposal from token-level entropy already in the forward pass. EGPS skips deterministic blocks, localizes each MCMC move to a high-entropy neighborhood, and applies Multiple-Try Metropolis at decision points -- making sampling cost scale with entropy mass rather than sequence length. On Qwen2.5-Math-7B, EGPS reaches best or tied-best accuracy on all three benchmarks (MATH500 75.8%, HumanEval 62.2%, GPQA 42.4%) at up to a 12.6× wall-clock speedup over the MH baseline.