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    <abstract>Sampling from the sequence-level power distribution 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: the power distribution mainly departs from the base distribution 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 approximate 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. EGPS targets significant speedup with accuracy that matches or improves on MH power sampling: across three base models and three benchmarks it attains best or tied-best accuracy on 5 of 9 settings; on Qwen2.5-Math-7B it is best or tied-best on all three (MATH500 75.8%, HumanEval 62.2%, GPQA 42.4%), with wall-clock speedups over the MH baseline of up to 12.6× across these benchmarks. Our code is available at https://github.com/hongguo7/EGPS.</abstract>
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%0 Conference Proceedings
%T Sample Where You Struggle: Sharpening Base Model Reasoning via Entropy-Guided Power Sampling
%A Guo, Hong
%A Guo, Nianhui
%A Meinel, Christoph
%A Yang, Haojin
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-459-0
%F guo-etal-2026-sample
%X Sampling from the sequence-level power distribution 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: the power distribution mainly departs from the base distribution 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 approximate 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. EGPS targets significant speedup with accuracy that matches or improves on MH power sampling: across three base models and three benchmarks it attains best or tied-best accuracy on 5 of 9 settings; on Qwen2.5-Math-7B it is best or tied-best on all three (MATH500 75.8%, HumanEval 62.2%, GPQA 42.4%), with wall-clock speedups over the MH baseline of up to 12.6× across these benchmarks. Our code is available at https://github.com/hongguo7/EGPS.
%U https://aclanthology.org/2026.emnlp-main.761/
%P 17623-17639

Markdown (Informal)

[Sample Where You Struggle: Sharpening Base Model Reasoning via Entropy-Guided Power Sampling](https://aclanthology.org/2026.emnlp-main.761/) (Guo et al., EMNLP 2026)

• Sample Where You Struggle: Sharpening Base Model Reasoning via Entropy-Guided Power Sampling (Guo et al., EMNLP 2026)

ACL

• Hong Guo, Nianhui Guo, Christoph Meinel, and Haojin Yang. 2026. Sample Where You Struggle: Sharpening Base Model Reasoning via Entropy-Guided Power Sampling. In Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing, pages 17623–17639, Budapest, Hungary. Association for Computational Linguistics.