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The paper introduces Entropy-Cut Metropolis-Hastings, a novel sampling algorithm for eliciting reasoning from base language models via power distributions, which sharpens the model's output distribution without additional training. This algorithm improves upon prior methods by using next-token entropy to identify and resample from key decision points in reasoning traces, rather than uniformly sampling cut positions. Empirically, the proposed method demonstrates superior performance compared to baselines and RL-trained models across several reasoning benchmarks, and theoretically, it's shown to have mixing time dependent on the number of decisions, not tokens.
Forget uniform resampling – targeting high-entropy decision points in reasoning traces unlocks better performance than RL-trained models, all without extra training data or compute.
Frontier reasoning models are produced by posttraining 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.
