Reasoning with Sampling: Your Base Model is Smarter Than You Think
This work addresses the challenge of efficiently leveraging base models for reasoning tasks, offering a training-free alternative that avoids diversity collapse, which is incremental but practical for broad applications.
The paper tackles the problem of eliciting reasoning capabilities from base language models without additional training, showing that a simple iterative sampling algorithm can achieve substantial performance boosts on tasks like MATH500, HumanEval, and GPQA, nearly matching or outperforming reinforcement learning post-training.
Frontier reasoning models have exhibited incredible capabilities across a wide array of disciplines, driven by posttraining large language models (LLMs) with reinforcement learning (RL). However, despite the widespread success of this paradigm, much of the literature has been devoted to disentangling truly novel behaviors that emerge during RL but are not present in the base models. In our work, we approach this question from a different angle, instead asking whether comparable reasoning capabilites can be elicited from base models at inference time by pure sampling, without any additional training. Inspired by Markov chain Monte Carlo (MCMC) techniques for sampling from sharpened distributions, we propose a simple iterative sampling algorithm leveraging the base models' own likelihoods. Over different base models, we show that our algorithm offers substantial boosts in reasoning that nearly match and even outperform those from RL on a wide variety of single-shot tasks, including MATH500, HumanEval, and GPQA. Moreover, our sampler avoids the collapse in diversity over multiple samples that is characteristic of RL-posttraining. Crucially, our method does not require training, curated datasets, or a verifier, suggesting broad applicability beyond easily verifiable domains.