Improving reasoning at inference time via uncertainty minimisation
This work addresses the computational expense of existing inference-time scaling methods for LLMs, offering a more efficient approach for researchers and practitioners working with multi-step reasoning tasks.
This paper proposes an inference-time reasoning strategy for large language models (LLMs) that minimizes uncertainty at the thought level, rather than token level. The method selects continuations that maximize the model's self-certainty, achieving significant improvements on MATH500 and GSM8K datasets, outperforming greedy decoding and matching or exceeding self-consistency with comparable token budgets.
Large language models (LLMs) now exhibit strong multi-step reasoning abilities, but existing inference-time scaling methods remain computationally expensive, often relying on extensive sampling or external evaluators. We propose a principled strategy that frames reasoning as uncertainty minimisation and operates at the level of individual thoughts rather than tokens. Our method selects, at each reasoning step, the continuation that maximizes the model's self-certainty, a metric computed from its internal predictive distribution. This approach achieves significant improvement with a small number of samples, relies exclusively on model-internal signals, and applies to open-ended questions as opposed to methods like majority voting. Experiments on MATH500 and GSM8K across multiple model sizes demonstrate that thought-level self-certainty maximization consistently outperforms greedy decoding and matches or exceeds self-consistency under comparable token budgets. Cross-linguistic evaluations further indicate that the method transfers robustly beyond high-resource languages. Furthermore, analysis of self-certainty dynamics reveals that correct reasoning trajectories converge early to stable paths, suggesting that early decisions, likely associated with the planning of the reasoning process, are predictive of final accuracy. Building on this result, we show that self-certainty maximisation applied to the early steps can explain most of the performance gain and provide a simple yet efficient inference-time scaling method.