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.
Figures & tables
Figure 1: Inference time scaling using uncertainty minimisation. We posit that reasoning in LLMs and humans proceeds by uncertainty minimisation. Each reasoning step, is selected for its potential to reduce uncertainties towards a required solution. We emulate such a selection process by sampling multiple candidates at every step and retaining the generation with the highest self-certainty score.
Figure 2: Performance of self-consistency and self-certainty maximisation calling methods across different sizes of the Qwen and Llama family. Inference-time scaling based on self-certainty maximisation (blue bars) was found to be more efficient than the simple pass (grey bar and black dots), and equalled or outperformed self-consistency (grey bars black dots) with comparable token budgets (samples 2, 4, and 8) in several instances. For the forward pass, each question was evaluated 8 times; the eight dots represent the scores over the full dataset for each generation. The dashed horizontal line indicates the performance of the early stop method, using 16 samples and a maximum of 3 reasoning steps.
Figure 3: Performance of self-consistency and self-certainty maximisation for English and Danish versions of GSM8K questions, across different sizes of the Qwen and Llama family. Inference-time scaling methods based on self-certainty maximisation were found more efficient than a single pass (red and blue dots), both with English-based questions from the GSM8k dataset (blue bars), and the same questions translated into Danish (red bars). In a majority of cases, the performances were also higher than self-consistency (black dots) with comparable token budgets (samples 2, 4, and 8).
Figure 4: Evolution of self-certainty across reasoning steps for Qwen and Llama models. Correct trajectories exhibit consistently higher self-certainty than incorrect ones from the earliest reasoning steps. Incorrect trajectories are more frequently associated with long chains of thought.
Figure 5: Self-certainty gain across reasoning steps. Correct trajectories show smaller incremental gains after initialization, indicating early uncertainty resolution.
Figure 6: Early self-certainty optimization yields maximal gains. We tested Qwen-3B against 100 selected questions from MATH500. Sampling is restricted to the first k reasoning steps ( k∈1,2,5,40 ). Limiting uncertainty minimization to the early steps (i.e., 1 or 2) explains most of the performance increase observed, while optimizing along the entire path decrease gain over time.
Figure 7: Token usage for the different inference time scaling methods.