# Improving reasoning at inference time via uncertainty minimisation

arXiv: https://arxiv.org/abs/2603.07159 · HTML: https://mlsanity.com/paper/2603.07159/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 27 of its 37 references that are in the map.
- First posted on arXiv 7 Mar 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 27 of 27)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [Measuring Faithfulness in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2307.13702/) (2023)
- [Language Agent Tree Search Unifies Reasoning Acting and Planning in Language Models](https://mlsanity.com/paper/2310.04406/) (2023)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinking](https://mlsanity.com/paper/2501.04519/) (2025)
- [Towards Large Reasoning Models: A Survey of Reinforced Reasoning with Large Language Models](https://mlsanity.com/paper/2501.09686/) (2025)
- [A Survey on Test-Time Scaling in Large Language Models: What, How, Where, and How Well?](https://mlsanity.com/paper/2503.24235/) (2025)
- [Learning to Reason without External Rewards](https://mlsanity.com/paper/2505.19590/) (2025)
- [Efficient Guided Generation for Large Language Models](https://mlsanity.com/paper/2307.09702/) (2023)
- [Scalable Best-of-N Selection for Large Language Models via Self-Certainty](https://mlsanity.com/paper/2502.18581/) (2025)
- [The Unreasonable Effectiveness of Entropy Minimization in LLM Reasoning](https://mlsanity.com/paper/2505.15134/) (2025)
- [LM-Polygraph: Uncertainty Estimation for Language Models](https://mlsanity.com/paper/2311.07383/) (2023)
- [Efficient Test-Time Scaling via Self-Calibration](https://mlsanity.com/paper/2503.00031/) (2025)
- [Cognitive Foundations for Reasoning and Their Manifestation in LLMs](https://mlsanity.com/paper/2511.16660/) (2025)
- [Can Reasoning Models Obfuscate Reasoning? Stress-Testing Chain-of-Thought Monitorability](https://mlsanity.com/paper/2510.19851/) (2025)
- [Rollout Roulette: A Probabilistic Inference Approach to Inference-Time Scaling of LLMs using Particle-Based Monte Carlo Methods](https://mlsanity.com/paper/2502.01618/) (2025)
- [Can We Trust LLMs? Mitigate Overconfidence Bias in LLMs through Knowledge Transfer](https://mlsanity.com/paper/2405.16856/) (2024)
- [DynScaling: Efficient Verifier-free Inference Scaling via Dynamic and Integrated Sampling](https://mlsanity.com/paper/2506.16043/) (2025)
- [A*-Decoding: Token-Efficient Inference Scaling](https://mlsanity.com/paper/2505.13672/) (2025)

## Abstract (arXiv)

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.