Abstract
Problem decomposition guided by the models’ self-reward has recently shown promise for enhancing complex reasoning in Large Language Models (LLMs). However, existing reward functions primarily rely on local evaluation of decomposed subproblems, and often fail to explicitly model the reasoning utility-the global contribution of subproblems to solving the original task. This leads to weak subproblem relevance, ultimately compromising reasoning accuracy and reliability. To address this limitation, we propose a new approach called Reasoning Utility Guided Problem Decomposition (RUG-PD), which introduces two reasoning utility metrics to enhance the relevance of subproblems from the perspectives of both the original problem and the final answer: (1) Reasoning Uncertainty Utility, which encourages the generation of solution-relevant subproblems by maximally reducing the uncertainty of the original problem; and (2) Reasoning Consistency Utility, which promotes the selection of subproblem paths that best support the final answer by evaluating the consistency between re-reasoned and original answers. Experiments on four complex reasoning datasets demonstrate that our approach substantially improves the complex reasoning performance of LLMs and generalizes across model architectures. On the SVAMP dataset, RUG-PD surpasses the strong baseline rStar-PD in accuracy by 3.90 % with LLaMA2-7B, and by an average of 2.60 % across four backbone LLMs. Further analysis confirms its effectiveness in generating subproblems that carry rich problem-solving information and support the final answer.