A truly intelligent Large Language Model (LLM) should be capable of correcting errors in its responses through external interactions. However, even the most advanced models often face challenges in improving their outputs. In this paper, we explore how to cultivate LLMs with the self-refinement capability through iterative preference training, and how this ability can be leveraged to improve model performance during inference. To this end, we introduce a novel post-training and inference framework, called ARIES: Adaptive Refinement and Iterative Enhancement Structure. This method iteratively performs preference training and self-refinement-based data collection. During training, ARIES strengthen the model's direct question-answering capability while simultaneously unlocking its self-refinement potential. During inference, ARIES harnesses this self-refinement capability to generate a series of progressively refined responses, which are then filtered using either the Reward Model Scoring or a simple yet effective Rule-Based Selection mechanism, specifically tailored to our approach, to construct a dataset for the next round of preference training. Experimental results demonstrate the remarkable performance of ARIES. When applied to the Llama-3.1-8B model and under the self-refinement setting, ARIES surpasses powerful models such as GPT-4o, achieving 62.3% length-controlled (LC) and a 63.3% raw win rates on AlpacaEval 2, outperforming Iterative DPO by 27.8% and 35.5% respectively, as well as a 50.3% win rate on Arena-Hard, surpassing Iterative DPO by 26.6%. Furthermore, ARIES consistently enhances performance on mathematical reasoning tasks like GSM8K and MATH.

Although Large Language Models (LLMs) achieve remarkable performance across various tasks, they often struggle with complex reasoning tasks, such as answering mathematical questions. Recent efforts to address this issue have primarily focused on leveraging mathematical datasets through supervised fine-tuning or self-improvement techniques. However, these methods often depend on high-quality datasets that are difficult to prepare, or they require substantial computational resources for fine-tuning. Inspired by findings that LLMs know how to produce the right answer but struggle to select the correct reasoning path, we propose a purely inference-based searching method -- MindStar (M*). This method formulates reasoning tasks as searching problems and proposes two search ideas to identify the optimal reasoning paths. We evaluate the M* framework on both the GSM8K and MATH datasets, comparing its performance with existing open and closed-source LLMs. Our results demonstrate that M* significantly enhances the reasoning abilities of open-source models, such as Llama-2-13B and Mistral-7B, and achieves comparable performance to GPT-3.5 and Grok-1, but with substantially reduced model size and computational costs.