Large Language Models (LLMs) exhibit impressive performance across various domains but still struggle with arithmetic reasoning tasks. Recent work shows the effectiveness of prompt design methods in enhancing reasoning capabilities. However, these approaches overlook crucial requirements for prior knowledge of specific concepts, theorems, and tricks to tackle most arithmetic reasoning problems successfully. To address this issue, we propose a novel and effective Teaching-Inspired Integrated Prompting Framework, which emulates the instructional process of a teacher guiding students. This method equips LLMs with essential concepts, relevant theorems, and similar problems with analogous solution approaches, facilitating the enhancement of reasoning abilities. Additionally, we introduce two new Chinese datasets, MathMC and MathToF, both with detailed explanations and answers. Experiments are conducted on nine benchmarks which demonstrates that our approach improves the reasoning accuracy of LLMs. With GPT-4 and our framework, we achieve new state-of-the-art performance on four math benchmarks (AddSub, SVAMP, Math23K and AQuA) with accuracies of 98.2% (+3.3%), 93.9% (+0.2%), 94.3% (+7.2%) and 81.1% (+1.2%).

Large language models (LLMs) develop the in-context learning capability through pretraining and instruction tuning, enabling task adaptation without parameter updates. Self-refinement is a manifestation of this capability, which allows LLMs to iteratively refine the output using self-generated feedback. However, empirical observations reveal Inference-Free Self-Refinement (IFSR) in preference alignment: LLMs generate preference-improved output via fixed instructions, requiring no specific feedback, even no initial responses. There are two key components of the IFSR in preference alignment. The refining instruction is a fixed instruction that constrains the output distribution from a preference-semantic perspective. During training, it facilitates joint learning of preference-related semantic representations and data distribution alignment. The pseudo reference response is constructed from paired preference data and serves as a demonstration to guide the output distribution. It mitigates off-policy distributional bias while enhancing token-level preference learning in training. Experiments across multiple datasets demonstrate that incorporating IFSR into preference alignment yields performance improvement over 10%. Further ablation studies reveal additional characteristics and potential principles of IFSR.