让小模型学会真推理，避免被错误理由带偏

Large language models (LLMs) excel at reasoning tasks but are expensive to deploy. Thus small language models (SLMs) are fine-tuned on CoT data generated by LLMs to copy LLMs' abilities. However, these CoT data may include noisy rationales that either fail to substantiate the answers or contribute no additional information to support answer prediction, which leads SLMs to capture spurious correlations between questions and answers and compromise the quality of reasoning. In this work, we propose Chain-of-Thought Correctness Perception Distillation (CoPeD), which aims to improve the reasoning quality of the student model from the perspectives of task setting and data utilization. Firstly, we introduce a correctness-aware task setting that encourages the student model to predict answers based on correct rationales and revise them when they are incorrect. This setting improves the faithfulness of reasoning and allows the model to learn from its mistakes. Then, we propose a Correctness-Aware Weighted loss, which dynamically adjusts the contribution of each training instance based on the combined loss of the rationale and the answer. This strategy encourages the model to focus more on samples where the rationale offers stronger support for the correct answer. Experiments have shown that CoPeD is effective on both in-distribution (IND) and out-of-distribution (OOD) benchmark reasoning datasets.