This paper investigates the impact of incorrect data on the performance and safety of large language models (LLMs), specifically gpt-4o, during supervised fine-tuning (SFT). Although LLMs become increasingly vital across broad domains like finance, coding, law, and health, fine-tuning on incorrect data can lead to "emergent misalignment," producing harmful or deceptive outputs unrelated to the intended task. We evaluate gpt-4o models fine-tuned with varying ratios (10\% to 90\% correct) of both obviously and subtly incorrect data across four domains: coding, finance, health, and legal. Our findings show that even modest amounts of incorrect data (10-25\%) dramatically degrade domain performance and not moral alignment. A clear threshold of at least 50\% correct data is needed for models to consistently recover strong performance, though they rarely match the robustness and safety of the base model, which exhibits near-perfect alignment and zero dangerous completions out-of-the-box. This research emphasizes that the cost of incorrect data is heavy, highlighting the critical need for extremely high-quality data curation or, alternatively, leveraging robust base models without unnecessary fine-tuning for high-stakes applications.

Large Language Models (LLMs) have exhibited strong mathematical reasoning and computational prowess, tackling tasks ranging from basic arithmetic to advanced competition-level problems. However, frequently occurring subtle errors, such as miscalculations or incorrect substitutions, limit the models' full mathematical potential. Existing studies to improve mathematical ability typically involve distilling reasoning skills from stronger LLMs or applying preference learning to step-wise response pairs. Although these methods leverage samples of varying granularity to mitigate reasoning errors, they overlook the frequently occurring subtle errors. A major reason is that sampled preference pairs involve differences unrelated to the errors, which may distract the model from focusing on subtle errors. In this work, we propose a novel preference learning framework called eRror-Injected Self-Editing (RISE), which injects predefined subtle errors into partial tokens of correct solutions to construct hard pairs for error mitigation. In detail, RISE uses the model itself to edit a small number of tokens in the solution, injecting designed subtle errors. Then, pairs composed of self-edited solutions and their corresponding correct ones, along with pairs of correct and incorrect solutions obtained through sampling, are used together for subtle error-aware DPO training. Compared with other preference learning methods, RISE further refines the training objective to focus on predefined errors and their tokens, without requiring fine-grained sampling or preference annotation. Extensive experiments validate the effectiveness of RISE, with preference learning on Qwen2-7B-Instruct yielding notable improvements of 3.0% on GSM8K and 7.9% on MATH.