Differential Fine-Tuning Large Language Models Towards Better Diverse Reasoning Abilities

Reasoning abilities of large language models (LLMs) require explicit derivations compared to general question-answering, supervised fine-tuning (SFT) can empower multiple reasoning abilities in LLMs via learning from various datasets. However, neither training the datasets jointly (mix-up) nor continually can maintain the performance of single-dataset SFT, sometimes better while sometimes even worse, illustrating vanilla SFT can not only facilitate reasoning abilities but also introduce conflicts. In this paper, we propose a novel framework to mitigate the conflicts and preserve benefits among different reasoning tasks, and even surpass each task's single dataset SFT performance. We start by exploring the differences between reasoning fine-tuned and base LLMs by analyzing their parameter variations during model inference, and we discover that each reasoning capability has exclusive parameters that benefit itself more evidently than others. In contrast, the overlapped parameters of tasks can bring benefits or conflicts. Inspired by the findings, we propose to update the exclusive and overlapped parameters according to specific reasoning task combinations differentially, thereby avoiding unnecessary conflicts while maintaining benefits. Consistent improvements in mix-up and continual SFT experiments demonstrate that the proposed SFT strategy can achieve better performance on various LLMs (Llama3-8B, Mistral-7B, and Qwen2.5-14B) and diverse reasoning tasks with fewer conflicts, showing the superiority and generality of our analysis findings and the proposed approach.