daDPO: Distribution-Aware DPO for Distilling Conversational Abilities

Large language models (LLMs) have demonstrated exceptional performance across various applications, but their conversational abilities decline sharply as model size decreases, presenting a barrier to their deployment in resource-constrained environments. Knowledge distillation with Direct Preference Optimization (dDPO) has emerged as a promising approach to enhancing the conversational abilities of smaller models using a larger teacher model. However, current methods primarily focus on "black-box" KD, which only uses the teacher's responses, overlooking the output distribution offered by the teacher. This paper addresses this gap by introducing daDPO (Distribution-Aware DPO), a unified method for preference optimization and distributionbased distillation. We provide rigorous theoretical analysis and empirical validation, showing that daDPO outperforms existing methods in restoring performance for pruned models and enhancing smaller LLM models. Notably, in indomain evaluation, our method enables a 20% pruned Vicuna1.5-7B to achieve near-teacher performance (-7.3% preference rate compared to that of dDPO's -31%), and allows Qwen2.5-1.5B to occasionally outperform its 7B teacher model (14.0% win rate). * Zhang and Wang contributed equally to this work: Zhang leads experiments and refined the methodology, while Wang originates the idea and leads the theoretical proofs. All authors contributed to the writing, discussion, and overall development of the paper.