GrayKD: Distilling Better Knowledge from Black-box LLM via Multi-rationale Injection

Knowledge distillation (KD) is a promising compression technique for reducing the computational burden of large language models (LLMs). Depending on access to the teacher model’s internal parameters, KD is typically categorized into white-box and black-box KD. While white-box KD benefits from full access to intrinsic knowledge such as softmax distributions, black-box KD adopts a black-box LLM (e.g., GPT-4) as the teacher, which provides only text-level outputs via API calls. This limited supervision makes black-box KD generally less effective than its white-box counterpart. To bridge the gap between white-box and black-box KD, we propose GrayKD, a novel framework that can effectively distill text-level knowledge from a black-box LLM in a single-stage manner. In particular, rationales generated by the black-box LLM are injected into the student via a lightweight cross-attention module (teacher mode), enabling the model to approximate the black-box teacher’s output distribution without access to internal parameters. The student is then trained with the softmax-level knowledge provided by the teacher mode (student mode). Since both the teacher and student modes share the same backbone, the proposed teacher mode remains highly parameter-efficient, requiring only a small number of additional parameters for rationale injection. Experimental results on instruction-following tasks demonstrate that GrayKD achieves substantial performance improvements over existing KD methods.