While large language models (LLMs) are empowered with broad knowledge, their task-specific performance is often suboptimal. It necessitates fine-tuning LLMs with task-specific data, but such data may be inaccessible due to privacy concerns. In this paper, we propose a novel approach to enhance LLMs with smaller language models (SLMs) that are trained on clients using their private task-specific data. To enable mutual enhancement between LLMs and SLMs, we propose CrossLM, where the SLMs promote the LLM to generate task-specific high-quality data, and both the LLM and SLMs are enhanced with the generated data. We evaluate CrossLM using publicly accessible language models across a range of benchmark tasks. The results demonstrate that CrossLM significantly enhances the task-specific performance of SLMs on clients and the LLM on the cloud server simultaneously while preserving the LLM's generalization capability.
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