By adapting Large Language Models (LLMs) to domain-specific tasks or enriching them with domain-specific knowledge, we can fully harness the capabilities of LLMs. Nonetheless, a gap persists in achieving simultaneous mutual enhancement between the server's LLM and the downstream clients' Small Language Models (SLMs). To address this, we propose FedCoLLM, a novel and parameter-efficient federated framework designed for co-tuning LLMs and SLMs. This approach is aimed at adaptively transferring server-side LLMs knowledge to clients' SLMs while simultaneously enriching the LLMs with domain insights from the clients. To accomplish this, FedCoLLM utilizes lightweight adapters in conjunction with SLMs, facilitating knowledge exchange between server and clients in a manner that respects data privacy while also minimizing computational and communication overhead. Our evaluation of FedCoLLM, utilizing various public LLMs and SLMs across a range of NLP text generation tasks, reveals that the performance of clients' SLMs experiences notable improvements with the assistance of the LLMs. Simultaneously, the LLMs enhanced via FedCoLLM achieves comparable performance to that obtained through direct fine-tuning on clients' data.

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