Recent research in federated large language models (LLMs) has primarily focused on enabling clients to fine-tune their locally deployed homogeneous LLMs collaboratively or on transferring knowledge from server-based LLMs to small language models (SLMs) at downstream clients. However, a significant gap remains in the simultaneous mutual enhancement of both the server's LLM and clients' SLMs. To bridge this gap, we propose FedMKT, a parameter-efficient federated mutual knowledge transfer framework for large and small language models. This framework is designed to adaptively transfer knowledge from the server's LLM to clients' SLMs while concurrently enriching the LLM with clients' unique domain insights. We facilitate token alignment using minimum edit distance (MinED) and then selective mutual knowledge transfer between client-side SLMs and a server-side LLM, aiming to collectively enhance their performance. Through extensive experiments across three distinct scenarios, heterogeneous, homogeneous, and one-to-one, we evaluate the effectiveness of FedMKT using various public LLMs and SLMs on a range of NLP text generation tasks. Empirical results demonstrate significant performance improvements in clients' SLMs with the aid of the LLM. Furthermore, the LLM optimized by FedMKT achieves a performance comparable to that achieved through direct fine-tuning based on clients' data, highlighting the effectiveness and adaptability of FedMKT.
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