Three Birds, One Stone: Solving the Communication-Memory-Privacy Trilemma in LLM Fine-tuning Over Wireless Networks with Zeroth-Order Optimization

Abstract

Federated Learning (FL) offers a promising pathway for collaboratively fine-tuning Large Language Models (LLMs) at the edge; however, this paradigm faces a critical bottleneck: the prohibitive communication and memory overheads incurred by exchanging high-dimensional gradients. Furthermore, recent studies reveal that user training data can still be recovered from these local gradients, undermining the core privacy promise of FL. In this paper, we address this trilemma of communication, memory, and privacy by proposing pAirZero, a novel framework that synergizes Zeroth-Order (ZO) optimization with Over-the-Air (OTA) computation. Uniquely, pAirZero enables resource-constrained devices to submit their local gradient with only bit-level communication loads while participating in federated fine-tuning of LLMs with inference-level memory costs. This approach not only eliminates the high memory requirements needed for LLM fine-tuning but also alleviates the strict synchronization requirements that plague conventional OTA methods. We further formulate a rigorous optimization model to adaptively determine the optimal transmit power and noise levels, ensuring consistent privacy protection regardless of channel conditions. Numerical experiments demonstrate the superiority of pAirZero in enabling secure, efficient LLM fine-tuning over wireless networks, with only 25% peak memory cost on OPT-125M and communication load orders of magnitude lower than conventional methods.