  Federated learning is a promising distributed training paradigm that
effectively safeguards data privacy. However, it may involve significant
communication costs, which hinders training efficiency. In this paper, we aim
to enhance communication efficiency from a new perspective. Specifically, we
request the distributed clients to find optimal model updates relative to
global model parameters within predefined random noise. For this purpose, we
propose Federated Masked Random Noise (FedMRN), a novel framework that enables
clients to learn a 1-bit mask for each model parameter and apply masked random
noise (i.e., the Hadamard product of random noise and masks) to represent model
updates. To make FedMRN feasible, we propose an advanced mask training
strategy, called progressive stochastic masking (PSM). After local training,
each client only need to transmit local masks and a random seed to the server.
Additionally, we provide theoretical guarantees for the convergence of FedMRN
under both strongly convex and non-convex assumptions. Extensive experiments
are conducted on four popular datasets. The results show that FedMRN exhibits
superior convergence speed and test accuracy compared to relevant baselines,
while attaining a similar level of accuracy as FedAvg.
