  In this paper, we question the rationale behind propagating large numbers of
parameters through a distributed system during federated learning. We start by
examining the rank characteristics of the subspace spanned by gradients across
epochs (i.e., the gradient-space) in centralized model training, and observe
that this gradient-space often consists of a few leading principal components
accounting for an overwhelming majority (95-99%) of the explained variance.
Motivated by this, we propose the "Look-back Gradient Multiplier" (LBGM)
algorithm, which exploits this low-rank property to enable gradient recycling
between model update rounds of federated learning, reducing transmissions of
large parameters to single scalars for aggregation. We analytically
characterize the convergence behavior of LBGM, revealing the nature of the
trade-off between communication savings and model performance. Our subsequent
experimental results demonstrate the improvement LBGM obtains in communication
overhead compared to conventional federated learning on several datasets and
deep learning models. Additionally, we show that LBGM is a general
plug-and-play algorithm that can be used standalone or stacked on top of
existing sparsification techniques for distributed model training.
