Temporal Predictive Coding for Gradient Compression in Distributed Learning

This paper proposes a prediction-based gradient compression method for distributed learning with event-triggered communication. Our goal is to reduce the amount of information transmitted from the distributed agents to the parameter server by exploiting temporal correlation in the local gradients. We use a linear predictor that \textit{combines past gradients to form a prediction of the current gradient}, with coefficients that are optimized by solving a least-square problem. In each iteration, every agent transmits the predictor coefficients to the server such that the predicted local gradient can be computed. The difference between the true local gradient and the predicted one, termed the \textit{prediction residual, is only transmitted when its norm is above some threshold.} When this additional communication step is omitted, the server uses the prediction as the estimated gradient. This proposed design shows notable performance gains compared to existing methods in the literature, achieving convergence with reduced communication costs.

Over-the-Air Federated Learning with Compressed Sensing: Is Sparsification Necessary?

Over-the-Air (OtA) Federated Learning (FL) refers to an FL system where multiple agents apply OtA computation for transmitting model updates to a common edge server. Two important features of OtA computation, namely linear processing and signal-level superposition, motivate the use of linear compression with compressed sensing (CS) methods to reduce the number of data samples transmitted over the channel. The previous works on applying CS methods in OtA FL have primarily assumed that the original model update vectors are sparse, or they have been sparsified before compression. However, it is unclear whether linear compression with CS-based reconstruction is more effective than directly sending the non-zero elements in the sparsified update vectors, under the same total power constraint. In this study, we examine and compare several communication designs with or without sparsification. Our findings demonstrate that sparsification before compression is not necessary. Alternatively, sparsification without linear compression can also achieve better performance than the commonly considered setup that combines both.