Exploiting Correlations in Federated Learning: Opportunities and Practical Limitations

The communication bottleneck in federated learning (FL) has spurred extensive research into techniques to reduce the volume of data exchanged between client devices and the central parameter server. In this paper, we systematically classify gradient and model compression schemes into three categories based on the type of correlations they exploit: structural, temporal, and spatial. We examine the sources of such correlations, propose quantitative metrics for measuring their magnitude, and reinterpret existing compression methods through this unified correlation-based framework. Our experimental studies demonstrate that the degrees of structural, temporal, and spatial correlations vary significantly depending on task complexity, model architecture, and algorithmic configurations. These findings suggest that algorithm designers should carefully evaluate correlation assumptions under specific deployment scenarios rather than assuming that they are always present. Motivated by these findings, we propose two adaptive compression designs that actively switch between different compression modes based on the measured correlation strength, and we evaluate their performance gains relative to conventional non-adaptive approaches. In summary, our unified taxonomy provides a clean and principled foundation for developing more effective and application-specific compression techniques for FL systems.

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.