PolarAir: A Compressed Sensing Scheme for Over-the-Air Federated Learning

TL;DR

PolarAir is a low-complexity compressed sensing scheme designed for over-the-air federated learning, significantly reducing communication costs while maintaining training performance over noisy channels.

Contribution

It introduces a novel linear compression method using compressed sensing and multiple access techniques tailored for federated learning over noisy channels.

Findings

Reduces channel use by approximately 30% compared to uncompressed transmission.

Maintains low time complexity for encoding and decoding.

Provides insights into gradient behavior and scheme performance during training.

Abstract

We explore a scheme that enables the training of a deep neural network in a Federated Learning configuration over an additive white Gaussian noise channel. The goal is to create a low complexity, linear compression strategy, called PolarAir, that reduces the size of the gradient at the user side to lower the number of channel uses needed to transmit it. The suggested approach belongs to the family of compressed sensing techniques, yet it constructs the sensing matrix and the recovery procedure using multiple access techniques. Simulations show that it can reduce the number of channel uses by ~30% when compared to conveying the gradient without compression. The main advantage of the proposed scheme over other schemes in the literature is its low time complexity. We also investigate the behavior of gradient updates and the performance of PolarAir throughout the training process to obtain insight on how best to construct this compression scheme based on compressed sensing.