A tale of interference in machine learning over-the-air

This tutorial aims to present the current research efforts on implementing machine learning algorithms in wireless systems. Specifically, we provide a comprehensive coverage of a distributed learning paradigm based on over-the-air computing, a.k.a. over-the-air machine learning (OTA-ML). We will present the general architecture, model training algorithm, and an analytical framework that quantifies the convergence rate of OTA-ML. The analysis takes into account key effects from wireless transmissions, such as channel fading and interference, on the convergence performance. It discloses how interference is deteriorating the model training process. Then, we elaborate on several improvements to the OTA-ML from different aspects. Particularly, we introduce model pruning schemes that reduce the computation and communication overheads for OTA-ML. We also discuss the system enhancements from an algorithmic perspective, e.g., adopting adaptive optimization methods to accelerate the training, leveraging gradient clipping to improve the robustness of the training process, as well as how foundation models could be integrated to boost the performance of OTA-ML. Moreover, a personalization framework will be introduced to enhance performance and robustness for OTA-ML. Finally, we will elaborate on the analysis of generalization error of the statistical models trained by OTA-ML, revealing that wireless interference has the potential of improving the generalization capability. A few signal processing methods that exploit interference for a better generalization will also be discussed. We will conclude this tutorial by shedding light on future works.