On the Role of Network Topology in Decentralized Federated Learning: Empirical Insights and Theoretical Foundations

This thesis examines the fundamental role of network topology in fully decentralized federated learning (FDFL) systems, combining empirical investigation with rigorous the- oretical analysis. As data volumes grow and edge devices proliferate, current centralized federated learning (CFL) architectures that depend on a central server face substantial challenges including limited scalability, communication bottlenecks, and vulnerability to single points of failure. FDFL addresses these limitations by eliminating the central server and enabling direct peer-to-peer communication among nodes, making it par- ticularly suitable for large-scale distributed applications. However, the decentralized structure of FDFL creates intricate interdependencies between network topology and learning behavior that are not yet well understood. This thesis seeks to clarify these interdependencies through a dual-strategy that combines extensive empirical analysis with theoretical framework development. Using comprehensive experiments on standard benchmark datasets (MNIST, Fashion- MNIST, CIFAR-10, EMNIST), we show that network topology has significant and non- trivial effects on learning dynamics. Our findings indicate that nodes with high central- ity can either facilitate or hinder knowledge propagation depending on how data is dis- tributed across the network, and that FDFL systems possess inherent resilience against node failures. From the theoretical standpoint, we investigate the FDFL learning dynamics trough the lens of Complex Network Theory. We develop a framework based on spectral graph theory that rigorously relates network structural properties to learning dynamics, en- abling both explanation of observed phenomena and prediction of system performance. Our model goes beyond previous research, which usually only takes into account simpler network architectures, by characterising convergence behaviour on arbitrary graphs. Notably, our framework captures both the asymptotic convergence properties and the transient dynamics of the learning process. Through extensive numerical validation, we demonstrate strong quantitative agreement between theoretical predictions and empiri- cal observations across various topological configurations. These contributions provide both theoretical insights and practical guidance for designing and implementing decen- tralized learning systems in real-world networked environments, advancing both the fundamental understanding and practical application of distributed machine learning at scale