On the Loss-Landscape Connectivity in Federated Learning

Federated learning is a collaborative and distributed machine learning framework that has emerged as an effective way to train a global model across decentralized data sources while preserving privacy. Despite its empirical success and broad applications, our theoretical understanding has lagged behind, and many fundamental questions remain open. We ask what it does to the geometry of the search itself and what underlying mechanisms make it work. $\textit{(Q1)}$ Why does coordinate-wise averaging work: how are the client models connected to each other and to the barycenter, and when do barriers appear? $\textit{(Q2)}$ Does per-round re-alignment actively constrain clients into a shared basin, changing the explored landscape rather than merely parallelizing gradient descent?