Technical Report: Aggregation on Learnable Manifolds for Asynchronous Federated Optimization

In Federated Learning (FL), a primary challenge to the server-side aggregation of client models is device heterogeneity in both loss landscape geometry and computational capacity. This issue can be particularly pronounced in clinical contexts where variations in data distribution (aggravated by class imbalance), infrastructure requirements, and sample sizes are common. We propose AsyncManifold, a novel asynchronous FL framework to address these issues by taking advantage of underlying solution space geometry at each of the local training, delay-correction, and aggregation stages. Our proposal is accompanied by a convergence proof in a general form and, motivated through exploratory studies of local behaviour, a proof-of-concept algorithm which performs aggregation along non-linear mode connections and hence avoids barriers to convergence that techniques based on linear interpolation will encounter.