FedTopo: Topology-Informed Representation Alignment in Federated Learning under Non-I.I.D. Conditions

Current federated-learning models deteriorate under heterogeneous (non-I.I.D.) client data, as their feature representations diverge and pixel-or patch-level objectives fail to capture the global topology which is essential for high-dimensional visual tasks. We propose FedT opo, a framework that integrates T opological-Guided Block Screening (TGBS) and T opological Embedding (TE) to leverage topological information, yielding coherently aligned cross-client representations by T opological Alignment Loss (T AL). First, Topology-Guided Block Screening (TGBS) automatically selects the most topology-informative block, i.e., the one with maximal topological separability, whose persistence-based signatures best distinguish within-versus between-class pairs, ensuring that subsequent analysis focuses on topology-rich features. Next, this block yields a compact Topological Embedding, which quantifies the topological information for each client. Finally, a Topological Alignment Loss (T AL) guides clients to maintain topological consistency with the global model during optimization, reducing representation drift across rounds. Experiments on Fashion-MNIST, CIFAR-10, and CIFAR-100 under four non-I.I.D. partitions show that FedTopo accelerates convergence and improves accuracy over strong baselines. Code is available in Supplementary Materials.