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 FedTopo, a framework that integrates Topological-Guided Block Screening (TGBS) and Topological Embedding (TE) to leverage topological information, yielding coherently aligned cross-client representations by Topological Alignment Loss (TAL). First, Topology-Guided Block Screening (TGBS) automatically identifies the most topology-informative block by selecting the layer with the highest topological separability, i.e., 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 (TAL) 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.