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

TL;DR

FedTopo tackles non-I.I.D. federated learning by enforcing cross-client topological consistency on intermediate representations. It introduces a three-part mechanism: TGBS to select the topology-rich block, TE as a compact persistence-image based descriptor, and TAL with an adaptive schedule to align local and global topologies. Theoretical guarantees include Lipschitz stability of TE and a FedProx-like convergence result, while experiments on FMNIST, CIFAR-10, and CIFAR-100 show faster convergence and higher accuracy across diverse non-I.I.D. partitions. Overall, the work demonstrates that multi-scale topological information can serve as a robust regularizer for cross-client representation learning in decentralized settings.

Abstract

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 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 (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.

Figures (7)

• Figure 1: Comparison of feature distributions, activation maps, and topological structure. (a) t-SNE of 'cat' feature embeddings. (b) Feature/activation map visualizations for two samples. (c) Persistence diagrams for the selected dog sample.
• Figure 2: Topological embedding pipeline illustrated using a CIFAR-10 cat image. We show the input image, its intermediate feature map (a), the persistence diagrams from selected channels (b), the corresponding persistence images (c), and the final averaged topological embedding (d).
• Figure 3: System overview of FedTopo, illustrated using ResNet-18 and CIFAR-10. (a) Before training, TGBS selects the most topology-informative block based on class separability in topological space. (b) During training, each client computes topological embeddings from intermediate features and applies Topological Alignment Loss (TAL) with adaptive scheduling.
• Figure 4: UMAP 2D feature projection of five clients and the global model at different communication rounds.
• Figure B.1: AUC heatmap across backbone layers and reduced dimensions. The best AUC (0.814) occurs at layer2 (dim 0), indicating the most topology-informative block for class separation.

Theorems & Definitions (9)

• Proposition 1: AUC Implies Mutual Information
• Proposition 2: Stability of Topological Embedding
• Proposition 3: FedProx-style Convergence under TAL
• Proposition 4: Monotonicity of MI Lower Bound via Bayes Error and Fano’s Inequality
• Corollary 1: Equal Class Priors and Total Variation Distance
• Remark 1: Applicability to Distance-Based AUCs
• Proposition 5: Lipschitz stability of TE
• Remark 2: Concatenated TE
• Proposition 6: FedProx-style convergence with TAL