Geometry-Aware Slow-Fast Learning for Decentralized Federated Learning

Data heterogeneity in decentralized federated learning is inherently non-uniform: different model parameters exhibit different levels of cross-client stability and adaptation speed, while different clients vary in their compatibility for knowledge exchange. However, most existing approaches still rely on largely uniform optimization and consensus rules, overlooking this fine-grained structure of heterogeneous collaboration. We therefore argue that effective decentralized learning should jointly account for two complementary dimensions: parameter-wise adaptation timescales and client-wise collaboration geometry. To this end, we propose Geometry-aware Slow-Fast Learning (GeoSF), a decentralized learning framework that explicitly models both forms of heterogeneity. At the parameter level, GeoSF organizes model parameters into two dynamically evolving groups: slow parameters that remain stable across clients and preserve transferable shared knowledge, and fast parameters that respond more strongly to local data and support client-specific adaptation. GeoSF then matches their distinct roles with different optimization and communication timescales, using smaller learning rates and more frequent synchronization for slow parameters, while allowing fast parameters to evolve more rapidly and synchronize less frequently. At the client level, GeoSF adapts peer-to-peer consensus according to the geometric compatibility of neighboring models, promoting beneficial information exchange while suppressing interference from heterogeneous peers. Together, these mechanisms establish a unified slow-fast learning paradigm that jointly coordinates parameter dynamics and client interactions under decentralized heterogeneity. Extensive experiments across feature-skew and label-skew settings, model architectures, communication topologies, and client scales demonstrate that GeoSF consistently outperforms representative federated and decentralized baselines.