Title: FlatLand: Personalized Graph Federated Learning via Tailored Lorentz Space
Primary area: alignment, fairness, safety, privacy, and societal considerations
Keywords: Federated Learning, Hyperbolic Geometry

Abstract: Personalized Federated Learning (PFL) has gained attention for privacy-preserving training on heterogeneous data. However, existing methods fail to capture the unique inherent geometric properties across diverse datasets by assuming a unified Euclidean space for all data distributions. Drawing on hyperbolic geometry's ability to fit complex data properties, we present FlatLand, a novel personalized federated learning method that embeds different clients' data in tailored Lorentz space. FlatLand is able to directly tackle the challenge of heterogeneity through the personalized curvatures of their respective Lorentz model of hyperbolic geometry, which is manifested by the time-like dimension. Leveraging the Lorentz model properties, we further design a parameter decoupling strategy that enables direct server aggregation of common client information, with reduced heterogeneity interference and without the need for client-wise similarity estimation. To the best of our knowledge, this is the first attempt to incorporate hyperbolic geometry into personalized federated learning. Empirical results on various federated graph learning tasks demonstrate that achieves superior performance, particularly in low-dimensional settings.