FlatLand Enhances Federated Learning with Hyperbolic Geometry for Graphs

Federated learning, while offering privacy-preserving collaborative model training, struggles with highly heterogeneous client data, particularly in graph-based scenarios where clients possess structurally diverse graphs. Existing personalized federated learning (PFL) methods often overlook the intrinsic geometric properties of these varied graph structures. A new method called FlatLand proposes to overcome this by embedding different clients' data into a tailored Lorentz space, which utilizes hyperbolic geometry. The core insight behind FlatLand is that hyperbolic geometry is naturally suited to accommodate the negative curvature often found in real-world graphs. Furthermore, the time-like dimension within Lorentz space provides a principled mechanism to encode client-specific heterogeneity. This allows for a parameter decoupling strategy where heterogeneous information (captured in time-like parameters) is separated from common knowledge (preserved in space-like parameters). This separation enables direct aggregation of models without needing complex client similarity estimations or additional computational modules. Empirical evaluations on various federated graph learning tasks demonstrated that FlatLand achieves superior performance, particularly when operating in low-dimensional settings, offering a more robust and efficient solution for personalized graph federated learning.