GeoProtoFL: Are Class Prototypes Geometrically Aggregatable in Heterogeneous Federated Learning?

Prototype-based heterogeneous federated learning (HtFL) enables clients with different model architectures to collaborate through class-prototype exchange instead of parameter aggregation. Existing methods commonly map client features to a shared prototype dimension and directly aggregate the resulting prototype coordinates, implicitly relying on their coordinate systems being comparable across clients. However, independently trained feature extractors across heterogeneous clients may represent equivalent class structures in different client-specific coordinate frames. Consequently, direct aggregation of unregistered prototypes may distort the resulting global prototypes. To address this issue, we introduce GeoProtoFL, a geometry-aware method designed to make heterogeneous class prototypes geometrically aggregatable. Each client learns a local bi-projection with equiangular tight frame (ETF) anchoring to map pooled backbone features onto a shared spherical prototype interface. The server registers each client prototype configuration to a server reference configuration through closed-form Procrustes registration performing gauge registration, then computes each global prototype as a class-wise Fr\'echet barycenter of the registered prototypes intrinsic aggregation. GeoProtoFL realizes geometric aggregatability through gauge-consistent server-side prototype construction and intrinsic consensus under the spherical metric defined by the shared interface, without requiring public data or homogeneous client architectures. Across standard benchmarks, it consistently improves over representative HtFL baselines, achieving gains of up to 2.61% over the strongest baseline in a given setting while remaining robust across varying statistical heterogeneity, model heterogeneity, and federation-scale settings.