On the Geometric Coherence of Global Aggregation in Federated GNN

Abstract: Federated Learning (FL) enables distributed training across multiple clients without centralized data sharing, while Graph Neural Networks (GNNs) model relational data through message passing. In federated GNN settings, client graphs often exhibit heterogeneous structural and propagation characteristics. When standard aggregation mechanisms are applied to such heterogeneous updates, the global model may converge numerically while exhibiting degraded relational behavior.Our work identifies a geometric failure mode of global aggregation in Cross- Domain Federated GNNs. Although GNN parameters are numerically represented as vectors, they encode relational transformations that govern the direction, strength, and sensitivity of information flow across graph neighborhoods. Aggregating updates originating from incompatible propagation regimes can therefore introduce destructive interference in this transformation space.This leads to loss of coherence in global message passing. Importantly, this degradation is not necessarily reflected in conventional metrics such as loss or accuracy.To address this issue, we propose GGRS (Global Geometric Reference Structure), a server-side framework that regulates client updates prior to aggregation based on geometric admissibility criteria. GGRS preserves directional consistency of relational transformations as well as maintains diversity of admissible propagation subspaces. It also stabilizes sensitivity to neighborhood interactions, without accessing client data or graph topology. Experiments on heterogeneous GNN-native, Amazon Co-purchase datasets demonstrate that GGRS preserves global message-passing coherence across training rounds by highlighting the necessity of geometry-aware regulation in federated graph learning.