On the Geometric Coherence of Global Aggregation in Federated Graph Neural Networks

TL;DR

This paper identifies a geometric mismatch problem in federated GNNs caused by naive aggregation, leading to degraded relational reasoning, and proposes GGRS to preserve operator coherence during aggregation.

Contribution

It formalizes the geometric failure in federated GNN aggregation and introduces GGRS, a novel server-side method to maintain operator coherence without data sharing.

Findings

GGRS improves structural sensitivity preservation in federated GNNs.

Traditional aggregation can cause destructive interference in operator space.

GGRS maintains message-passing dynamics despite data heterogeneity.

Abstract

Federated learning over graph-structured data exposes a fundamental mismatch between standard aggregation mechanisms and the operator nature of graph neural networks (GNNs). While federated optimization treats model parameters as elements of a shared Euclidean space, GNN parameters induce graph-dependent message-passing operators whose semantics depend on underlying topology. Under structurally and distributionally heterogeneous client graph distributions, local updates correspond to perturbations of distinct operator manifolds. Linear aggregation of such updates mixes geometrically incompatible directions, producing global models that converge numerically yet exhibit degraded relational behavior. We formalize this phenomenon as a geometric failure of global aggregation in cross-domain federated GNNs, characterized by destructive interference between operator perturbations and loss of coherence in message-passing dynamics. This degradation is not captured by conventional metrics such as loss or accuracy, as models may retain predictive performance while losing structural sensitivity. To address this, we propose GGRS (Global Geometric Reference Structure), a server-side aggregation framework operating on a data-free proxy of operator perturbations. GGRS enforces geometric admissibility via directional alignment, subspace compatibility, and sensitivity control, preserving the structure of the induced message-passing operator.