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.

翻译：图结构数据上的联邦学习暴露出标准聚合机制与图神经网络算子本质之间的根本性不匹配。联邦优化将模型参数视为共享欧氏空间中的元素，而图神经网络参数会诱导依赖于底层拓扑结构的图消息传递算子。当客户端图结构分布与数据分布存在异构性时，局部更新对应不同算子流形上的扰动。此类更新的线性聚合混合了几何不相容的方向，产生数值收敛但关系行为退化的全局模型。我们将这一现象形式化为跨域联邦图神经网络中全局聚合的几何失效，其表现为算子扰动间的破坏性干涉及消息传递动力学相干性的丧失。这种退化无法被损失值或准确率等传统指标捕捉——模型可能保持预测性能却丧失结构敏感性。针对该问题，我们提出GGRS（全局几何参考结构），一种在无数据代理上对算子扰动进行操作的服务器端聚合框架。GGRS通过方向对齐、子空间兼容性与敏感性控制实施几何可容纳性约束，从而保持诱导消息传递算子的结构完整性。