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

arXiv: https://arxiv.org/abs/2602.15510 · HTML: https://mlsanity.com/paper/2602.15510/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 21 references that are in the map.
- First posted on arXiv 17 Feb 2026.

## Builds on (most cited first, 15 of 15)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Image-based Recommendations on Styles and Substitutes](https://mlsanity.com/paper/1506.04757/) (2015)
- [On the Bottleneck of Graph Neural Networks and its Practical Implications](https://mlsanity.com/paper/2006.05205/) (2020)
- [Train faster, generalize better: Stability of stochastic gradient descent](https://mlsanity.com/paper/1509.01240/) (2015)
- [Community Detection and Stochastic Block Models](https://mlsanity.com/paper/1703.10146/) (2017)
- [Implicit Bias of Gradient Descent on Linear Convolutional Networks](https://mlsanity.com/paper/1806.00468/) (2018)
- [OpenFGL: A Comprehensive Benchmark for Federated Graph Learning](https://mlsanity.com/paper/2408.16288/) (2024)

## Abstract (arXiv)

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.