# Structural Negative Transfer in Federated Graph Neural Networks: Diagnosis, Causal Investigation, and the Limits of Divergence-Aware Mitigation

arXiv: https://arxiv.org/abs/2609.16977 · HTML: https://mlsanity.com/paper/2609.16977/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 34 references that are in the map.
- First posted on arXiv 15 Sep 2026.

## Builds on (most cited first, 24 of 24)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [Adaptive Federated Optimization](https://mlsanity.com/paper/2003.00295/) (2020)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Tackling the Objective Inconsistency Problem in Heterogeneous Federated Optimization](https://mlsanity.com/paper/2007.07481/) (2020)
- [GradNorm: Gradient Normalization for Adaptive Loss Balancing in Deep Multitask Networks](https://mlsanity.com/paper/1711.02257/) (2017)
- [Model-Contrastive Federated Learning](https://mlsanity.com/paper/2103.16257/) (2021)
- [Byzantine-Robust Distributed Learning: Towards Optimal Statistical Rates](https://mlsanity.com/paper/1803.01498/) (2018)
- [Ditto: Fair and Robust Federated Learning Through Personalization](https://mlsanity.com/paper/2012.04221/) (2020)
- [Personalized Federated Learning with Moreau Envelopes](https://mlsanity.com/paper/2006.08848/) (2020)
- [Federated Learning Based on Dynamic Regularization](https://mlsanity.com/paper/2111.04263/) (2021)
- [Federated Learning with Personalization Layers](https://mlsanity.com/paper/1912.00818/) (2019)
- [Exploiting Shared Representations for Personalized Federated Learning](https://mlsanity.com/paper/2102.07078/) (2021)
- [An Efficient Framework for Clustered Federated Learning](https://mlsanity.com/paper/2006.04088/) (2020)
- [Conflict-Averse Gradient Descent for Multi-task Learning](https://mlsanity.com/paper/2110.14048/) (2021)
- [Robust Aggregation for Federated Learning](https://mlsanity.com/paper/1912.13445/) (2019)
- [Subgraph Federated Learning with Missing Neighbor Generation](https://mlsanity.com/paper/2106.13430/) (2021)
- [Federated Graph Classification over Non-IID Graphs](https://mlsanity.com/paper/2106.13423/) (2021)
- [Cross-Node Federated Graph Neural Network for Spatio-Temporal Data Modeling](https://mlsanity.com/paper/2106.05223/) (2021)
- [Personalized Subgraph Federated Learning](https://mlsanity.com/paper/2206.10206/) (2022)
- [OpenFGL: A Comprehensive Benchmark for Federated Graph Learning](https://mlsanity.com/paper/2408.16288/) (2024)
- [FedGraph: A Research Library and Benchmark for Federated Graph Learning](https://mlsanity.com/paper/2410.06340/) (2024)

## Abstract (arXiv)

Federated learning lets multiple participants train a shared model without pooling raw data, by exchanging locally trained model updates instead. Federated averaging assumes that averaging local models is a reasonable way to solve one shared problem when participants' data are broadly similar. Work on non-IID federated learning has shown that this assumption can withstand differences in label and feature distributions. We ask whether it survives a different strain specific to graph neural networks, where client graphs differ not in label or feature distribution but in structure itself, requiring the same shared weights to operate over fundamentally different topologies. We call the resulting harm structural negative transfer. In a federation of real citation networks and synthetic structural proxies, a structurally atypical client lost more than half its achievable accuracy simply by joining. In an initial six-client federation, two label-free structural statistics computable before training were strongly associated with this harm. Expanding to twenty clients showed that degree divergence remained associated with harm, although more weakly, and survived removal of domain contrast. Spectral divergence did not replicate, which we trace to a confound caused by the composition of the reference pool used for leave-one-out statistics. A causal intervention isolating topology found no significant effect. A degree-normalization mechanism held across twenty-four seeds but did not explain the harm when corrected. The best of five candidate fixes beat a tuned baseline only until a matched, structurally blind control was applied, after which the gain disappeared. What survives is a modest, partially replicated, degree-specific signal that is not yet a validated predictor at scale.