# S2FGL: Spatial Spectral Federated Graph Learning

arXiv: https://arxiv.org/abs/2507.02409 · HTML: https://mlsanity.com/paper/2507.02409/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 51 of its 74 references that are in the map.
- First posted on arXiv 3 Jul 2025.

## Builds on (most cited first, 30 of 51)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Tackling the Objective Inconsistency Problem in Heterogeneous Federated Optimization](https://mlsanity.com/paper/2007.07481/) (2020)
- [Federated Multi-Task Learning](https://mlsanity.com/paper/1705.10467/) (2017)
- [Federated Learning Based on Dynamic Regularization](https://mlsanity.com/paper/2111.04263/) (2021)
- [Rethinking Graph Transformers with Spectral Attention](https://mlsanity.com/paper/2106.03893/) (2021)
- [Data-Free Knowledge Distillation for Heterogeneous Federated Learning](https://mlsanity.com/paper/2105.10056/) (2021)
- [A critical look at the evaluation of GNNs under heterophily: Are we really making progress?](https://mlsanity.com/paper/2302.11640/) (2023)
- [BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation](https://mlsanity.com/paper/2106.10994/) (2021)
- [Rethinking Graph Neural Networks for Anomaly Detection](https://mlsanity.com/paper/2205.15508/) (2022)
- [SCAFFOLD: Stochastic Controlled Averaging for Federated Learning](https://mlsanity.com/paper/1910.06378/) (2019)
- [How Powerful are Spectral Graph Neural Networks](https://mlsanity.com/paper/2205.11172/) (2022)
- [Revisiting Heterophily For Graph Neural Networks](https://mlsanity.com/paper/2210.07606/) (2022)
- [A Semi-supervised Graph Attentive Network for Financial Fraud Detection](https://mlsanity.com/paper/2003.01171/) (2020)
- [Subgraph Federated Learning with Missing Neighbor Generation](https://mlsanity.com/paper/2106.13430/) (2021)
- [FairFed: Enabling Group Fairness in Federated Learning](https://mlsanity.com/paper/2110.00857/) (2021)
- [Federated Graph Classification over Non-IID Graphs](https://mlsanity.com/paper/2106.13423/) (2021)
- [Federated Learning with Label Distribution Skew via Logits Calibration](https://mlsanity.com/paper/2209.00189/) (2022)
- [Specformer: Spectral Graph Neural Networks Meet Transformers](https://mlsanity.com/paper/2303.01028/) (2023)
- [Federated Learning for Generalization, Robustness, Fairness: A Survey and Benchmark](https://mlsanity.com/paper/2311.06750/) (2023)
- [Asynchronous Federated Learning on Heterogeneous Devices: A Survey](https://mlsanity.com/paper/2109.04269/) (2021)
- [Federated Learning on Non-IID Graphs via Structural Knowledge Sharing](https://mlsanity.com/paper/2211.13009/) (2022)
- [Preservation of the Global Knowledge by Not-True Distillation in Federated Learning](https://mlsanity.com/paper/2106.03097/) (2021)
- [Convolutional Neural Networks on Graphs with Chebyshev Approximation, Revisited](https://mlsanity.com/paper/2202.03580/) (2022)
- [Federated Learning on Heterogeneous and Long-Tailed Data via Classifier Re-Training with Federated Features](https://mlsanity.com/paper/2204.13399/) (2022)
- [FedCorr: Multi-Stage Federated Learning for Label Noise Correction](https://mlsanity.com/paper/2204.04677/) (2022)
- [Personalized Subgraph Federated Learning](https://mlsanity.com/paper/2206.10206/) (2022)
- [Federated Graph Neural Networks: Overview, Techniques and Challenges](https://mlsanity.com/paper/2202.07256/) (2022)

## Built on by (most cited first, 7 of 7)

- [MM-OpenFGL: A Comprehensive Benchmark for Multimodal Federated Graph Learning](https://mlsanity.com/paper/2601.22416/) (2026)
- [STAGE: Tackling Semantic Drift in Multimodal Federated Graph Learning](https://mlsanity.com/paper/2605.11919/) (2026)
- [PRISM: Topology-Aware Cross-Modal Imputation for Modality-Deficient Federated Graph Learning](https://mlsanity.com/paper/2606.09301/) (2026)
- [Towards Effective Federated Multimodal Graph Learning via Navigating Multifaceted Heterogeneity](https://mlsanity.com/paper/2608.00623/) (2026)
- [Low-pass Personalized Subgraph Federated Recommendation](https://mlsanity.com/paper/2603.20338/) (2026)
- [Towards Federated Long-Tailed Graph Learning: An Energy-Guided Dual Decoupling Approach](https://mlsanity.com/paper/2606.24237/) (2026)
- [Towards Adaptive Federated Graph Clustering: A Global Community-aware Contrastive Learning-based Approach](https://mlsanity.com/paper/2609.26063/) (2026)

## Abstract (arXiv)

Federated Graph Learning (FGL) combines the privacy-preserving capabilities of federated learning (FL) with the strong graph modeling capability of Graph Neural Networks (GNNs). Current research addresses subgraph-FL from the structural perspective, neglecting the propagation of graph signals on spatial and spectral domains of the structure. From a spatial perspective, subgraph-FL introduces edge disconnections between clients, leading to disruptions in label signals and a degradation in the semantic knowledge of the global GNN. From a spectral perspective, spectral heterogeneity causes inconsistencies in signal frequencies across subgraphs, which makes local GNNs overfit the local signal propagation schemes. As a result, spectral client drift occurs, undermining global generalizability. To tackle the challenges, we propose a global knowledge repository to mitigate the challenge of poor semantic knowledge caused by label signal disruption. Furthermore, we design a frequency alignment to address spectral client drift. The combination of Spatial and Spectral strategies forms our framework S2FGL. Extensive experiments on multiple datasets demonstrate the superiority of S2FGL. The code is available at https://github.com/Wonder7racer/S2FGL.git.