# Beyond Rigid Alignment: Graph Federated Learning via Dual Manifold Calibration

arXiv: https://arxiv.org/abs/2605.06260 · HTML: https://mlsanity.com/paper/2605.06260/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 44 references that are in the map.
- First posted on arXiv 7 May 2026.

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

- [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)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Federated Learning with Personalization Layers](https://mlsanity.com/paper/1912.00818/) (2019)
- [Clustered Federated Learning: Model-Agnostic Distributed Multi-Task Optimization under Privacy Constraints](https://mlsanity.com/paper/1910.01991/) (2019)
- [FedProto: Federated Prototype Learning across Heterogeneous Clients](https://mlsanity.com/paper/2105.00243/) (2021)
- [A critical look at the evaluation of GNNs under heterophily: Are we really making progress?](https://mlsanity.com/paper/2302.11640/) (2023)
- [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)
- [Graph Attention Multi-Layer Perceptron](https://mlsanity.com/paper/2206.04355/) (2022)
- [Unified Optimal Transport Framework for Universal Domain Adaptation](https://mlsanity.com/paper/2210.17067/) (2022)
- [Personalized Subgraph Federated Learning](https://mlsanity.com/paper/2206.10206/) (2022)
- [Rectangular Flows for Manifold Learning](https://mlsanity.com/paper/2106.01413/) (2021)
- [FedGTA: Topology-aware Averaging for Federated Graph Learning](https://mlsanity.com/paper/2401.11755/) (2024)
- [Geometric Understanding of Deep Learning](https://mlsanity.com/paper/1805.10451/) (2018)
- [Federated Graph Semantic and Structural Learning](https://mlsanity.com/paper/2406.18937/) (2024)
- [FedTAD: Topology-aware Data-free Knowledge Distillation for Subgraph Federated Learning](https://mlsanity.com/paper/2404.14061/) (2024)
- [AdaFGL: A New Paradigm for Federated Node Classification with Topology Heterogeneity](https://mlsanity.com/paper/2401.11750/) (2024)
- [How Universal Polynomial Bases Enhance Spectral Graph Neural Networks: Heterophily, Over-smoothing, and Over-squashing](https://mlsanity.com/paper/2405.12474/) (2024)
- [Hardness of Learning Neural Networks under the Manifold Hypothesis](https://mlsanity.com/paper/2406.01461/) (2024)
- [On a linear Gromov-Wasserstein distance](https://mlsanity.com/paper/2112.11964/) (2021)
- [CSOT: Curriculum and Structure-Aware Optimal Transport for Learning with Noisy Labels](https://mlsanity.com/paper/2312.06221/) (2023)
- [Guiding Neural Collapse: Optimising Towards the Nearest Simplex Equiangular Tight Frame](https://mlsanity.com/paper/2411.01248/) (2024)
- [Modeling Inter-Intra Heterogeneity for Graph Federated Learning](https://mlsanity.com/paper/2412.11402/) (2024)
- [Hyperspectral Image Classification With Contrastive Graph Convolutional Network](https://mlsanity.com/paper/2205.11237/) (2022)
- [Atom-Motif Contrastive Transformer for Molecular Property Prediction](https://mlsanity.com/paper/2310.07351/) (2023)
- [Homophily Heterogeneity Matters in Graph Federated Learning: A Spectrum Sharing and Complementing Perspective](https://mlsanity.com/paper/2502.13732/) (2025)
- [Heterogeneity-Aware Knowledge Sharing for Graph Federated Learning](https://mlsanity.com/paper/2601.21589/) (2026)

## Abstract (arXiv)

Graph Federated Learning (GFL) enables collaborative representation learning across distributed subgraphs while preserving privacy. However, heterogeneity remains a critical challenge, as subgraphs across clients typically differ significantly in both semantics and structures. Existing methods address heterogeneity by enforcing the rigid alignment of model parameters or prototypes between clients and the server. However, these alignments implicitly rely on a restrictive global linearity assumption that summarizes local data distributions using a single and globally consistent representation space. This severely compresses the personalized representation space of clients and fails to preserve diverse local graph distributions. To overcome these limitations, we propose Federated Graph Manifold Calibration (FedGMC), a novel paradigm that tackles semantic heterogeneity and structural heterogeneity from a unified manifold perspective. Instead of enforcing rigid alignment, FedGMC introduces a dual manifold calibration mechanism that preserves global commonalities while maximizing the personalized representation space of local clients. Specifically, for semantic heterogeneity, the server constructs a geometrically optimal semantic manifold via equidistant semantic anchors, so as to guide the calibration of local semantic manifolds. For structural heterogeneity, the server constructs a global structural manifold by building global structural templates, so as to guide the calibration of local structural manifolds. Finally, the server dynamically refines both global semantic manifolds and structural manifolds by aggregating local manifolds. Extensive experiments on eleven homophilic and heterophilic graphs demonstrate that FedGMC effectively balances global commonality and local personalization, thereby significantly outperforming state-of-the-art baseline methods.