FedGL: Federated Graph Learning Framework with Global Self-Supervision

• Graph data are distributed across organizations because privacy, security, and competition make centralized collection impractical.The paper frames collaborative graph learning without compromising privacy as an open and crucial problem.Source: §1 · pp. 1–2
• Federated graph learning faces heterogeneity from Non-IID client graphs and complementarity from overlapping nodes with incomplete local structure.These challenges can produce divergent local models and prevent clients from exploiting information available elsewhere.Source: §1 · p. 2
• FedGL is presented as a general framework rather than one restricted to a specific graph model, while the experiments instantiate graph neural networks.The framework uses federated local training with a server and K clients, alongside the additional self-supervision exchange.Source: §1 · p. 3
• FedGL uploads client prediction results and node embeddings to discover global pseudo labels and a global pseudo graph.The server distributes pseudo labels to enrich training labels and the pseudo graph to complement each client’s structure.Source: §1 · p. 3
• Global pseudo labels let client information flow in a privacy-preserving manner, mitigating heterogeneity and allowing stronger clients to aid weaker ones.The global pseudo graph similarly shares client structure while preserving privacy and exploiting complementarity.Source: §1 · pp. 3–4
• FedGL significantly outperforms centralized, simple federated, and local methods on four widely used graph datasets.The paper also reports parameter and ablation experiments verifying FedGL’s stability and robustness.Source: §1 · p. 4

2.1 Federated Learning

• 2.1 Federated Learning: Federated learning trains a shared global model by aggregating locally computed client updates while keeping training data distributed.The process iterates between local training, server aggregation, and redistribution of the updated model.Source: §2.1 · p. 4
• 2.1 Federated Learning: Federated learning addresses isolated data settings where data cannot be directly aggregated because of privacy, security, or intellectual-property constraints.Source: §2.1 · p. 4

2.2 Graph Learning

• 2.2 Graph Learning: Graph learning mines graph data through representations such as node embeddings for downstream tasks including node classification, clustering, and link prediction.Graph neural networks jointly use graph topology, node attributes, and neural networks to learn node embeddings.Source: §2.2 · p. 5
• 2.2 Graph Learning: Spectral-based GCNs require the whole graph as input and cannot scale to large graphs, motivating spatial methods that aggregate information from neighbors.Sampling and subgraph training can improve the computational efficiency of spatial-based methods.Source: §2.2 · p. 5

2.3 Self-Supervised Learning

• 2.3 Self-Supervised Learning: Graph self-supervision uses label-free pretext tasks such as node clustering, link prediction, and graph partitioning, or constructs pseudo labels from data or predictions.Self-supervised learning can also serve as pre-training or regularization for the main task.Source: §2.3 · p. 5
• 2.3 Self-Supervised Learning: Self-supervised learning has been applied to graph data and can be used alone, for pre-training, or as a regularization item to improve the main task.Source: §2.3 · p. 5

3.1 Notations

• 3.1 Notations: A graph is represented by nodes and edges, with adjacency and degree matrices describing connectivity, node features describing attributes, and one-hot labels describing classes.Source: §3.1 · pp. 5–6

3.2 Graph Neural Networks

• 3.2 Graph Neural Networks: The representative GCN propagates information through immediate neighbors across layers, starting from node features and producing final node embeddings and class probabilities.The model uses added self-connections and a nonlinear activation, with weights updated by minimizing cross-entropy on labeled nodes.Source: §3.2 · p. 6
• 3.2 Graph Neural Networks: For semi-supervised node classification, the GCN computes cross-entropy over labeled nodes and obtains predicted class probabilities through Softmax.Source: §3.2 · p. 6

3.3 Federated Learning Framework

• 3.3 Federated Learning Framework: Federated training is expected to achieve testing performance equivalent to centralized training while keeping data distributed across clients.Source: §3.3 · pp. 6–7
• 3.3 Federated Learning Framework: Federated learning consists of clients that train local models and a server that aggregates their parameters into a global model.The global model is redistributed and training repeats until convergence or a maximum iteration count.Source: §3.3 · p. 6
• 3.3 Federated Learning Framework: Server aggregation updates the global model from client-uploaded parameters, commonly using a weighted average, before sending it back to clients.Clients may be selected for participation, and gradients may be uploaded instead of parameters.Source: §3.3 · p. 7

4.1 Problem Definition

• FedGL targets a global model that performs well on a jointly determined global test set and locally on each client’s test set.The global model is intended to approach centralized-training performance globally and outperform independently trained client models locally.Source: §4.1 · p. 7

4.2 The Framework of FedGL

• Clients train GCNs locally and upload model parameters, node embeddings, and prediction results, while the server aggregates parameters and returns the global model.Client training proceeds in parallel, and server aggregation uses a weighted average before distributing the resulting model.Source: §4.2 · p. 8
• FedGL discovers global pseudo labels and a global pseudo graph from client predictions and embeddings, then redistributes them to improve local and global models privacy-preservingly.Global pseudo labels help information flow from higher-quality to lower-quality clients, while the pseudo graph shares complementary graph structure across clients.Source: §4.2 · pp. 8–9

4.3.1 Global Pseudo Label Utilization.

• Global pseudo labels are projected onto each client’s unlabeled nodes and added as self-supervised targets alongside the GCN loss.Rows corresponding to labeled training nodes are removed, and the resulting cross-entropy self-supervised loss is controlled by coefficient α.Source: §4.3.1 · pp. 9–10

4.3.2 Global Pseudo Graph Utilization.

• Each client projects the global pseudo graph onto its nodes and fuses it with the original normalized graph to restore or strengthen connections.Coefficient β controls the strength of pseudo-graph-based structural complementation in the GCN.Source: §4.3.2 · p. 10

4.4 Global Model

• The global GCN aggregates client parameters with FedAvg-style weights proportional to each client’s node count, reducing the effect of data-volume imbalance.Direct aggregation requires consistent input and hidden feature dimensions across clients.Source: §4.4 · p. 10

4.5 Global Self-supervision Discovery

• Global self-supervision is motivated by heterogeneity in clients’ graph structures and label distributions, which causes their locally trained models to differ.Data-volume weighting alone can only alleviate imbalance to some extent, motivating additional cross-client supervision.Source: §4.5 · p. 11
• FedGL has clients upload prediction results and node embeddings so the server can discover global pseudo labels and a global pseudo graph for privacy-preserving information sharing.The server distributes these self-supervision signals to enrich training labels and complement graph structure, alleviating heterogeneity and exploiting graph-data complementarity.Source: §4.5 · p. 11

4.5.1 Global Pseudo Label Discovery

• The server fuses client prediction results with data-volume weights, then selects predictions above confidence threshold λ as global pseudo labels.Smaller λ selects more pseudo labels, whereas larger λ selects fewer but more reliable labels.Source: §4.5.1 · p. 11

4.5.2 Global Pseudo Graph Construction

• The server fuses client node embeddings and reconstructs a global pseudo graph from embedding similarities, retaining at most s neighbors per node to preserve sparsity.The constructed adjacency rows are normalized after keeping only their largest s elements.Source: §4.5.2 · p. 12

4.6 Model Training

• FedGL trains local models in parallel while clients use server-discovered self-supervision and the server aggregates models and refreshes pseudo labels and graphs until convergence.Clients and server alternate these operations iteratively to obtain the global model.Source: §4.6 · p. 12

• The evaluation uses extensive node-classification experiments and includes studies under different federated-learning settings and parameter configurations.The experiments are designed to evaluate FedGL’s effectiveness and answer the stated research questions.Source: §5 · p. 12
• FedGL’s experiments assess whether it learns a high-quality global graph model, mitigates client heterogeneity, improves over local methods, and remains effective across federated settings.The study also examines how global self-supervision parameters affect performance.Source: §5 · pp. 12–13
• FedGL alternates client-side local training with server-side global model aggregation and discovery of global pseudo labels and a global pseudo graph.Clients obtain embeddings and predictions, optimize GCN and self-supervised losses, and the server updates the shared model and self-supervision signals.Source: §5 · p. 13
• The server obtains global predictions, discovers pseudo labels, aggregates node embeddings, and constructs the global pseudo graph for subsequent client training.These operations are specified as the server-side steps of FedGL’s algorithm.Source: §5 · p. 13

5.1 Datasets

• Experiments use Cora, Citeseer, ACM, and Wiki, covering citation, academic, and web-page graphs with bag-of-words node features.Cora, Citeseer, and ACM are academic networks, while Wiki is a web-page hyperlink network.Source: §5.1 · pp. 13–14
• The fixed split uses 20 labels per class for training, 500 validation labels, and 1,000 testing labels, while random splits use fewer class labels.Random splits use 5, 10, or 15 labels per class for Cora, Citeseer, and Wiki, and 15, 25, or 35 for ACM.Source: §5.1 · p. 14

5.2 Comparison Methods

• The comparison methods include centralized and local GCN training, simple federated averaging without global self-supervision, and FedGL ablations removing GPG or GPL.The ablations isolate the contributions of the global pseudo graph and global pseudo label.Source: §5.2 · p. 14
• The centralized method is an ideal reference rather than a feasible deployment option because it requires gathering distributed data despite privacy and competition constraints.This comparison establishes a practical boundary for interpreting centralized results.Source: §5.2 · p. 14

5.3.1 Data Settings for Federated Learning.

• Client graphs are formed by random sampling under different proportions so that node counts, graph structures, and label distributions are diverse and Non-IID.Random sampling also creates overlapping nodes between clients.Source: §5.3.1 · pp. 14–15
• The global goal evaluates the final model on a merged global testing set, whereas the local goal evaluates that model separately on each client’s local testing set.The two goals distinguish shared global performance from client-specific performance.Source: §5.3.1 · p. 15

5.3.2 Parameter Settings.

• The model uses a two-layer GCN with 16 hidden units, 0.5 dropout, 0.01 learning rate, and 5 × 10^-4 L2 regularization.These GCN parameters follow the settings of the original paper [22].Source: §5.3.2 · p. 15
• Federated training uses six clients, full participation per round, 10 local epochs, up to 300 rounds, and early stopping after 30 rounds.Client sampling proportions are [30%,40%,50%,50%,60%,70%].Source: §5.3.2 · p. 15
• Global self-supervision uses dataset-dependent confidence and learning coefficients, with global pseudo graph coefficient β=1 and neighbor number s=100.The confidence threshold λ is 0.1 for Wiki and 0.5 for other datasets; α is 0.1 for Wiki and 0.2 otherwise.Source: §5.3.2 · p. 15

5.4.1 Fixed Split.

• 2%-7% absolute performance improvement over Centralized across various datasets shows FedGL learns a high-quality global model despite distributed data.The reported explanation combines global self-supervision with client graph overlap and sampling complementarity.Source: §5.4.1 · p. 15
• 5.8% is the largest reported absolute improvement over Federated on Citeseer, with FedGL outperforming Federated across all datasets.FedGL differs by discovering and exploiting global self-supervision to address client heterogeneity and graph complementarity.Source: §5.4.1 · p. 16
• Using both global pseudo labels and the global pseudo graph performs best in most cases, while the pseudo label alone is generally more helpful than the pseudo graph alone.The two components are described as complementary, with pseudo labels closer to full FedGL performance than pseudo graphs.Source: §5.4.1 · p. 16

5.4.2 Random Split.

• More than 10% absolute improvement over Centralized occurs on Cora, ACM, and Wiki when only 5 labels per class are available.ACM uses 15 labels per class in this comparison, and the advantage is described as especially pronounced under scarce labels.Source: §5.4.2 · p. 16
• More than 5% absolute improvement over Federated under most random label ratios demonstrates stable performance across random splits.FedGL still outperforms Centralized and Federated across most datasets and label ratios.Source: §5.4.2 · p. 16

5.4.3 Visualization of Node Embedding.

• FedGL produces compact, clearly separated node embeddings, whereas Centralized and Federated embeddings remain more scattered or overlap across classes.Embeddings are visualized with t-SNE on Cora, Citeseer, and ACM; Wiki is omitted because it has 17 classes.Source: §5.4.3 · pp. 16–17

5.5.1 Graph Data Distribution of Clients.

• Fig. 10 evaluates node classification accuracy for clients C1-C6 across different datasets under the local goal.The surrounding analysis reports FedGL's superiority to Local and Federated.Source: Figure 10 · p. 18, §5.5.2 · p. 18
• Client graphs are Non-IID and highly heterogeneous yet complementary, with differing label proportions and degree distributions.Client 1 has more isolated and one-edge nodes, indicating particularly poor graph structure.Source: §5.5.1 · p. 18

5.5.2 Performance Comparison.

• FedGL is distinctly superior to Federated under the local goal by enriching training labels and complementing graph structure.The resulting local models contribute to a higher-quality global model.Source: §5.5.2 · pp. 18–19
• FedGL outperforms Local on every client and dataset, with relatively stable performance despite Non-IID graph data.Federated cooperation and global self-supervision are identified as the two reasons for this improvement.Source: §5.5.2 · pp. 18–19

5.6.1 Client Participation Ratio per Round.

• Almost no performance decline occurs when only 30%, 50%, 70%, or 90% of clients participate per round, while FedGL remains better than Federated.Citeseer even shows a slight accuracy improvement, despite reduced uploaded predictions and embeddings.Source: §5.6.1 · p. 19

5.6.2 Number of Clients and Data Size.

• The [50%,60%,70%,80%] setting gives the best results for FedGL and Federated, indicating that client data size matters more than client count.Higher-quality global models are associated with relatively large, similarly sized client datasets.Source: §5.6.2 · p. 19
• FedFL still outperforms Federated in most cases, especially under [20%, 40%, 50%, 70%, 70%, 90%], indicating that global self-supervision effectively alleviates graph heterogeneity.Source: §5.6.2 · p. 19
• FedGL maintains promising results and its superiority when clients have different numbers of clients and data sizes, including relatively severe Non-IID settings.The cited experiment reports continued performance despite changed client sampling proportions.Source: §5.6.2 · p. 20

5.6.3 Overlapping Node Ratio between Clients.

• With overlapping node ratios controlled at 5%, 10%, and 15%, FedGL still outperforms Centralized and Federated, while its two ablation versions achieve the best results in different datasets when used alone.Source: §5.6.3 · p. 20

5.7.1 Confidence Threshold.

• At least 5% accuracy improvement over Federated on Citeseer occurs whenever the global pseudo label is used across tested confidence thresholds.FedGL and FedGL w/o GPG outperform Federated under various λ values, with [0.1, 0.3] identified as desirable overall.Source: §5.7.1 · p. 21

5.7.2 Self-supervised Learning Coefficient.

• FedGL performance first increases and then drops sharply as α grows beyond a threshold, confirming that self-supervision should support rather than dominate the main task.For relatively small α, FedGL and FedGL w/o GPG outperform Federated.Source: §5.7.2 · p. 21

5.7.3 Global Pseudo Graph Coefficient.

• FedGL and FedGL w/o GPG remain relatively stable and above Federated as β increases, despite small fluctuations.β controls the strength of complementing the graph structure through the global pseudo graph.Source: §5.7.3 · p. 21

5.7.4 Neighbor Number of Global Pseudo Graph.

• FedGL and FedGL w/o GPG remain relatively stable and above Federated as the global pseudo graph neighbor number s varies.The tested neighbor numbers range from 5 to 1000, and s controls pseudo-graph sparsity.Source: §5.7.4 · p. 22

• FedGL collaborates across clients to train a high-quality graph model while protecting data privacy.Source: §6 · p. 22
• Global self-supervision lets client information flow and share in a privacy-preserving manner, mitigating heterogeneity and exploiting graph-data complementarity.Source: §6 · p. 22
• Clients upload prediction results and node embeddings so the server can discover global pseudo labels and a global pseudo graph.Source: §6 · p. 22
• The server distributes these self-supervision signals to enrich training labels and complement each client’s graph structure.Source: §6 · p. 22
• Experiments on node classification show that FedGL significantly outperforms centralized, simple federated, and local methods.Source: §6 · p. 22
• FedGL is not limited to specific graph models, but future work will evaluate it on more models and settings with heterogeneous models or multimodal client data.Source: §6 · p. 22