Research map / Federated learning and privacy / Personalized and heterogeneous FL

Subgraph Federated Learning via Spectral Methods

NeurIPS 2025 · Federated learning and privacy › Personalized and heterogeneous FL · approach: Federated semi-supervised and graph learning · 0 citations (OpenAlex)

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Proposes FedLap, a subgraph federated learning framework that uses Laplacian smoothing and a decentralized, encrypted Arnoldi iteration over the global Laplacian to share only spectral structure, with a membership-inference privacy analysis.

Problem

Subgraph federated learning for node classification where clients hold interconnected subgraphs; existing methods either share sensitive node embeddings/features or are computationally and communication-heavy and lack formal privacy guarantees.

Approach

Replace explicit global structural embeddings with a Laplacian regularizer in the spectral domain: the offline phase computes a truncated set of low-frequency Laplacian eigenvectors via a decentralized Arnoldi iteration using additively homomorphic encryption, after which training reduces to standard FedAvg; a membership-inference analysis bounds edge leakage.

Key results

• On Cora with 5 clients, FedLap reaches 80.85% accuracy versus 83.40% for centralized GNN and 81.48% for FedGCN-2hop.
• On PubMed with 10 clients, FedLap achieves 86.43% versus FedStruct 85.40%.
• On Chameleon, FedLap drops to about 33% while FedLap+ reaches about 54%, close to FedStruct's 55.8%.

Measured effects reported in the paper

Surprising findings

• FedLap performs poorly on heterophilic Chameleon (~33% vs ~54% for FedLap+), since Laplacian smoothing assumes neighboring nodes are similar.
• FedGCN, a non-private method, is reported to rely on a server seeing aggregated node features, and the authors note its official code omits isolated external neighbor removal, possibly inflating its numbers.

Limitations

• Privacy analysis is for a two-client worst-case attacker with known connection probability and delocalized eigenvector assumptions; the authors note the real attack is weaker than the theory.
• FedLap underperforms on heterophilic graphs such as Chameleon.
• Privacy analysis covers only the offline phase; the online phase is assumed protected by standard FL techniques.

Experimental setup

Datasets: Cora Citeseer PubMed Chameleon Amazon Photo ogbn-arxiv

Benchmarks: Cora Citeseer PubMed Chameleon Amazon Photo ogbn-arxiv

Metrics: node classification accuracy precision + recall (membership inference)

Baselines: FedSGD FedSage+ FedPub FedGCN FedStruct Central GNN Local GNN

Builds on: FedStruct Hop2Vec FedAvg GCN

Closest papers by meaning

• Decoupled Subgraph Federated Learning (ICLR 2025 · similarity 0.92)
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• Federated Graph Learning under Domain Shift with Generalizable Prototypes (AAAI 2024 · similarity 0.90)
• $S^2$FGL: Spatial Spectral Federated Graph Learning (ICML 2025 · similarity 0.89)
• Federated Graph Condensation with Information Bottleneck Principles (AAAI 2025 · similarity 0.89)
• FedSPA: Generalizable Federated Graph Learning under Homophily Heterogeneity (CVPR 2025 · similarity 0.88)