cs.LGSep 5, 2026

Rethinking One-Shot Federated Graph Learning: Training-Free Statistical Estimation

Authors: Shutong Zheng, Sijia Chen

Organizations: Sun Yat-sen University · The Hong Kong University of Science and Technology (Guangzhou)

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Abstract

One-shot federated graph learning generally aims to train Graph Neural Networks (GNNs) across clients with disconnected subgraphs in a single communication round. Existing methods predominantly design advanced optimization strategies under the premise that local GNN training is indispensable. However, empirical observations reveal that under extreme non-IID conditions, local GNN training suffers from severe cross-client representation misalignment, becoming a major source of error rather than a remedy. Motivated by this, we reformulate one-shot FGL as a statistical estimation problem. We propose SPEAR (Statistical Prototype Estimation with Adaptive Reliability), a completely training-free framework that directly computes topology-smoothed class prototypes from local graphs in the original feature space. The server then aggregates these prototypes using a sample-size-adaptive shrinkage estimator that down-weights unreliable local estimates, producing robust global class prototypes. Extensive experiments across seven benchmarks demonstrate that SPEAR consistently achieves state-of-the-art accuracy under extreme heterogeneity. Moreover, SPEAR delivers at least an order-of-magnitude speedup over all baselines, reaching several orders of magnitude against generative and distillation-based methods. Our findings suggest that training-free statistical estimation, rather than local GNN optimization, provides the key to robust and efficient one-shot federated graph learning. The code is available at https://github.com/Yodeesy/SPEAR .

Figures & tables

Figure 1: Time-Performance Pareto frontier on Coauthor-CS ( β=0.05\beta=0.05 ). Bubble size indicates the number of clients. To ensure fair overhead comparison, traditional FL (e.g., FedAvg) runs 100 rounds, whereas one-shot methods complete in 1 round. SPEAR breaks the accuracy-efficiency trade-off, delivering superior performance and multi-magnitude speedups across all scales.
Figure 2: UMAP Visualization and quantitative evaluation of node representations under extreme non-IID conditions (Cora, β=0.05\beta=0.05 ). Parameter-driven local optimization actively destroys the intrinsic structural alignment present in the raw features, leading to severe representation degradation.
Figure 3: Architecture of SPEAR. (Left) Clients estimate local prototypes pk,c\mathbf{p}_{k,c} via local topology smoothing (PPR) and transmit them alongside class sample sizes nk,cn_{k,c} . (Center) The server calibrates each local prototype via reliability-adaptive shrinkage (fusing it with the peer mean pˉ−k,c\bar{\mathbf{p}}_{-k,c} ) and performs sample-size weighted aggregation to yield the global prototype gc\mathbf{g}_{c} . (Right) For inference, predictions are made via cosine similarity matching between gc\mathbf{g}_{c} and the globally smoothed node features.
TypeMethodsCoraCiteSeerPubMedAmz-CompWikiCSCoauthor-CSogbn-arxiv
BLFedAvg [AISTATS17]34.7436.0861.9237.7019.4725.3314.58
FLFedProx [MLSys20]28.24 ↓6.5030.48 ↓5.6054.62 ↓7.3024.74 ↓12.964.22 ↓15.2523.33 ↓2.0013.37 ↓1.21
FedOPT [ICLR21]29.68 ↓5.0621.82 ↓14.2643.86 ↓18.0612.42 ↓25.2810.57 ↓8.907.76 ↓17.572.14 ↓12.44
MOON [CVPR21]27.98 ↓6.7622.12 ↓13.9645.50 ↓16.4223.71 ↓13.994.13 ↓15.3411.44 ↓13.8911.57 ↓3.01
FGLFedProto [AAAI22]30.50 ↓4.2424.56 ↓11.5252.86 ↓9.0637.66 ↓0.046.67 ↓12.8026.51 ↑1.185.20 ↓9.38
FedPub [ICML23]21.16 ↓13.5819.16 ↓16.9241.16 ↓20.7637.70 ↓0.0017.49 ↓1.988.51 ↓16.8210.16 ↓4.42
Table 1: Performance comparison on node classification tasks under the extreme non-IID setting (Dirichlet β=0.05\beta=0.05 with K=10K=10 clients). The abbreviations in the first column denote: BL (Baseline), and OSFL (One-shot Federated Learning). The best results are highlighted in bold , and the second-best results are underlined . The small numbers indicate the performance gap compared to FedAvg ( ↑\uparrow improvement, ↓\downarrow degradation).
MethodsCoraCiteSeerPubMedogbn-arxiv
Edge ( ρ=0.5\rho=0.5 )Feat. ( η=0.5\eta=0.5 )Edge ( ρ=0.5\rho=0.5 )Feat. ( η=0.5\eta=0.5 )Edge ( ρ=0.5\rho=0.5 )Feat. ( η=0.5\eta=0.5 )Edge ( ρ=0.5\rho=0.5 )Feat. ( η=0.5\eta=0.5 )
FedAvg31.90 ↓2.8431.90 ↓2.8418.10 ↓17.9818.20 ↓17.8842.40 ↓19.5248.30 ↓13.6222.28 ↑7.7010.22 ↓4.36
DENSE16.40 ↓8.7014.90 ↓10.2018.20 ↓0.1618.20 ↓0.1641.60 ↓0.1040.70 ↓1.003.48 ↓2.383.78 ↓2.08
FedCVAE15.10 ↑0.3231.90 ↑17.1217.20 ↑0.0313.80 ↓3.3741.00 ↑7.3240.80 ↑7.1221.56 ↑10.0412.55 ↑1.03
FedSD2C14.90 ↓6.7831.85 ↑10.1716.90 ↓1.7616.84 ↓1.8241.20 ↑8.3040.70 ↑7.807.87 ↑2.0018.87 ↑13.00
GHOST32.75 ↓5.4433.46 ↓4.7340.60 ↑1.6536.85 ↓2.1048.94 ↓10.0947.11 ↓11.9217.54 ↑2.0112.79 ↓2.74
Table 2: Robustness comparison under edge perturbation ( ρ=0.5\rho=0.5 ) and feature perturbation ( η=0.5\eta=0.5 ) on four representative datasets. Subscripts denote the absolute performance deviation ( ↑ improvement, ↓ degradation) compared to the clean setting.
MethodsCoraCiteSeerPubMedogbn-arxiv
FedAvg66s68s67s80s
2814MB7246MB984MB330MB
GHOST71s102s5716s20028s
16.0MB38.0MB7.0MB3.0MB
OASIS179s189s7004sOOM
44.0MB111MB17.0MB-
Table 3: Efficiency comparison on four representative datasets. Total federated training time (top) and communication cost (bottom) are reported for each method. The multiplier indicates SPEAR’s speedup relative to FedAvg.
VariantsCoraCiteSeerPubMedAmz-CompWikiCSCoauthor-CSogbn-arxiv
SPEAR (Full Model)63.3565.4774.0676.4263.7690.8137.24
w/o PPR59.00 ↓4.3562.03 ↓3.4472.60 ↓1.4674.32 ↓2.1061.01 ↓2.7589.85 ↓0.9633.78 ↓3.46
w/o Shrinkage55.13 ↓8.2259.27 ↓6.2065.20 ↓8.8662.84 ↓13.5860.16 ↓3.6087.14 ↓3.6732.96 ↓4.28
w/o Both (Baseline)59.70 ↓3.6561.70 ↓3.7772.30 ↓1.7674.33 ↓2.0960.99 ↓2.7789.84 ↓0.9733.79 ↓3.45
Table 4: Ablation study of SPEAR across seven datasets. The full model is systematically degraded by removing specific components to assess their individual contributions. Subscripts denote the absolute performance degradation ( ↓ ) relative to the complete SPEAR architecture.
Figure 4: Robustness analysis of SPEAR on Cora.
Figure 5: UMAP of SPEAR representations on Cora ( β=0.05\beta=0.05 ). Background scatter points are PPR-smoothed features. (a) Diamonds: uncalibrated local prototypes. (b) Stars: global prototypes calibrated via reliability-adaptive shrinkage.
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