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

Shutong Zheng; Sijia Chen

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)

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 (

\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.

Panel of Figure 2 — Figure 2: UMAP Visualization and quantitative evaluation of node representations under extreme non-IID conditions (Cora, $\beta=0.05$ ). 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 $\mathbf{p}_{k,c}$ via local topology smoothing (PPR) and transmit them alongside class sample sizes $n_{k,c}$ . (Center) The server calibrates each local prototype via reliability-adaptive shrinkage (fusing it with the peer mean $\bar{\mathbf{p}}_{-k,c}$ ) and performs sample-size weighted aggregation to yield the global prototype $\mathbf{g}_{c}$ . (Right) For inference, predictions are made via cosine similarity matching between $\mathbf{g}_{c}$ and the globally smoothed node features.

Type	Methods	Cora	CiteSeer	PubMed	Amz-Comp	WikiCS	Coauthor-CS	ogbn-arxiv
BL	FedAvg [AISTATS17]	34.74	36.08	61.92	37.70	19.47	25.33	14.58
FL	FedProx [MLSys20]	28.24 ↓6.50	30.48 ↓5.60	54.62 ↓7.30	24.74 ↓12.96	4.22 ↓15.25	23.33 ↓2.00	13.37 ↓1.21
	FedOPT [ICLR21]	29.68 ↓5.06	21.82 ↓14.26	43.86 ↓18.06	12.42 ↓25.28	10.57 ↓8.90	7.76 ↓17.57	2.14 ↓12.44
	MOON [CVPR21]	27.98 ↓6.76	22.12 ↓13.96	45.50 ↓16.42	23.71 ↓13.99	4.13 ↓15.34	11.44 ↓13.89	11.57 ↓3.01
FGL	FedProto [AAAI22]	30.50 ↓4.24	24.56 ↓11.52	52.86 ↓9.06	37.66 ↓0.04	6.67 ↓12.80	26.51 ↑1.18	5.20 ↓9.38
	FedPub [ICML23]	21.16 ↓13.58	19.16 ↓16.92	41.16 ↓20.76	37.70 ↓0.00	17.49 ↓1.98	8.51 ↓16.82	10.16 ↓4.42

Table 1: Performance comparison on node classification tasks under the extreme non-IID setting (Dirichlet

\beta=0.05

with

K=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).

Methods	Cora		CiteSeer		PubMed		ogbn-arxiv
Methods	Edge ( $\rho=0.5$ )	Feat. ( $\eta=0.5$ )	Edge ( $\rho=0.5$ )	Feat. ( $\eta=0.5$ )	Edge ( $\rho=0.5$ )	Feat. ( $\eta=0.5$ )	Edge ( $\rho=0.5$ )	Feat. ( $\eta=0.5$ )
FedAvg	31.90 ↓2.84	31.90 ↓2.84	18.10 ↓17.98	18.20 ↓17.88	42.40 ↓19.52	48.30 ↓13.62	22.28 ↑7.70	10.22 ↓4.36
DENSE	16.40 ↓8.70	14.90 ↓10.20	18.20 ↓0.16	18.20 ↓0.16	41.60 ↓0.10	40.70 ↓1.00	3.48 ↓2.38	3.78 ↓2.08
FedCVAE	15.10 ↑0.32	31.90 ↑17.12	17.20 ↑0.03	13.80 ↓3.37	41.00 ↑7.32	40.80 ↑7.12	21.56 ↑10.04	12.55 ↑1.03
FedSD2C	14.90 ↓6.78	31.85 ↑10.17	16.90 ↓1.76	16.84 ↓1.82	41.20 ↑8.30	40.70 ↑7.80	7.87 ↑2.00	18.87 ↑13.00
GHOST	32.75 ↓5.44	33.46 ↓4.73	40.60 ↑1.65	36.85 ↓2.10	48.94 ↓10.09	47.11 ↓11.92	17.54 ↑2.01	12.79 ↓2.74

Table 2: Robustness comparison under edge perturbation (

\rho=0.5

) and feature perturbation (

\eta=0.5

) on four representative datasets. Subscripts denote the absolute performance deviation ( ↑ improvement, ↓ degradation) compared to the clean setting.

Methods	Cora	CiteSeer	PubMed	ogbn-arxiv
FedAvg	66s	68s	67s	80s
FedAvg	2814MB	7246MB	984MB	330MB
GHOST	71s	102s	5716s	20028s
GHOST	16.0MB	38.0MB	7.0MB	3.0MB
OASIS	179s	189s	7004s	OOM
OASIS	44.0MB	111MB	17.0MB	-

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.

Variants	Cora	CiteSeer	PubMed	Amz-Comp	WikiCS	Coauthor-CS	ogbn-arxiv
SPEAR (Full Model)	63.35	65.47	74.06	76.42	63.76	90.81	37.24
w/o PPR	59.00 ↓4.35	62.03 ↓3.44	72.60 ↓1.46	74.32 ↓2.10	61.01 ↓2.75	89.85 ↓0.96	33.78 ↓3.46
w/o Shrinkage	55.13 ↓8.22	59.27 ↓6.20	65.20 ↓8.86	62.84 ↓13.58	60.16 ↓3.60	87.14 ↓3.67	32.96 ↓4.28
w/o Both (Baseline)	59.70 ↓3.65	61.70 ↓3.77	72.30 ↓1.76	74.33 ↓2.09	60.99 ↓2.77	89.84 ↓0.97	33.79 ↓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.

Panel of Figure 4 — Figure 4: Robustness analysis of SPEAR on Cora.

Panel of Figure 5 — Figure 5: UMAP of SPEAR representations on Cora ( $\beta=0.05$ ). Background scatter points are PPR-smoothed features. (a) Diamonds: uncalibrated local prototypes. (b) Stars: global prototypes calibrated via reliability-adaptive shrinkage.

Shrinkage Estimation

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Sep 6, 2026J/K move · Enter open · S save

Structural Entropy-Driven Graph Diffusion Generation for One-Shot Federated Graph Learning

Shutong Zheng, Lele Fu, Sheng Huang, Wei Yang Bryan Lim+1

Sun Yat-sen University Guangzhou, China · Nanyang Technological University Singapore

Federated Graph Learning Non-IID Federated Learning Graph Generation

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One-shot federated graph learning (FGL) requires the server to estimate client contributions from highly compressed information, yet conventional volume-based weighting captures the amount of client data while overlooking how its connectivity is organized. In this paper, we propose SPIRE, a Structural Entropy-Driven Graph Diffusion Generation method that introduces topology-aware client differentiation into one-shot FGL. Specifically, we employ first-order degree-distribution structural entropy as a compact descriptor of degree-mass dispersion and use it to derive structural client weights, providing an inductive bias that accounts for differences in graph topology beyond data volume. On the generation side, a graph diffusion model on the server synthesizes pseudographs conditioned on the weighted client prototypes, capturing both semantic and structural information without requiring additional client-side training. The generated pseudographs are then assembled via disjoint union fusion to train a global graph neural network. Extensive experiments on seven real-world graph datasets demonstrate that SPIRE consistently outperforms conventional and one-shot FGL methods, with particularly strong gains under highly heterogeneous (non-IID) and graph-perturbed settings.

Abstract

Shrinkage Estimation

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