GHOST: Generalizable One-Shot Federated Graph Learning with Proxy-Based Topology Knowledge Retention
Authors: Jiaru Qian
Guancheng Wan
Wenke Huang
Guibin Zhang
Yuxin Wu
Bo Du
Mang Ye
Venue: ICML 2025 poster (2025)
Keywords: Federated Learning
Graph Learning
Primary area: social_aspects->privacy

Abstract: Federated Graph Learning (FGL) proposes an effective approach to collaboratively training Graph Neural Networks (GNNs) while maintaining privacy. Nevertheless, communication efficiency becomes a critical bottleneck in environments with limited resources. In this context, one-shot FGL emerges as a promising solution by restricting communication to a single round. However, prevailing FGL methods face two key challenges in the one-shot setting: 1) They heavily rely on gradual personalized optimization over multiple rounds, undermining the capability of the global model to efficiently generalize across diverse graph structures. 2) They are prone to overfitting to local data distributions due to extreme structural bias, leading to catastrophic forgetting. To address these issues, we introduce **GHOST**, an innovative one-shot FGL framework. In GHOST, we establish a proxy model for each client to leverage diverse local knowledge and integrate it to train the global model. During training, we identify and consolidate parameters essential for capturing topological knowledge, thereby mitigating catastrophic forgetting. Extensive experiments on real-world tasks demonstrate the superiority and generalization capability of GHOST. The code is available at https://github.com/JiaruQian/GHOST.

GHOST: Generalizable One-Shot Federated Graph Learning with Proxy-Based Topology Knowledge Retention
Jiaru Qian
Guancheng Wan
Wenke Huang"
Guibin Zhang 2
Yuxin Wu
Bo Du
Mang Ye
Abstract
Constrained Resources
Federated Graph Learning (FGL.) proposes an ef- fective approach collaboratively training Graph Neural Networks (GNNs) while maintaining pri- vacy. Nevertheless, communication efficiency be- comes critical bottleneck in environments with limited resources. In this context, one-shot FGL emerges as a promising solution by restricting communication to a single round. However, pre- vailing FGL methods face two key challenges in the one-shot setting: 1) They heavily rely gradual personalized optimization over mul- tiple rounds, undermining the capability of the global model to efficiently generalize across di- verse graph structures. 2) They are prone to overfitting to local data distributions due to ex- treme structural bias, leading to catastrophic for- getting. To address these issues, we introduce GHOST, an innovative one-shot FGL framework. In GHOST, we establish proxy model for each client to leverage diverse local knowledge and integrate to train the global model. During training, we identify and consolidate parameters essential for capturing topological knowledge, thereby mitigating catastrophic forgetting. Ex- tensive experiments real-world tasks demon- strate the superiority and generalization capabil- ity of GHOST. The code is available at https: / ///ittuubl com Jaroom//aaae htt////iaaiiianoaSSSS.
Local Update
Server
One Round
Communication
Chents
Structure
*9
Features
Iterative Training
1 1...0
1 1...0 0....
Dual-Shift
?
m
Topology Forgetting
Global Model
Learning
(a) Poor Ceneralizable Ability
(b) Catastrophic Forgetting
Figure 1. Problem Illustration. environments with constrained
resources, one-shot FGL becomes promising solution by limiting communication to one round. We identify two key challenges in the one-shot setting. (a) Poor Generalizable Ability: Traditional FGL. methods depend on gradual personalized updates. However, pattern shifts in both feature structure dimension and limited communication rounds hinder the ability of the global model to efficiently generalize across diverse graphs (b) Catastrophic For- getting: Structural biases across clients cause the model to overfit to current local data distributions, leading to the loss of critical topology knowledge acquired previously.
1. Introduction
model training across multiple clients while ensuring data privacy by avoiding the aggregation raw data. However, many real-world datasets are graph-structured (Xia et al., 2021; Wang et al., 2021; Li al., 2025b; Wan al., 2025b; 2024b), where nodes represent entities and edges capture the relationships connections between them. In the context of graph-structured data, the integration of Graph Neural Networks (GNNs) (Wu et al., 2020; Scarselli et al., 2008; Li et al., 2025a; Wan et al., 2025a: Huang et al., 2023a) has given rise to Federated Graph Learning (FGL). FGL has ap- plications across various domains, including healthcare (Xu
Federated Learning (FL) (Li et al., 2020a; Kairouz et al., 2021; Konečný, 2016; Hu et al., 2023) enables decentralized
'Equal contribution National Engineering Research Center for Multimedia Software, School of Computer Science. Wuhan University, Wuhan, China "National University of Singapore, Sin- gapore "Renmin University of China. Correspondence to: Mang Ye <<yemangee www.cdu.cn>>
Proceedings of the ndnd International Conference Machine Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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GHOST: Generalizable One-Shot Federated Graph Learning with Proxy-Based Topology Knowledge Retention
et al., 2021; Antunes et al., 2022), social networks (Khan et al., 2021; He et al., 2019), and recommendation systems (Gao et al., 2023; Wu et al., 202 The primary challenge in FGL lies in addressing the heterogeneity (Huang et al., 2023c; Sun et al., 2024; Liao et al., 2024), of graph data, es- pecially in topology dimension. Recent studies (Huang et al., 2025; Tan et al., 2025) have proposed various strategies to overcome the challenge. Approaches such as topology- aware aggregation (Fu et al., 2025; Li et al., 2024d; Fu et al., 2024), graph simplification techniques (Chen et al., 2021; Lei et al., 2023), and knowledge distillation (Huang et al., 2023b; Zhu et al., 2024b) have demonstrated their potential to improve model alignment across clients.
overfit the current data distributions encountered during training. As a result, critical topology knowledge acquired during previous training epochs are gradually forgotten, cul- minating in catastrophic forgetting (Serra et al., 2018; Lee et al., 2017; Kemker et al., 2018). 8). This limitation not only reduces effectiivneess of the model on previously encoun- tered data but also impairs its ability to generalize across diverse graph structures. This leads to another crucial ques- tion: II) how can we alleviate catastrophic forgetting while ensuring generalization across diverse graph structures?
To address the aforementioned questions, we introduce GHOST: Generalizable One-SHOr Federated Graph Learn- ing with Proxy-BaSer Topology Knowledge Retention. To address I), we first adopt a one-shot generalized FGI. ap- proach. For each client, we establish proxy model to ex- tract diverse knowledge from its local data. Specifically, we construct Dual-Level Alignment (DLA) to train the proxy model, enabling it to fully explore both feature and structural information. Each client uploads its proxy model parame- ters to the central server only once. The acquired knowledge is then integrated to collaboratively train GNN, enhancing its generalization capability while mitigating the negative impact of inherent data heterogeneity.
Despite the effectiveness of these methods in traditional FGL scenarios, they face significant challenges when ap- plied to environments with constrained communication sources, such as edge-computing systems or decentralized networks with limited bandwidth (Zhou et al., 2021). In such contexts, the efficiency of information exchange be- comes a critical bottleneck, hindering the sharing and ex- ploration of knowledge across clients during training. As communication costs escalate, the ability to transfer mean- ingful updates between clients is compromised, leading to performance degradation and ultimately impeding the learn- ing process (Yao et al., 2024). A promising solution to this issue is one-shot FGL. which streamlines the communica- tion process by reducing it to a single round. By minimizing the need for repeated communication, one-shot FGL can alleviate the strain on communication resources while still enabling effective model training, potentially overcoming the limitations of traditional multi-round methods.
Since topological information plays a crucial role during training, we propose Soobloyy-Consiouus Knowledge Re- tention (TCKR) to address II). Our approach explicitly ex- plores partial structures within the input graph by computing the
Criterion, which identifies the pa- rameters essential for capturing topological information. By stabilizing these critical parameters from diverse graphs, we enable the model to consolidate acquired knowledge while balancing the integration of information under extreme struc- tural bias, thereby alleviating catastrophic forgetting. Our principal contributions are summarized as follows.
However, existing FGL methods largely depend on person alized updates and multiple iterative communication rounds, focusing primarily on optimizing local models tailored to client data distributions (Chen et al., 2022; Zhang et al., 2023). While effective, personalized approaches are prone to overfit to local data, and the one-round communication setting further limits opportunities for iterative knowledge exchange. As result, the chance to gradually capturing lo- cal diverse knowledge across multiple rounds is constrained, preventing models from efficiently refining generalizable knowledge. Consequently, the aggregated global model often struggles to generalize effectively to diverse graph data. This raises the following question: 1) How can we efficiently capture diverse local knowledge to train gener- alized model in one communication round?
We are the first to incorporate the one-shot setting into generalized FGL. We identify that existing FGL methods face challenges in constrained communication scenarios, where they struggle to efficiently train a generalized global model. Additionally, catastrophic forgetting hampers the retention of topological knowledge across diverse graphs. We introduce GHOST, generalized one-shot FGL ap- proach. For each client, we introduce proxy model to fully explore dual-level knowledge. Furthermore, we em-- phasize the retention of acquired topological information during global training to mitigate catastrophic forgetting. Extensive experiments validate the superiority and robust generalization capability of GHOST, demonstrating its adaptability across graphs of varying scales.
In addition, under conditions of extreme structural bias, ex- isting FGL models face a significant challenge in retaining previously learned structural knowledge while maintaining generalization capacity. Structural bias (Kong et al., 2024; Zhang al., 2021), characterized by substantial differences in graph topologies across clients, can cause the model to
2. Related Work
Federated Graph Learning. Federated Graph Learning (FGL.) enables collaborative training among multiple clients
2

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GHOST: Generalizable One-Shot Federated Graph Learning with Proxy-Based Topology Knowledge Retention
via a trusted server without sharing graph data (He al., 2021; Liu et al., 2024; Li et al., 2024c; Huang et al., 2023b; Wan et al., 2025c; Zhang et al., 2024a). FGL approaches are categorized into two types: inter-graph and intra- intra-graph (Li et al., 2025c; Tan et al., 2025). Inter-graph methods such as GCFL+ (Xie et al., 2021) and FedStar (Tan et al., 2023) assume clients possess disjoint graphs, while intra- graph methods like FedSSP (Tan al.. 2024b) and FGGP (Wan et al., 2024a) handle clients that hold subgraphs of global graph. However, these methods rely substantial iterative communication, incurring significant costs. We are the first to address this issue by establishing a proxy model for each client to capture the knowledge from local data. Furthermore, each client uploads the parameters of its proxy model only once, enhancing both efficiency and security.
compromises F-dimensional feature vectors 24 correspond- ing node Vi. The adjacency matrix of g is denoted as A E RRXN,, where Aii,j) = 1 if there is an edge between nodes and j and A(i,j) = 0 otherwise. Then, Graph Neu- ral Networks (GNN) obtains a representation of the node by recursively aggregating and transforming the representa- tions of its neighbors. Specifically, the hidden representation h4 of node vs at the 1-th layer is computed as:
h
(PD( oy E ((a))))
(I)
where hy is the representation of node o; at 1-th layer, (()) denotes the neighbor nodes set of node vi, AGG(.) aggre- gates the neighbor representations and UPD(..) updates the representation of node d/2 given its representation and the aggregated neighbor representations at the previous layer. Specifically, 4ς = Vi.
One-shot Federated Learning. One-shot Federated Learn- ing (Guha et al., 2019; Zeng et al., 2024) has emerged as an efficient solution by minimizing communication rounds and enhancing security against eavesdropping attacks. Re- cent methods (Zhang et al., 2022; Heinbaugh et al., 2023; Jhunjhunwala et al., 2024; Yang et al., 2024) utilize knowl- edge distillation or neuron-matching techniques to optimize the global model. However, existing one-shot FL methods primarily limited to computer vision tasks, overlooking graph structures, which results in significantly poorer perfor- mance and slower convergence in graph-based applications. In this study, we take an innovative approach by focusing on the multifaceted topological characteristics (Li et al., 2024b; Shi et al., 2024; Deng et al., 2025) of graphs, addressing feature-structure dual heterogeneity across clients.
One-shot Federated Graph Learning, In the federated setting, there is one server and a set of clients C, with [C] = K clients (indexed by k). Rach client stores local graph dataset G = (V* ) and the adjacency matrix for the k-th client's 's graph g is denoted as A A Each node v; E V has a feature vector x and a label y!" Within the system, each client has a local differentiable model parameterized by w* and uploads its parameters w² to the server. In contrast to traditional Federated Graph Learning (FGL), one-shot FGL restricts the communication single round.
4. Methodology
4.1. Overview.
Catastrophic Forgetting. Catastrophic forgetting is a criti- cal issue in continual learning, where models continuously learn from a stream of data with the aim of gradually ex- tending acquired knowledge for future learning (Kirkpatrick et al., 2017; Wang et al., 2024). Existing approaches (Wang et al., 2020b; Liu et al., 2021: Sun et al.. 2023) to mitigate catastrophic forgetting can be broadly categorized into three paradigms: replay methods, regularization-ben based methods, and parameter isolation methods. A persistent challenge across these methodologies lies in balancing the integra- tion of knowledge from varying data distributions (Huang et al., 2022), particularly for graph data in non-Euclidean spaces. To address this, our work stabilizes the key pa- rameters involved in learning topological properties across diverse graphs, thereby alleviating catastrophic forgetting.
The proposed GHOST can be decomposed into two com- ponents: Dual-Level Aligned Proxy Model and Topology- Conscious Knowledge Retention, corresponding to Sec. 4.2 and Sec. 4.3, respectively. In Sec. 4.2, we introduce a proxy model for each client that captures both feature- and topological knowledge. Each proxy model captures the di- verse local knowledge and uploads its parameters to the server only once, thereby enhancing communication elfi- ciency. In Sec. 4.3, we construct the Coherence Factor and Topology- Consistency Criterion to evaluate the contribu- tion of each parameter in preserving structural knowledge. During the global training phase, we adopt the Knowledge Retention Loss to stabilize those critical parameters, thus al- leviating overfitting and catastrophic forgetting. The frame- work illustration of our method is shown in Figure 2.
3. Motivation
4.2. Dual-Level Aligned Proxy Model
3.1. Preliminaries
Motivation. In one shot setting, existing FGL methods often fail to efficiently leverage the underlying diverse knowledge of all the clients, leading to the poor generalizable ability of the global model. As a consequence, the inherent data heterogeneity in both feature and structure dimension will
Graph Neural Networks Define the graph data as g = (V, E) with V as the node-set encompassing N nodes and E as the edge-set. The feature matrix X {01 .2....,
3

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GHOST: Generalizable One-Shot Federated Graph Learning with Proxy-Basce -aaed Topolegy Knowledge Retention
Client k
Dual-Level Aligned Proxy Model
Feature-Less Alignment
Ld
Psesado Features
Caup
Cosine Simularity
Labels
Need To Be Aliinedi
Local Dataset
Capture Knowlodge
Real Giraph
Real Graph
Divergence
Eater
Pscudo Graph
Random Noise
Structure-Leve Alignment
Pseudo Adjacencc Matrix
Generate
Aligument
Passed Grumov-
Wasserstein
Promy Model
Transport Plan
Upload
Graph
L
Reall Graph
Pseudo Graph
Knowledge Integration
Topology-Consciout Conscious Knowledge Retention
Server
Glohal Model
crusk
Doo
Liuch
Aggregation
M
Peatures
9
Consolidate
Ly
Change Next Epoch??
Generated Froen All Proxy Models
Laper
hg Coherence Pactor
Uliden--Lap Representations
Consistency Criterion
Figure 2. Architecture illustration of GHOST. The upper part represents client-side steps, while the lower part illustrates the server-side process. Upper left is the local training process where the proxy model the client effectively captures local knowledge. Upper right shows the specific implementation of Dual-Leve Alignment, which is divided into feature-level and structure- level. Lower left illustrates the server-side process of aggregating the knowledge learned by proxy models from all clients and generating an integrated knowledge set for training the global model. Lower right shows the global model training on downstream tasks with crucial parameters stabilized alleviate catastrophic forgetting. The far-right section displays the legend. Zoom in for details.
inevitably undermine the model performance. To overcome this, we aim to develop proxy model that efficiently cap- tures diverse local knowledge and align the model in both feature and topological dual-level dimension with only one communication round.
X and pseudo adjacency matrix Å, while their correspond- ing labels y [31, .e.....NN' remain unchanged.
Dual-Level Alignment. For graph data residing in non- Euclidean spaces, structure plays an indispensable role, en- capsulating wealth of unique information that crucial for understanding the relationships and dynamics within the data. Thus, our objective is to ensure that the proxy model of each client thoroughly captures both feature-based and topological information from local data.
Local Proxy Model. To fully capture the specific pattern of local graph data, we establish proxy model P(.) for each client. For each node v E y in the graph G, we input random noise sampled from a Gaussian distribution, along with the label y of the node. The proxy model then generates a new feature vector è; E R.F:
To facilitate the accurate representation of statistical proper- ties in the proxy model, it is essential to align the probability distributions between the local data and the pseudo graph. To address this challenge, we introduce the Divergence Loss, novel loss function designed to minimize the discrepancy between the probability distributions of the local data and the pseudo graph. This loss ensures that the proxy model maintains consistency with the underlying data distribution, thereby improving its ability to capture both feature-baser and topological information.
f P(z; ys).
In the same way, obtain the pseudo feature matrix X f NN E NxF. Based on X, we utilize the K-Neuresi Neighbors strategy to construct the pseudo adjacency matrix A:
1, if E TopK(H(i)) (H(i), otherwise,
H = (XXT) . A(..)
M
(3)
Lasv
1
ΣΣ
8: (f) log
si( 3.(
(4)
where (-) represents the sigmoid function, TopK(-) selects the indices of the IC largest values from given input vector, and Hi) denotes the i-th row vector of H. Subsequently, we obtain the pseudo graph Ó with the pseudo feature matrix
where $; = softmax(z;), 8, = softmax (f:) and f denotes the f-th dimension of the vector. Moreover, to ensure that

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GHOST: Generalizable One-Shot Federated Graph Learning with Proxy-Based Topolegy Knowledge Retention
the proxy model effectively aligns the local feature represen- tation while mitigating the risk of mode collapse, apply the Dispersion Loss to the proxy model:
Knowledge Integration. After local training, the server aggregates the proxy models to integrate diverse knowledge. Specifically, for the proxy model (h( from client k. we input random noise = sampled from a Gaussian distribu- tion. To simulate real-world data diversity, we generate a pseudo-label vector g² E R where the distribution across all classes uniform, ensuring that all aspects of knowl- edge are considered. Then, by applying Equation (2) and Equation (3), generate the pseudo graph G with fea- ture matrix X and adjacency matrix A through the proxy model Pk (t). The knowledge set for client k can be denoted as G3 = { , &h J. erated graphs. Subsequently, the integrated knowledge set is given by 9s = O3 U 9 U...U...... which is used to jointly train the global model.
V
1
R3 I Ij
ddisp = 1
(5)
IV
8:ll2
112:122
Meanwhile, capturing the topological essence of graph data is equally important. To address this, we incorporate the Fused Gromov- -asseerttttt (FGW) Loss, which combines both feature and structural alignment. This ensures that the proxy model not only aligns with the statistical properties of the local features but also preserves the intrinsic topological relationships encoded in the graph structure. Specifically, the FGW Loss is defined as:
where M is the number of gen-
Hopology-Consistence Criterion. Given the extensive knowledge generated by all proxy models, the global model faces the risk of overfitting to the current knowledge set and catastrophic forgetting. Therefore, it is crucial to ex- tract topological commonalities across diverse graphs and consolidate the acquired information during the global train- ing phase. Specifically, we aim identify critical parame- ters for capturing topological consensus among the diverse knowledge in the integrated set.
Lig
min
Σ (a(A(1,)) v))
T(PAA)
+ (1 (1-a) (I-x) xw)11B T.a
where a [0. 1] and X(i) represents the i-th row vector of X. The transport plan I N is optimized align nodes between the local graph G and the pscudo graph G, such that Ti quantifies the amount of mass transported between node i in G and node in G. The optimization is constrained by the distributions μ and é. which represent the marginal distributions of nodes in G and G, respectively. These are typically assumed to be uniform distributions, reflecting the equal importance of all nodes: Σラ=1 Fi. = uuii, Σ Piş- = A(j). Thus, we establish the Dual- Level Alignment Loss as follows:
For pseudo graph 9% in knowledge set G we denote the hidden representation of node 0; at the 1-th layer as ht. Then, we introduce Coherence Factor 7is to measure the alignment between the hidden representations of connected nodes i; and By, which is computed as:
(8) where represents the parameters of the global GNN, and 0 denotes the weight matrix of the 1-th layer. Then, we obtain the vector 7/4 = Ih ........ 7md for node u. where n = (W(x;)) The Coherence Factor Ni quantifies the similarity between the acquired representations of two con- nected nodes, thereby encouraging the model to maintain the memory of consistent topological structures across different graphs in the integrated knowledge set.
N = (hi, (TT) tanh(h', e'w).
Lduat = Ldiep + AaCdio + Agw
(7)
where \a and 'y are hyperparameters that balance the con- tributions of each loss function. After local training with the Dual-Level Alignment Loss, each client uploads the parameters of its proxy model, restricting communication to a single round. On the server side, the diverse information gathered from all proxy models is aggregated to collabo- ratively train a generalizable global GNN, enabling to effectively handle downstream tasks.
As demonstrated in (Zenke al., 2017), the infinitesimal up- date 8()) in the parameters O during the training phase leads to a corresponding change 8(1ig) in the Coherence Factor. Building on this relationship, we compute the Topology- Consistency Criterion to assess the importance of each pa- rameter in capturing the structural knowledge of the input graphs. The knowledge set 9' can be calculated as:
4.3. Tonslogy-Conseious Knowledge Retention.
Motivation. Extreme structural bias in FGL models causes them to overfit the current data distribution, leading to catas- trophic forgetting and poor generalization ability. To ad- Knowl-
Criterion T, for each
dress this issue, we propose Coppoloy-Conscionn edge Retention, which explicitly leverages the topological information in graphs. This approach helps the model con- solidate acquired knowledge while balancing the integration of diverse information from heterogeneous graph structures.
V Σ
T
I
(9)
00 Wi
where W = 10%, denotes the number of weight parame-
5

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GHOST: Generalizable One-Shot Federated Graph Learning with Proxy-Based Topolegy Knowledge Retention
ters. The Criterion THe has the same shape as the weight matrix 0g representing the importance of each parame- ter in capturing the structural knowledge. We then define T = [T ........ Th I as the criterion for the entire model with I. layers (excluding the projection head).
prove that the attacker has no effective means recover meaningful data through such guessing attempts.
.....
5. Experiment
In this section, we comprehensively evaluate our proposed GHOST by addressing the following key questions.
When the global model transitions to new training phase with the knowledge set g after learning from G it crucial stabilize the key parame- Cri-
Knowledge Retention.
ters identified by the previous Happolgy--Cosistern teria (7', ,T, ..... }. To achieve this, we introduce the Knowledge Retention Loss, which aims to consolidate the
Q1: Superiority. Does GHOST maintain or surpass
baseline performance?
Q2: Resilience How does GHOST perform under varying degrees of data heterogeneity?
acquired topological knowledge:
Q3: Effectiveness. Do different modules of GHOST
1-11 th @ (0' -ft),
contribute to its overall performance?
c++1
(10)
Q4: Sensitivity. How does GHOST perform under differ- ent hyper-parameter settings?
where & denotes element-wise multiplication, and 0.- rep- resents the optimal parameters of the 1-th layer after training on the knowledge set G'.. However, some values in T may become excessively large. reducing the flexibility of the model and its ability to assimilate new knowledge, To ad- dress this, we introduce the 12 norm as regularization term for T, thereby enhancing the robustness and plasticity of the global model. Thus, we define the loss function for training the global GNN with the knowledge set g as:
The answer of Q1-Q3 are illustrated in Sec. 5,2-Sec. 5.4, and the analyses of Q4 can be found in Appendix F.
5.1. Experimental Setup
We perform experiments on node classification tasks in vari- ous scenarios to validate the superiority of our framework.
Datasets. To effectively evaluate the performance of our approach, we employed seven benchmark graph datasets of various scales and features, including Cora (McCallum et al., 2000), CiteSeer (Giles et al., 1998), PubMed (Canese & Weis, 2013), Chameleon (Pei et al., 2020), Amazon- Photo, Coauthor-CS (Shchur et al., 2018) and Ogbn-Arxiv (Hu et al., 2020). Detailed descriptions and splits for these datasets can be found in Appendix B.
C =
ch+1 task Ax + 112,
(11)
where Lrask represents the task-specific loss function. For instance, we can employ Cross-Entropy (CE) Loss or Nega- tive Log-Likee Likelioodd (NLL) Loss. The hyperparameters X, and X, control the relative importance of each loss term.
Baselines. We compare our method with several tradi- tional FL Approaches: (1) FedAvg [ASTATI7 17] (McMahan et al., 2017), (2) FedProx [MLSys20] (Li et al., 2020b), (3) FedNova [NeurIPS20] (Wang et al., 2020a), (4) Fe- dRCL [CVPR24] (Seo et al., 2024); three popular FGL approaches: (5) FedPub [ICML23] (Back et al., 2023), (6) FedTAD [ICCA124] (Zhu al., 2024b), (7) FedGTA [VLDB24] (Li et al., 2024d); three One-shot FL methods: (8) DENSE [NeurIPS22] (Zhang et al., 2022), (9) FedC- VAE [ICLR23) (Heinbaugh et al., 2023), (10) FedSD2C [NeurIPS24] (Zhang et al., 2024b). Detailed descriptions of all the baselines can be found in Appendix C.
4.4. Discussions on Privacy.
Privacy security plays crucial role in FGL systems. In GHOST, we propose the Center-Shifting method to enhance privacy security. Specifically. the proxy model generates pseudo graphs using labels and random noise sampled from Gaussian distribution. For simplicity, a standard normal distribution is typically used, where the center X is set to O. However, we introduce shift e to the center of the distribu- tion, X. at the client side and communicate this shift to the server either offline or through encryption methods (Hein- baugh et al., 2023; Zhou et al., 2020). In our approach, each client only uploads the parameters of its proxy model to the server online once. We consider the worst-case scenario where an eavesdropping attacker intercepts all the param- eters. However, without knowledge of the specific shift c, the attacker can only randomly select a center X. which is likely to differ from the true center (x + e). Alternatively, the attacker might attempt to overlap the center using a wide uniform distribution, trying to align with the original distri- bution. Nevertheless, experiments conducted in Appendix G
Implement Details. Following the mainstream research practices, we utilize node classification as the downstream task. We set |C| = 10 clients and draw pk ~ Dir(a) from Dirichlet distribution and assign fraction pf of class to client k. Ablation Study on varying numbers of clients can be found in Appendix E. The parameter a governs the degree of nIn-es,, and we set a = 0.05 to sim- ulate the high heterogeneity senario. For the alignment phase of each proxy model, we set the local training epoch
6

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GHOST: Generalizable One-Shot Federated Graph Learning with Proxy-Based Topolegy Knowledge Retention
Table Comparison with the state-of-the-art methods seven real-world datasets. We report node classification accuracies (%) for downstream task performance. Green arrows denote advancements in accuracy metrics than FedAvg while red arrows indicate regressions. OOM means out-of-memory error. The best and second results highlighted with bold and underline. respectively.
Methods
Cora
CiteSeer
PubMed
Chameleon
Amz-Photo
Coauthor-CS
Obgn-Arxiv
FedAvg [ASTAT17]
30.61
32.88
57.91
19.89
23.12
22.50
14.58
Traditional FL
FedProx [MLSys20]
30.98 10.37
35.73
y7.56
19.78
24. 24.16
21.44 (1.06
13.99.0.50
FedNova [Neu
14.21,16.44 16.44
(8.58,117.0
33.48
$3.48.22443
J24.43
21.30
6.15 $16.97
18.8 18.83.ja.m
1.17
FedRCL [CVPR24]
17.60.13.00
12.73.22011
28.12
79
18.48
11.41
4.92 118.20
14.75,7.75
2.56_12.02
Traditional FGL
FedPub [ICML23]
30.52.0.09
12.03
11.222.16.6
17.61
12.28
21.91,1.21
26.75
10.02.4.50
FedTAD [[CAI144]
30.43Jo.18
33.86
39.32 18.59
20.11
(0.22
10.22
22.01
14.09
18.09
OOM
FedGTA [VLDB24]
14.02.16. 16.59
17.75_15.13
31.45 426.46
21.20 11:31
4.10 g19.02
10.80
111.70
1.14_11.43
One-shot FL
DENSE [Nur]PS22]]
12.72 17771
7.87
20.84 L37.07
19.90f0.01
18.19
3.96.
0.33 .4.22
FedCVAE [CCR233]
30.89 ro.28
34.76,1.88
52.01 52.0116.90 15.90
21.74;1.86
31.62 78.50
14.60.7.90
13.71 Lo.87
FedSD2C [NrulPS24]
17.78 12.83
29.96 j2.92
26. (3..2231179
22.72
12.63
8.73
114.99
3.88 18.62
0.76 0.76.13.82
Ours
50 41
37.75 85
58. 87.87
25. 5.33
37.22 114.10
29.91
17 17.2412- 2.66
A GHOSST PeDDRE de PelProx O PedPub
45
40
Ag Ablation
Ag Ablation
40
30
25
25
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35
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25
0.01
0.09
0.01
0.09
$
0.05
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Climt
a
(a) CiteSeer
(b) Coauthor-CS
(a) Label Distribution
(b) Varying a in Dir(a))
Figure 4. Hyperparameter Analysis on on datascts CiteSeer and Coauthor-CS. The green dash denotes the baseline perfor- mance. See details and more ablation results Appendix
Figure Resilience Study of GHOST on the Cora dataset. (a),
we illustrate the label distribution under high data heterogeneity. In (b), we vary within the range (0.05, 0.25] with step size of 0.05 in Dir(o), representing different degrees of data heterogencity. Further details are provided in Sec. 5.3.
for FGL such as FedPub and FedTAD perform better most datasets than traditional FL methods due to their specific designs for graph-structure data in Eucllidll space. However, they heavily rely on gradual personalized iterative updates that optimize models tailored to local data distribu- tions. This leads to severe performance degradation in the generalized one-shot setting where they fail to efficiently capture all the local knowledge. One-shot FL approaches such as FedCVAE perform well in some small-scale graphs. However, their generative models ignore unique structural properties within the graph data, leading to poor perfor- mance in large-scale graphs with complex structures.
TE to 100. As for hyperparameters, A and Xy are deter- mined through a grid search within (0.01, 0.05, 0.1, 0.5) and (0.1, 0.2, 0.5, 13 respectively. More implement details and parameter settings be found in Appendix D.
5.2. Superiority
To address Q1, we analyze the superior performance of GHOST. We conduct the generalization setting where one global model is evaluated demonstrate the node classification performance with differ- ent graph datasets and summarize the final test accuracy in Tab. 1. Notably, three key observations emerge: GHOST outperforms all other baselines in all datasets by fully cap- turing shared patterns among clients and consolidating the acquired knowledge. The dual-level knowledge obtained from all proxy models ensures the global model perform well across diverse data distributions. @ Algorithms tailored
test data of all clients. We
5.3. Resilience
To address Q2, we evaluate the performance of GHOST in comparison with other baselines under various degrees of data heterogeneity. Specifically, we manipulate a in the Dirichlet distribution Dir(a) with values in [0.05, 0.25] and step size as 0.05. lower a corresponds to more skewed label distribution across clients. To better illustrate it, we
7

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GHOST: Generalizable One-Shot Federated Graph Learning with Proxy-Based Topology Knowledge Retention
80
40
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CiteSeer
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CiteSeer
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Original
Original
Original
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Distance
Distance
Bounds
Bounds
(a)
Center Guess Attempt
(b) Overlapping Attempt
Figure 5. Security Analysis Cora and CiteSeer. (a) shows the performance of the global model varying distances from the shifted distribution center (x + e). (b) presents the corresponding performance under different guesses hased on the range of the uniform distribution. Original refers the performance of the global model trained by the server, where the specific is communicated offline via encryption methods securely. See Appendix G for more details.
Table Ablation study of key modules (DL.A, TCKR) in GHOST on Cora, CiteSeer, Chameleon and Coathor-SS. Green arrows denote advancements in accuracy metries. The best results are highlighted with bold.
Table 3. Ablation study components (Liisps Laiv, Lggw) DLA module Cora, CiteSeer, Chameleon and Coathor-CS. Green arrows denote advancements accuracy metries. The best results are highlighted with bold.
Dataset
Dataset
DLA
TCKR
Lev
Cav
Cyge
Cora
CiteSeer
Chameleon
Coauthor-C
Cora
CiteSeer
Chameleon
Coauthor-CS
x
x
12.65
14.46
17.17
4.32
X
X
12.65
14.46
17.17
4.32
x
/
15.12
18.18
21.32
7,86
27.31
18.63
20.11-2.04
12. 12.19
/
x
26.93
y7.00
27.80
g5.85
26.31
21.11-424 24
13.85
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37.
70.33.9
25.22 05
29.91-25.59
46. 10.93
36.10.a1.04
25. 25.00,7
27.80
use the Cora dataset as example and visualize the label distribution across clients for 0.05 through heatmap in Figure 3(a). We compare GHOST with three strong baselines (FedProx [FL], FedPub [FGL], and FedCVAE [One-shot FLJ) under different values of a. The experi- mental results shown in Figure 3(b) indicate that GHOST consistently outperforms the baselines in all settings, demon- strating its strong resilience to data heterogeneity.
mance. Notably, the introduction of the DLA module leads to substantial accuracy improvements across all settings. This demonstrates that the DLA module effectively lever- ages the embedded knowledge in data and aligns the proxy model's understanding with local data at both feature and structural levels. Motivated by this, we further explore the key components of the DLA module.
Effects of Components in DLA. To further investigate the role of components within DLA, we conduct an abla- tion study by varying the three alignment loss functions (Cdisp: fgw)) excluding the TCKR module to iso- late the effects of these components. The experimental results are shown in Tab. 3. We observe that all three com- ponents contribute to the alignment process. Edisp and Laiv focus on feature-level consistency, while L provides sig- nificant improvements by emphasizing structural alignment. This underscores the importance of structure in Federated Graph Learning systems.
5.4. Effectiveness
To address Q3, we conduct an ablation study to evaluate the contributions of different modules in GHOST respec- tively. In GHOST, we first establish proxy model for each client and perform Dual-Level Alignment (DLA) to fully explore local knowledge. During the global traing phase, we apply Topology-Conscious Conscious Knowledge Retention (TCKR) to consolidate previously acquired topological information. In this section, we utilize Cora, Citeseer, Emazon-Phhode and Coauthor-CS example datasets, varying these com- ponents assess their effectiveness.
6. Conclusion
Effects of Modules in GHOST. First, we perform an ab- lation study for DLA and TCKR in our framework. We adopt node classification as the downstream task. The ex- perimental results are shown in Tab. 2. We observe that both DLA and TCKR significantly enhance model perfor-
In this paper, we are pioneers in addressing two key chal- lenges of existing FGL approaches in the one-shot setting: their poor generalizable capability and catastrophic forget- ting. We introduce GHOST: Generalizable One-SHOt Federated Graph Learning with Proxy-BaSed Topology
8

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GHOST: Generalizable One-Shot Federated Graph Learning with Proxy-Based Topolegy Knowledge Retention
Knowledge Retention. First, we propose a proxy model for each client, enabling the capture local knowledge in both
process, 2025c. URL https://arxiv.org//
feature and structural dimension. Then, the integration of knowledge from all clients into a global model enhances its ability to generalize across diverse graph structures. To mitigate catastrophic forgetting, we compute the Topology- Consistency Criterion to identify and consolidate parame- ters erucial for extracting underlying topological knowledge. Extensive experiments real-world datasets demonstrate the effectiveness and generalization capability of GHOST in high data heterogeneity scenarios, offering promising direction for scalable FGL applications in practical setting.
Canese, K. and Weis, S. Pubmed: the bibliographic database. The NCBI handbook, 2(1), 2013.
Chen, F,, Li, P., Miyazaki, T., and Wu, C. Fedgraph: Fed- erated graph learning with intelligent sampling. IEEE Transactions on Parallel and Distributed Systems, 33(8):
1775-1786, 2021.
Chen, F., Long, G., Wu, Z., Zhou, T., and Jiang, Per- sonalized federated learning with graph. arXiv preprint arXiv:2203.00S3 2022.
Acknowledgement.
Deng, B., Wang, T., Fu, L.,, Huang, S., Chen, C., and Zhang, T. THESAURUS, contrastive graph clustering by swap- ping fused gromov-wasserster couplings. In Pruceed- ings of the AAAI Conference on Artificial Intelligence, pp. 16199-16207, 2025.
This research is supported by the National Key Research and Development Project of China (2024FFC3008400) the National Natural Science Foundation of China (Grants 62361 166629, 62176188, 623B2080), the Wuhan Univer- sity Undergraduate Innovation Research Fund Project. The supercomputing system at the Supercomputing Center of Wuhan University supported the numerical calculations in this paper.
Doersch, C. Tutorial on variational autoencoders. arXiv preprint arXiv: 1606. 05900, 2016.
Fu, L., Huang, S., Lai, Y., Liao, T., Zhang, C., and Chen, C. Beyond federated prototype learning: Learnable semantic anchors with hyperspherical contrast for domain-skewer data. In Proceedings of the AAAI Conference on Artificial Intelligence, pp. 16648-16656, 2025.
Impact Statement
This paper presents work whose goal is to advance the field of Machine Learning. There are many potential societal consequences of our work, none of which we feel must specifically highlighted here.
Fu, X., Chen, Z., Zhang, B., Chen, C., and Li, Federated graph learning with structure proxy alignment. In ACM SIGKDD, pp. 827-838, 2024.
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Zhang, T., Mai, C., Chang, Y., Chen, C., Shu, L., and Zheng, Z. Fedego: privacy-preserve personalized federated graph learning with ego-gra ggo-graphs. ACM Transactions on Knowledge Discovery from Data, 18(2):1-27, 2023.
Zhou, Y., Pu, G., Ma, X., Li, X., and Wu, D. Distilled one- shot federated learning. arXiv preprint arXiv:2009.07999 2020.
Zhou, Y., Ye, Q., and Lv, J. Communication-effiiiii fed- erated learning with compensated overlap-fedavg. IEEE Transactions on Parallel and Distributed Systems, 33(1): 192-205 202, 2021.
Zhu, Y., Li, X., Hu, M., and Wu, D. Federated continual graph learning. arXiv preprint 1rXXv:2411.18911 2024a.
Zhu, Y., Li, X., Wu, Z., Wu, D., Hu, M., and Li, R.-H. Fedtad: Topology-aware data-free knowledge distilla- tion for subgraph federated learning. arXiv preprint orXiv:2404.14066 2024b.
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GHOST: Generalizable One-Shot Federated Graph Learning with Proxy-Based Topology Knowledge Retention
A. Notations.
present a comprehensive review of the commonly used notations and their definitions in Tab. 4.
Table 4. Notation and Definitions
Notation
Definition
Graph data.
V
The node set of g.
E
The edge set of G.
X
The feature matrix of G.
A
The adjacency matrix of G. The proxy model.
P()
F
The dimension of the node feature.
K
The number of clients.
The generated graph for client k.
X
The pseudo feature matrix.
H
The activated similarity matrix.
A
The pseudo adjacency matrix. Node in V.
The representation of o; at the 1-th layer of GNN.
(())
The set of neighbours of node u;-
The transport plan in Fused Gromov-Wasserster distance.
The knowledge set for client k.
Gs
The integrated knowledge set. The Coherence Factor at the (-th layer between node v, and ey.
T
The Topology-Consistens Criterion of GJ at the /-th layer.
0 The weight matrix of the 1-th layer.
B. Dataset Details
We evaluate GHOST on seven real-world graph datasets: Cora, CiteSeer, PubMed, Chameleon, Amazon-Phott CoAuthor- CS, and Ogbn-Arxiv. For all datasets, statistics for these datasets are provided in Tab. 5. The details are follows:
common split of 20%/44%//40% for training/validaiionnessnng sets. The
Cora, CiteSeer, and PubMed. These three datasets are widely used benchmarks in graph-based machine learning, particularly for node classification and link prediction tasks. Each dataset consists of a citation network where nodes represent scientific papers and edges represent citation relationships between them. The nodes are categorized into multiple classes, and each paper is represented by feature vector derived from its content (e.g., words from titles or abstracts). These datasets are sparse, digh-dimensional, and well-suited for testing models on real-world, graph graph-structured data. They especially popular for evaluating graph neural networks (GNNs) and other graph-based algorithms, given their complex structure and scalability challenges.
Chameleon. The Chameleon dataset represents citation network of academic papers, where nodes correspond to papers and edges indicate citation relationships. This dataset is notable for its heterogeneous and complex community structure, containing densely connected subgraphs. These characteristics pose challenges for tasks such as community detection and graph clustering. With sparse feature vectors derived from paper content, Chameleon is often used to evaluate performance, scalability, and robustness of graph-basee based models, particularly in large-scale and heterogeneous networks. Amazon-Phote The Amazon-Phoon dataset used for node classification tasks, where nodes represent photos and edges represent co-purchase relationships between them. This dataset consists of images from the Amazon product catalog, with each photo labeled by category. Features are derived from image metadata, making the dataset suitable for evaluating graph-based models in visual domains.
CoAuthor-CS. The CoAuthor-CS dataset a citation network of computer science research papers, where nodes represent papers and edges represent co- ro-authorship relationships. The papers are categorized into several topics, with features derived from their titles and abstracts. This dataset serves challenging benchmark for node classification and
14

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GHOST: Generalizable One-Shot Federated Graph Learning with Proxy-Based Topolegy Knowledge Retention
community detection algorithms in academic citation networks.
Ogbn-Arxiv. The Ogbn-Arxiv dataset is large-scale citation network where nodes represent academic papers from the arXiv repository, and edges represent citation relationships. It includes node features based on paper abstracts and categorizes papers into variety of subjects, including physics, computer science, and mathematics. Ogbn-Arxit is frequently used to benchmark GNNs and provides a real-world challenge with diverse categories.
Table 5. Statisties of datasets used in experiments.
Dataset
#Nodes
#Edges
#Classes
#Features
Cora
2,708
5,278
7
1,433
Citeseer
3,327
4,552
6
3,703
Pubmed
19,717
44,324
3
500
Chameleon
2277
36101
5
2325
Amz-Photo
7,650
287,326
745
Coauthor-CS
18,333
327,576
15
6,805
Obgn-Arxiv
169,343
1,166,243
40
128
C. Baseline Details
In this section, we make descriptions of all the baseline methods in our experiment.
FedAvg [ASTATI7]. FedAvg is a widely-used baseline algorithm in Federated Learning, where local clients independently train models on their local data and then aggregate their model updates on a central server. The server computes a weighted average of the model parameters based on the clients' updates and uses this to update the global model, which is then sent back to the clients for further training. This method reduces communication overhead by transmitting only model updates instead of raw data, making suitable for crivacy-preeervin distributed learning (Li al., 2019; Mehta & Aneja, 2024). However, its performance can degrade in scenarios with heterogeneous data distributions across clients.
FedProx [M]))s20). FedProx is an enhanced version of the FedAvg algorithm, designed to address the challenges posed by data heterogeneity (Non-IID data) in federated learning. In FedProx, each client optimizes its local model with an additional regularization term that penalizes large deviations from the global model. This proximal term helps to mitigate the negative effects local data distributions that may differ significantly from the global data distribution, thus improving the convergence of the global model (Yuan & Li, 2022; Li & Richtárik, 2024). By balancing the local training process with the global model, FedProx ensures that each client's updates are more consistent with the global model, resulting in better model performance and stability, particularly in the presence of non-IID data across clients.
FedNova [NeurIPS20]. FedNova is another extension of the FedAvg algorithm that aims improve the performance of federated learning under data heterogeneity. Unlike FedAvg, which averages model updates directly, FedNova normalizes the local updates before aggregation. This normalization ensures that the contribution of each client to the global model is proportional to the scale of its local data. By normalizing the local gradients or updates, FedNova addresses issues such as the unequal influence clients with varying amounts of data, leading to more stable and efficient convergence. This approach is particularly useful in federated learning scenarios where clients' data distributions are highly skewed, as ensures that the global model is better aligned with the diversity of the local data.
FedRCL [CVPR24]. FedRCL is novel approach designed to tackle data heterogeneity challenges in FL with contrastive learning ( (You et al., 2020; Wan et al., 2024b). It begins by analyzing the inconsistencies in gradient updates across clients during local training. which are found to be influenced by the distribution of feature representations. FedRCL introduces a relaxed contrastive learning loss that applies a divergence penalty to excessively similar sample pairs within each class, preventing collapsed representations. This strategy improves feature transferability and enhances collaborative learning across clients. As a result, FedRCL leads to significant performance improvements over existing federated learning methods, as demonstrated by extensive experimental results on standard benchmarks.
FedPub [ICML23). FedPub is designed to address the challenges of heterogeneity in subgraph-based graph learning. Unlike traditional methods that focus on learning single global model, FedPub emphasizes the joint improvement of local GNN in a personalized manner. It utilizes functional embeddings to compute similarities between local GNNs, enabling weighted averaging for server-side aggregation. Additionally, FedPub introduces a personalized sparse mask for each client to select and update only the subgraph-relevant parameters. This approach effectively handles data privacy and heterogeneity, outperforming existing methods on various subgraph datasets.
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GHOST: Generalizable One-Shot Federated Graph Learning with Proxy-Based Topolegy Knowledge Retention
FedTAD [ICCA124). FedTAD is novel approach designed to address the challenge of subgraph heterogeneity in subgraph federated learning- In subgraph-FI., the variation in node attributes and graph topology across different clients can impair the performance of the global GNN. FedTAD decouples these variations into label distribution differences and structure homophily, revealing how they affect the reliabilitt of knowledge from local models. This variation results in misguiding model aggregation, as local models contribute differently depending on the class-wise knowledge reliability. FedTAD enhances the knowledge transfer from local models to the global model by utilizing lopology-aware data-free knowledge distillation, which improves the reliability and efficiency of the aggregation process.
FedGTA [VLDB24]. FedGTA is personalized optimization strategy designed address the challenges in FGL, particularly in handling large-scale subgraphs and improving performance. While existing FGL approaches either focus on optimization for multi-client training or complex local models, they often fall short due to slow convergence and scalability issues, especially when applied to graph data. FedGTA optimizes FGL through topology-aware local smoothing and mixed neighbor features, taking into account the graph structure for more efficient aggregation (Zhu et al., 2024a), FedGTA is among the first to bridge large-scale graph learning with federated learning, contributing significantly to the development of scalable FGL methods.
DENSE [NeurIPS22]. DENSE a novel framework designed to address the limitations of existing one-shot Federated Learning (FL) methods, which typically require additional data or model information and often assume homogeneous client models. DENSE overcomes these challenges by utilizing two-stage process: data generation stage and a model distillation stage. This approach enables the global model to be trained in single communication round, without requiring extra data or model information to be transferred between clients and the server. Additionally, DENSE accommodates model heterogeneity, allowing clients to use different model architectures.
FedCVAE [ICLR23]. FedCVAE is a data-free one-shot FL method designed to handle high statistical heterogeneity and improve security. It utilizes a Conditional Variational Autoencoder (CVAE) (Doersch, 2016; Kipf & Welling, 2016; Kim et al., 2021) to reframe the local learning task, enabling effective model aggregation despite differences in local data distributions. An extended version, FEDCVAE -D. incorporates knowledge distillation (Gou et al., 2021; Bi et al., 2025b;a) to compress local decoders into single global decoder, further enhancing performance. FedCVAE does not require additional data or auxiliary datasets, supports heterogeneous local models, and improves security by shifting the CVAE prior distribution. It significantly outperforms traditional methods, especially under conditions of high heterogeneity, In our experiment, we utilize FedCVAE-ENS as the baseline.
FedSD2C [NeurIPS24]. FedSD2C is a novel one-shot FL framework designed to address the challenges of data heterogeneity and scalability in federated settings. While one-shot FL offers advantages in communication efficiency and privacy preservation, it often compromises model performance due to inconsistent local data distributions and information loss during knowledge transfer. FedSD2C tackles these issues by introducing a distiller that synthesizes informative distillates directly from local data, reducing the two-step information loss typically seen in traditional methods. Instead of aggregating inconsistent local models, FedSD2C shares these synthetic distillates, ensuring better consistency and more reliable knowledge transfer to the global model.
D. Implementation Details
The experiments are conducted using NVIDIA GeForce RTX 3090 GPUs as the hardware platform, coupled with Intel(R) Xeon(R) CPU E5-2678 v3 @ 2.50GHz. The deep learning framework employed was Pytorch, version 2.3.1, alongside CUDA version 1..1. We adopt two-layer GCN the backbone, with the hidden layer size as 128. Moreover, hidden linear layers and projection head as the proxy model which concats random noise and one-hot label as the input and generates pseudo features as the output. We set draw pk: ~ Dir(a) from Dirichlet distribution (Minka, 2000) and assign a fraction PK of class e to client k. As for optimization of the proxy model, Adaptive Moment Estimation (Adam) (Kingma, 2014) was chosen, featuring a learning rate of 5e - and a weight decay of 4e 4. For the aligmment phase of each proxy model of 10 clients, we set the local training epoch Tr, to 100. Aa and Xy are determined through a grid search (Liashchynskyi & Liashchynskyi. 2019) within (0.01, 0.05. 0.1, 0.5) and {0.1, 0.2, 0.5, 1) respectively. To make sure that frw on the same scale as other loss functions for Amz-Photo and Ogbn-Arxiv datasets, we set their Xy scales to 1e 4 and le- - 7, respectively. We set in Lig as 0.5 to balance the feature part and the structure part. The communication round is limited to one. At the server side, we set M = 3, Ta = 5 and adopt Adam as the optimizer for the global model with learning rate of le - 2 and weight decay of 4e - 4. As for X, and An. we conduct grid search within 10.1, 0.5, 1} respectively. The pseudo graphs generated by the proxy model of each client have the same scale as the corresponding local subgraph. Considering the huge amount of model parameters, we set the scale for A and Xn as 1e - 11 to balance each loss function. As shown in Sec. 5.4, all the components and modules make significant contributions to the performance
utilize 3
16

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GHOST: Generalizable One-Shot Federated Graph Learning with Proxy-Based Topology Knowledge Retention
Algorithm 1 The framework of GHOST
Input: Initial Proxy model of the k-th client (*), random noise local training set G and labels y², local training epoch T2. initial global model M(-), number of layers L, global training epoch To, hyperparameters As, Ay. A and An.
1: for each client do
2: for local epoch <- 1, T, do
3: Input 2 and y to Pk (-);
4: Generate pseudo graph G through Equation (2) and Equation (3);
1e Dual-Level Alignment for the proxy model */
5: Compute Ldisp: Ldsu, Ligw between 9* and g*
6: Lduat = diep + 'a + Sgw
7: Update local proxy model via V dduat-
8: end for
9: end for
10: Each client uploads parameters of its proxy model the server.
1" Knowledge Integration */
11: for each proxy model (.) do
12: Input and uniform pscudo labels j":
13: Generate knowledge set ø of client l by Pk (.).
14: end for
Generate the integrated knowledge set 9s-
1a Global Training #/
16: for pseudo graphs 9 ...... Gh in g Gs do
17:
for global epoch / <- 1,..., To do
18:
Input .i...., 9h to global model M(-);
19:
Compute Ckask-
1e Topology Knowledge Retention */
20:
for 1-th hidden layer do
Compute 7,* through Equation (9).
22:
end for
23:
Compute C3 through Equation (10);
24:
Ck globbl Ckask + A, + X, || * 12;
Update global model via V globai
26: end for
27:
end for
enhancement. Furthermore, we provide the detailed description of our framework in Algorithm 1.
E. Ablation Study on Different Numbers of Clients.
In this section, we vary the number of clients in {5, 10, 20) and conduct the node classification task on CiteSeer, Chameleon, Amazon-Phote and Coauthor-CS datasets. Experimental Results shown in Tab. 6. From the table, we observe that GHOST outperforms most baselines with different numbers of clients, demonstrating the stability of GHOST across various data distributions and subgraph scales.
F. Sensitivity
To address Q4, we conduct analysis on hyperparameters GHOST. Specifically, we compare the node classification performance under different values of Ya and Xy We take Cora, Coauthor-CS as example datasets. For both datasets, we vary da and Ny in range [0.01, 0.09] and |0.05, 0.25] with 0.02 and 0.05 as step size respectively. Experimental results shown in Figure 4 and Figure 6. From the bar charts, values. Moreover, all studies of da and Ny outperform the baseline, proving the robustness and stability of GHOST.
observe that the performance is not influenced much at different
17

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GHOST: Generalizable One-Shot Federated Graph Learning with Proxy-Based Topolegy Knowledge Retention
Table Comparison with the state-of-the-ar methods with different numbers of clients. We report node classification accuracies (%) for downstream task performance. Green arrows 1 denote advancements in accuracy metrics than FedAvg while red arrwws 1 indicate regressions. 0OM means out-of-memony error. The best and second results are highlighted with bold and underline, respectively.
Datasets (-+)
CiteSeer
Chameleon
Methods (1)
5 Clients
10 Clients
20 Clients
5 Clients
10 Clients
20 Clients
FedAvg [ASTATI7]
35.43
32.88
38.13
21.31
19.89
20.02
Traditional FL
FedProx [MLSys20]
40.82
35.73 22.85
39.39
20.77 10.54
19.78
19.81 10.21
11.26
FedNova [NurIPS200]
18.43 117.00
18.58
(14.30
16.17 $21.96
20.33
11.01
21.30
17. 17.7542.22
FedRCI. [CVPR24]
15.88 119.55
12.73,
12.73,220.15
120.15
L31.08
26.89 15.58
18.48 p1.41
20.13
Traditional FGL
FedPub [ICML23]
20.07 415.36
34.91 12.03
32.27
15.86
20.33
10.98
17.61 12.28
23. 23.1613.14
FedTAD [ICCA124]
19.25,16.18
33.86
28.34
19.79
28.01 16.70
20. 10.22
23.05
FedGTA [VLDB24]
16.93 18.50
17.75.15.13
17.75
115.13
15.73 122.40
20.32 20.32.0.90 10.99
21.20
19.81
One-shot FL
DENSE [NeurIPS22]
7.64 (27.79
7.87
125.01
7.06131.00
20.00 11.31
19.90 fo.01
20.13
FedCVAE [ICLR23]
42.64 17.21
34.76;1.88
18.10 120.03
19.89
11.42
21.74f1.85
16.99 $3.03
FedSD2C [NeruIPS24]
20.97 114.46
29.96 (2.92
23.66 114.47
25.14
22.72 12.83
24.35 14.33
GHOST
42.92 17.49
37.75 -4.75...87
40.80
28.42 17.11
25.22 15.33
23.59 13.67
Datasets (-+
Amazon-Phon Photo
Coauthor-CS
Methods (4)
5 Clients
10 Clients
20 Clients
5 Clients
10 Clients
20 Clients
FedAvg [ASTAT17]
49.93
23.12
21.79
12.84
22.50
33.51
Traditional FL
FedProx [MLSys20]
46.54 (3.39
24. 24.16,1.04
23.58f1.79
16.25
21.44 11.06
29.33 (4.
FedNova NeurIPS20]
9.69 1.69.440.2
6.15 116.97
8.57 113.22
22.45 -1.14
18.83.3..6
16.37
FedRCL [CVPR24]
21.80
12.80.28.11 128.13
4.92 (18.20
10.69 111.10
8.3314.81
14.75
7.02.26.49
Traditional FGL
FedPub [CCML23]
42.00 $7.93
21.91 11.21
21.76
5.14
26.75
24.25
22.55 $10.6
FedTAD [ICAI124]
25.29 (24.64
22.01 11.11
21.57 (0.22
11.77 (1.07
14.09 18.41
36.42 12.91
FedGTA [VLDB24]
5.39 144.54
4.10
6.17 6.17,15.62 115.62
10.16.2.68
10.80
9.43 L24.08
One-shot FL
DENSE [NeuIIS222]
4.96 111.97
4.93 11
4.90.16.89 16.89
3.75.9.09
3.96 (15.93
3.71.290 129.80
FedCVAB [ICLR23]
52.39 2..54
31.62
88.50
24.87 13.08
210.21
14.60
14.6017.90
10.98
/22.53
FedSD2C [NeruIPS24]
11.75 11.75.38.18
8.73 14.399
23.38 11.59
3.95
3.88 118.62
9.94 [2.557
GHOST
033.07.3.10
37.22
10
37.50
24.99,12.14
29.9117.44
40.84.7.55
G. Privacy Security.
Privacy security plays crucial role in FGL systems (Zeng et al., 2022; Liao al., 2025). In this section, we conduct experiments two possible approaches for the cavesdropping attacker datasets Cora and CiteSeer, assuming the worst case where the attacker intercepts all the parameters (Li et al., 2021; Mothukuri et al., 2021). As illustrated in Sec. 4.4, without knowing the specific shift e, the attacker can only randomly select center X away from (x + E). or make a guess based on a uniform distribution with wide bounds. Firstly, we set the original noise distribution as standard normal distribution (x- = 0) with shift e varies in {10, 20, 30} while the attacker still takes X = as an attempt. Experimental results are shown in Figure 5(a). Then, we set (x + as O and set several guesses uniform distribution that attempt to overlap the ((-5000, 150)]. Experimental results are shown in Figure 5(b), in which we utilize bounds- 50 to denote the guess (0550, 50). From the bar charts, we observe that regardless of whether the attacker guesses the center or attempts to overlap the distribution over a wide range, the heuuo-graphss generated lead to a performance drop of 50%-80% This sigmificant drop demonstrates that the generated pseudo-graphs differ drastically from the real data held by clients, thereby preventing any leakage of private information. Consequently, the privacy security of our GHOST framework confirmed.
original distribution range: (-0 50),500,, 2((-000 100),
18

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GHOST: Generalizable One-Shot Federated Graph Learning with Proxy-Based Topology Knowledge Retention
45
40
A Ablation
Ablation
40
35
35
30
30
25
25
20
20
15
15
10
0.05
0.1
0.15
0.2
0.25
0.05
0.1
0.15
0.2
0.25
(a) CiteSeer
(b) Coauthor-CS
Figure Hyperparameter Analysis on X on datasets CiteSecr and Coauthor-CS. The green dash denotes the baseline performance. See details in Appendix F.
H. Discussion on Limitations.
Although GHOST has demonstrated sigmificant success in efficiently capturing diverse dual-level knowledge and mitigating catastrophic forgetting in the one-shot setting, it still faces some limitations proxy-based approach (Tan al., 2024a; Bi al., 2025c). Specifically, noise in local data (Kang et al., 2019) interfere with the ability of the proxy model to mine and learn local-specific knowledge, potentially hindering the training of the global model. Enhancing the robustness of the proxy model against such interference (Lu et al., 2024; Li et al., 2024a) presents an interesting direction for our future research.
19


Reviews:
[{"review_id": "dwtc8aBkb9", "reviewer": "Reviewer_AgVq", "summary": "This study tackles challenges such as communication overhead, limited generalization ability, and catastrophic forgetting. It introduces a one-shot strategy where clients independently build proxy models, which are later aligned in both feature-structural level and aggregated on the server to form a global model. To address catastrophic forgetting, the approach incorporates topology-aware knowledge retention. Additionally, this study conducts adequate experiments and addresses the privacy security.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "***Dear Reviewer AgVq:***\n\nThank you for your thoughtful review and for highlighting important concerns. Below, we provide detailed responses to clarify our proposed approach.\n\n**Weaknesses & Questions：**\n\n**W1:  Notation clarity and summarization.**\n\nWe sincerely appreciate the reviewer’s valuable suggestion regarding notation clarity. To enhance readability, we will incorporate a summary table of commonly used notations and their definitions in a future version of our work. Thank you for your insightful feedback.\n\n**W2 & Suggestions: Additional comparisons with more FGL and one-shot FL methods.**  \n\nThank you for your valuable suggestion. To further enhance our study, we have conducted experiments incorporating **FGSSL** (FGL) and **FENS** (one-shot FL). The results on six benchmark datasets are presented in Table 1.  \n\n*Table 1: Performance comparison including additional FGL and one-shot FL methods on six benchmark datasets.* \n\n| Method      | Cora | CiteSeer | Pubmed | Amz-Photo  | Coauthor-CS  | Ogbn-Arxiv |\n|--------------|--------|--------|--------|--------|-------|-----------|\n| FGSSL    | 30.25 | 21.95 | 39.68 |  13.06 | 22.44 | 9.24 \n| FENS  |  31.43 | 20.97 | 49.07 | 25.30 | 22.54 | 13.09\n| **GHOST** | **50.41** | **37.75** | **58.87** | **37.22** | **29.91** | **17.24**\n\nFrom the results, we observe that **GHOST** continues to achieve the best performance, further demonstrating its robustness and effectiveness. We greatly appreciate your insightful suggestion, as it has helped reinforce the comprehensiveness of our study.  \n\n**W3: Necessity and motivation for using both Divergence Loss (Eq. 4) and Dispersion Loss (Eq. 5).**\n\nThank you for raising this point. Although both losses act on the feature representations, they capture complementary aspects. The Divergence Loss minimizes the statistical discrepancy between the pseudo and real features, ensuring that overall properties (spread, variance, density) match. In contrast, the Dispersion Loss  preserves the angular (directional) relationships among features, maintaining the geometric configuration. This helps maintain the intrinsic relational patterns among the features regardless of their magnitudes. Together, they provide a comprehensive alignment, as confirmed by our ablation study (Sec. 5.4).\n\n**W4: Clarification on Equation 6 as a loss function and its gradient flow.**\n\nThank you for this important question. Although Equation 6 formulates the FGW loss in terms of the transport plan $\\mathbf{\\Gamma}$, the loss function is inherently a function of both the graph structures and the feature matrices of the real and pseudo graphs. \n\nIn practice, we use a differentiable optimal transport solver (implemented with a conditional gradient method with optional Armijo line-search) to obtain $\\mathbf{\\Gamma}$. Consequently, even though $\\mathbf{\\Gamma}$ is the immediate optimization variable in Equation 6, the overall FGW loss is differentiable with respect to $\\hat{\\mathbf{X}}$ (and $\\hat{\\mathbf{A}}$), allowing gradients to flow back to these pseudo graph parameters.\n\nThus, by minimizing the FGW loss, the model not only optimizes the transport plan for aligning the local and pseudo graphs but also adjusts the pseudo feature matrix to reduce the discrepancy in both feature and structural domains. This gradient propagation through the differentiable OT solver ensures that the pseudo feature matrix is updated in a manner that preserves the intrinsic topological relationships while matching the local statistical properties.\n\n**W5 & Q1: Explanation of Equation 9 (Topology-Consistency Criterion).**\n\nThank you for highlighting the need for clarification. The Topology-Consistency Criterion quantifies how much each global GNN parameter contributes to preserving learned topological structures. We first compute a Coherence Factor $\\gamma_{ij}^l$ for connected nodes, which quantifies the similarity of their hidden representations after a transformation by the corresponding layer’s weight matrix $\\boldsymbol{\\theta}_{\\boldsymbol{w}}^l$. Aggregating these values across nodes yields a global topological consistency measure for layer $l$. In Equation 9, the norm of the derivative for each parameter reflects its **“sensitivity”: a higher norm indicates that even a small change in that parameter would cause a significant alteration in the coherence.** In other words, parameters with high sensitivity are deemed more important for capturing the intrinsic topological structure across the diverse graphs in our integrated knowledge set.\n\nBy computing and then consolidating these sensitivity measures across layers, we obtain a comprehensive criterion $\\mathcal{T}^k$ that identifies which parameters are crucial for preserving structural knowledge. This process helps in selectively retaining important parameters during the global training phase, mitigating the risk of catastrophic forgetting.", "claims_and_evidence": "Claims made in this study are supported by clear and convincing evidence. This study precisely identifies the limitations of existing FGL methods and addresses these issues with effective and convincing approach (i.e. the “Dual-Level Alignment” module).", "methods_and_evaluation_criteria": "The proposed methods and evaluation criteria actually make sense for the identified problems. Two key modules (the “Dual-Level Alignment” module and the “Topology Knowledge Retention” module) are both highly related to those problems.", "theoretical_claims": "I have checked all the theoretical claims.", "experimental_designs_or_analyses": "I have checked the experimental designs and analyses. The authors have conducted the node classification task on graphs of various scales and make comprehensive comparisons with traditional FL/ FGL and one-shot FL methods. Moreover, the ablation study and the sensitivity study both strengthen the validity of this study.  However, I think it will be better with more FGL/ one-shot FL methods compared in the experimental part.", "relation_to_broader_scientific_literature": "This study proposes an novel one-shot FGL approach, effectively tackling the identified issues such as limited generalization ability and catastrophic forgetting. The study is meaningful and raises the concern of the communication overhead problem in FGL systems. I believe one-shot FGL is a promising solution.", "essential_references_not_discussed": "Essential related works are comprehensively cited in this study.", "other_strengths_and_weaknesses": "Strength:\nS1: It is novel and meaningful to propose a one-shot FGL approach. This study precisely identifies the challenges of existing FGL methods and tackles them effectively. The overall approach is well-motivated, and the motivation is also explained with clarity.\nS2: The figures of problem and framework illustration are clear and detailed, and the equations and explanations are reasonable. I believe this is a comprehensive  framework for the graph data.\nS3: The proposed approach throughout the study flows seamlessly. Both two key modules and their components are innovative and coherent. The Dual-Level Aligned Proxy Model effectively captures the feature-structural knowledge and the Topology Knowledge Retention module then integrates the diverse information against the data heterogeneity while mitigating catastrophic forgetting. \n\nWeaknesses:\nW1: This study uses many notations. To improve clarity, the authors should provide a summarize table of the commonly used notations and their definitions.\nW2: The authors compare the proposed approach with several traditional FL/FGL and one-shot FGL methods , but additional comparisons with more FGL and one-shot FL methods could strengthen this study.\nW3: Equation 4 is designed to align the label distributions of the true and pseudo data, and Equation 5 is designed to align the feature distributions of the true and pseudo data. Essentially they serve the same purpose, so the necessity and motivation for using them simultaneously needs to be made clear.\nW4: As shown in Equation 6, the optimization objective of fused GW-OT is the transport matrix T. How does Equation 6 serve a loss and yield the gradients on the pseudo feature matrix?\nW5: Equation 9 is very confusing. Actually, I can’t clearly understand the meaning of it. It’s suggested to add more explanations about Equation 9.", "other_comments_or_suggestions": "The authors should conduct comparison experiments with more traditional FGL and one-shot FL methods.", "questions_for_authors": "Q1: In Section 4.3, the authors propose the Topology-Conscious Knowledge Retention module and compute the Topology-Consistency Criterion to identify crucial parameters for capturing structural knowledge. Can you provide a more detailed explanation of how the Topology-Consistency Criterion reflects the importance of each parameter in learning topological information?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "5DCp3rjhKj", "reviewer": "Reviewer_9vCa", "summary": "This work focuses on issues of communication overload, generalizability and catastrophic forgetting and proposes a one-shot approach where each client constructs a proxy model After the alignment, these models are then uploaded to the server to train a global model in an ensemble manner. This work also adopts topology knowledge retention to mitigate catastrophic forgetting. Privacy protection is also a key component in this work, ensuring the security of client data. Experimental results indicate that GHOST outperforms existing methods, showing robust performance in the face of data heterogeneity.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "***Dear Reviewer 9vCa:***\n\nWe sincerely appreciate the time and effort you have dedicated to reviewing our paper. We hope that the detailed responses provided below will effectively address your concerns and offer the necessary clarifications.\n\n**Weakness：**\n\n**W1: Lack of further explanation of the pseudo labels.**\n\nWe appreciate the reviewer’s valuable comment regarding the assumption of a uniform distribution for the pseudo labels. While we acknowledge that real-world datasets may exhibit skewed class distributions, we believe that the uniform distribution assumption provides several benefits in our context.\n\nFirstly, adopting a uniform distribution avoids the need for clients to share class label distributions, which significantly mitigates the risk of data privacy leakage. This aligns with the principles of privacy preservation in Federated Graph Learning, ensuring that sensitive label information is not exposed during the training process.\n\nSecondly, the use of a uniform distribution ensures that data from all classes are taken into account, including minor or underrepresented classes. This prevents the model from neglecting the features and information from minority class data, thus promoting a more balanced learning process.\n\nWe believe that this design choice strikes a good balance between privacy preservation and model performance, and the effectiveness of this approach is supported by the results presented in the paper. \n\n**W2: Lack of more sensitivity study on different local training epoches.**\n\nTo demonstrate the robustness of our method under different local training epochs, we select Cora and CiteSeer datasets, and design the range of local training epochs as [90, 110] with a step size of 5. Experimental results are shown in Table 1 and Table 2.\n\n*Table 1: Different local training epoches on the Cora dataset.*\n| Epoches |  90 | 95 | 100 | 105 | 110 | Avg\n|----------|--------|--------|--------|---------|-----------|-------|\n|FedAVG | 30.52 | 30.55| 30.61 | 30.62 | 30.61 | 30.58\n|FedTAD | 30.09 | 30.21 | 30.43 | 31.15 | 30.43 | 30.46\n|FedCVAE | 26.86 | 21.72 | 30.89 | 29.61 | 32.36 | 28.29\n|**GHOST** | **46.93** | **47.39** | **50.41** | **47.02** | **47.57** | **47.86**\n\n*Table 2: Different local training epoches on the CiteSeer dataset.*\n| Epoches |  90 | 95 | 100 | 105 | 110 | Avg\n|----------|--------|--------|--------|---------|-----------|-------|\n|FedAVG |  32.73 | 33.03 | 32.88 | 32.36 | 32.66 | 32.73\n|FedTAD | 20.52 | 23.30 | 33.86 | 23.75 | 25.62 | 24.72\n|FedCVAE | 27.19 | 33.56 | 34.76 | 32.13 | 24.19 | 30.37\n|**GHOST** | **40.90** | **40.52** | **37.75** | **40.62** | **37.68** | **39.49**\n\nFrom the tables, we can observe that our method maintains strong performance across different epochs, demonstrating its stability under varying epoches.\n\n**W3: Lack of details of training epoches in other baselines**\n\nFor all the baselines compared in the experimental section, we uniformly set the local training epoch to 100 to ensure sufficient convergence of the local models. In the one-shot setting, too few local training epochs would prevent the model from adequately learning the local data, making the comparison unfair. Conversely, too many epochs could lead to overfitting to local data, resulting in degraded generalization performance. \n\n**Questions**\n\n**Q1: Model performance with varying client numbers**\n\n**A1:** We appreciate the insightful question regarding model performance under varying client numbers. The observed performance improvement with a higher number of clients, particularly in datasets with high data heterogeneity (e.g., Coauthor-CS), can be attributed to the impact of distributional bias among clients.\n\nWhen the number of clients is small, each client tends to hold a larger amount of data. However, in highly heterogeneous settings, this also means that the data distributions across clients can be significantly different, leading to greater heterogeneity in both data volume and feature distribution. Such imbalances can make it more challenging for the global model to effectively capture a generalizable representation, resulting in degraded performance. Conversely, increasing the number of clients leads to a finer-grained partitioning of the data, which can help mitigate extreme distribution shifts among clients. This, in turn, allows the global model to better learn shared patterns across clients, improving overall performance.\n\nAdditionally, different datasets have their own unique characteristics in terms of data features and structure. As a result, the effect of varying client numbers may manifest differently across datasets, leading to dataset-specific trends in performance. We hope this clarifies the phenomenon and appreciate the opportunity to further discuss our findings.", "claims_and_evidence": "This work identifies the challenges of poor generalizable ability and catastrophic forgetting and proposes clear evidence in the introduction part.", "methods_and_evaluation_criteria": "The framework figure (Figure 2) makes clear and vivid elaboration of the overall method. All the modules in the work are closely related to the identified problems. The benchmark datasets are highly relevant with the problem as well.", "theoretical_claims": "Both the proxy model alignment part and topological knowledge retention part are supported by rigorous analyses. The identification of parameters crucial for capturing topological knowledge is interesting, where the topological attributes at the hidden layers are fully explored and captured. I believe topological information is of great significance and is worth highlighting in graph learning.", "experimental_designs_or_analyses": "The experimental designs and analyses in this work are soundness to me. Performance on  seven datasets with various scales shows the superiority of this work. The ablation study and sensitivity study are sufficient, making strong proof for the contribution of each module. In Appendix D, the authors conduct the experiment with different client scales, showing the resilience of this work. However, I have one issue about the results, which will be proposed in details in **Questions For Authors:** part.", "relation_to_broader_scientific_literature": "GHOST represents a novel step forward in the field of FGL by presenting a unique one-shot approach. It overcomes some of the key limitations found in previous studies, creating new avenues for future research.", "essential_references_not_discussed": "None.", "other_strengths_and_weaknesses": "Strengths:\n\n1. Novel and well-motivated. This work points out the issue of communication overload and innovatively bridges the gap between FGL and one-shot setting. With efficient aligning and knowledge retention, this work effectively addresses the problems left by previous studies.\n\n2. Easy to follow. The paper is well-written with a detailed and exquisite framework visualization. Moreover, the precise descriptions of modules in the methodology makes the overall work clear and easy to follow.\n\n3. Topology-aware. The topology knowledge retention module is meaningful. Graph data significantly differ from image data due to their structure attribute in non-Euclidean space. This work highlights the importance of graph structure and strive to consolidate the topology knowledge during training, which makes sense.\n\nWeaknesses:\n\n1. Lack of further explanation of the pseudo labels: This work assumes that the pseudo labels have a uniform distribution across all classes. This assumption could be unrealistic in some real-world datasets, where the class distributions might be skewed.\n\n2. Lack of more sensitivity study. The work lacks analysis of model performance with different local training epochs of each proxy model.\n\n3. Lack of training details: The work lacks details of the local training epoch for other traditional FL/FGL or one-shot FL baselines in the experimental section.", "other_comments_or_suggestions": "None.", "questions_for_authors": "Model performance with varying client numbers: I noticed the experiment in Appendix D, which evaluates the model's performance with different client scales. Why does the model perform better with more clients on some datasets (e.g., Coauthor-CS)? With 5 clients, each client should have more training data compared to when there are 10 clients, so why does the model perform worse under the former condition (24.99 for 5 clients vs. 29.91 for 10 clients)?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "bUBA7qRxSU", "reviewer": "Reviewer_TQDx", "summary": "This paper proposes GHOST, a novel generalized one-shot FGL framework designed to address challenges related to generalizable capability and catastrophic forgetting. The method involves two main components: Dual-Level Aligned Proxy Model and Topology-Conscious Knowledge Retention. In the first component, each client constructs a proxy model that captures local feature and topological information. In the second component, the server aggregates the proxy models from all clients to form a global model. A Topology-Consistency Criterion is applied during global training to stabilize key parameters and retain important topological information, thus mitigating catastrophic forgetting. The framework also incorporates a privacy-preserving mechanism to secure client data. Experimental results demonstrate that GHOST outperforms existing methods and shows resilience to data heterogeneity.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "***Dear Reviewer TQDx:***\n\nWe greatly appreciate your positive feedback on our work, as well as the thoughtful concerns and questions you raised. We have carefully considered each of your comments and provided detailed responses.\n\n**Weakness:**\n\n**W1: Implementation details for applying one-shot FL methods to graph data.**\n\nWe sincerely appreciate the reviewer’s suggestion to clarify the implementation details of applying one-shot FL methods to graph data. In our experiments, we follow the overall process of the compared one-shot FL methods, utilizing the encoders and decoders from the corresponding papers to generate graph data features. Additionally, we adopt the k-nearest-neighbor (KNN) method to construct the topological structure for the generated graph data.  \n\nSpecifically, in FedCVAE, we adhere to the Conditional Variational Autoencoder framework as used in the original paper. We input the training data and labels into the encoder to obtain representations in the latent space, which are then fed into the decoder to generate features. The KNN algorithm is subsequently applied to construct the topology. Similarly, in FedSD2C, we follow the original paper’s Autoencoder framework (including both the encoder and decoder) for generating graph data features and use the KNN algorithm for topology construction.  By doing so, we retain the key processes and steps of the original baselines while reasonably adapting them to graph data.\n\n\n**W2: Performance under higher levels of data heterogeneity (e.g. $\\alpha = 0.01$)**\n\nTo demonstrate the performance of our method under higher data heterogeneity, we conduct experiments on the CiteSeer, and Coauthor-CS datasets with the Dirichlet distribution parameter $\\alpha$ set to 0.01. We select five baselines for comparison: FedAVG, FedNova, FedPub, FedTAD and FedCVAE. The experimental results are shown in Table 1.\n\n*Table 1: Performance of GHOST under higher data heterogeneity ($\\alpha = 0.01$) on CiteSeer and Coauthor-CS datasets.*\n\n| **Methods**   | **CiteSeer** | **Coauthor-CS** |\n|---------------|--------------|-----------------|\n| FedAVG    | 23.15        | 11.09           |\n| FedNova   | 19.12        | 16.94           |\n| FedPub   | 20.71        | 11.28           |\n| FedTAD    | 21.21        | 11.19           |\n| FedCVAE   | 23.53        | 8.97            |\n| **GHOST**     | **25.32**    | **17.61**       |\n\n\nFrom the table, we can observe that our method maintains the best performance even under higher data heterogeneity. For some datasets, when $\\alpha$ is smaller, certain clients have very few nodes, which does not align with real-world scenarios. Therefore, we set $\\alpha = 0.05$ in the experiments, as it ensures high data heterogeneity while avoiding overly extreme scenarios that do not reflect real-world conditions.", "claims_and_evidence": "This paper proposes a persuasive explanation of its claims. One-shot Federated Learning has emerged as an effective approach in environments with limited resources, and there indeed is a gap between One-shot FL and traditional FGL, especially in the generalized setting, as claimed in the paper. The figure of the problem illustration clearly presents the phenomenon.", "methods_and_evaluation_criteria": "The proposed method and evaluation criteria make sense for the problem. The Dual-Level Aligned Proxy Model and Topology-Conscious Knowledge Retention are both reasonable in the one-shot setting. The node classification task is widely used as a downstream task in FGL methods and is practically applicable.", "theoretical_claims": "I have checked the correctness of proofs for theoretical claims in this paper. The dual-level alignment loss can indeed capture fine-grained knowledge, thus achieving a good alignment.", "experimental_designs_or_analyses": "I have checked the soundness of the experimental designs and analyses in this paper. In the experimental part of this paper, the authors conducted the node classification task on seven real-world datasets. The privacy security part is meaningful and convincing to me. Moreover, the authors make detailed analyses on the experimental results in Sec 5.2.", "relation_to_broader_scientific_literature": "The proposed method pushes the boundaries of FGL by offering an innovative generalized one-shot approach, filling gaps left by previous studies and paving the way for more practical applications in FGL. Moreover, the Fused Gromov-Wasserstein distance [1] in the alignment part is novel and effective.\n\n[1] Vayer, T., Chapel, L., Flamary, R., Tavenard, R., & Courty, N. (2020). Fused Gromov-Wasserstein distance for structured objects. Algorithms, 13(9), 212.", "essential_references_not_discussed": "There are no related works that are essential to understanding key contributions of the paper, but are not currently cited in the paper.", "other_strengths_and_weaknesses": "- Strengths:\n1. The proposed method of generalized one-shot FGL appears interesting and innovative.\n2. The paper provides a clear and detailed explanation of the methodology, making the method easy to follow.\n3. This paper considers the structure attributes in graph data, introducing Topology-Consistency Criterion to mitigate catastrophic forgetting, which is an important addition to the field and is well-supported by both theory and experiments.\n4. The inclusion of a privacy analysis is a strong point, particularly in FL where data privacy is crucial. The Center-Shifting method provides a practical solution to safeguard client data.\n\n- Weaknesses: \n1. This paper does not provide implementation details for applying one-shot FL methods to graph data. Specifically, the one-shot baselines used in the experiments, such as FedCVAE and FedSD2C, rely on generative techniques designed for image data, which differs significantly from graph data. The paper does not address how graph data are generated in these methods. \n2. How does the method perform under higher levels of data heterogeneity? For example, what happens when the Dirichlet distribution parameter α is set to lower values (e.g., α=0.01)?", "other_comments_or_suggestions": "I have no other comments or suggestions.", "questions_for_authors": "See Weaknesses above.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: This paper is sufficient in its novelty of methodology and experimental design. The clear presentation also helps reviewers be able to fastly grasp this paper.
Decision: Accept (poster)