Graph Personalized Federated Learning via Client Network Learning
Authors: Jiachen Zhou
Han Xie
Carl Yang
Venue: Accepted by TMLR ()

Abstract: Graph classification is a widely studied problem for applications such as molecule/protein function prediction and drug discovery. Powerful graph neural networks (GNNs) have demonstrated state-of-the-art performance for the classification of complex graphs, but training such models can require significant amounts of high-quality labeled graphs that are expensive to collect. When individual institutes do not possess sufficient graph data, federated learning (FL) becomes a handy solution for them to collaboratively obtain powerful graph models without directly sharing their own graph data. However, existing FL frameworks for graph data do not consider the realistic setting of personalized FL with heterogeneous data, where each client aims to leverage the data of certain other clients to boost its own model performance. In this work, inspired by graph structure learning, we propose to learn a dynamic client network that tracks the graph data similarity across clients to guide model sharing along FL. Specifically, we rely on the marginal parameters of local GNNs to dynamically learn the client network, and refer to a set of fundamental graph properties to guide its learning. Extensive experiments on three real-world graph datasets demonstrate the consistent effectiveness of our two major proposed modules, which also mutually verify the effectiveness of each other.

Published in Transactions on Machine Learning Research (08/2025)
Graph Personalized Federated Learning via Client Network Learning
Jiachen Zhou
je30688cclumbbicccom edu
Department of Computer Science Columbia University
Xie Han
han.tieGemorg.com edu
Department of Computer Science Emory University
Carl Yang
J. Baarlyanggemorr..oom edu
Department of Computer Science
Emory Universily
Reviewed on OpenReview: https: // openreview. net/ forum? id- py pyTTR/pakU
Abstract
Graph classification is a widely studied problem applications such as molecule/ polecule/protein proteii function prediction and drug discovery. Powerful graph neural networks (GNNs) have demnnnstraed stale- of-the-art art performance for the classification of complex graphs, but training such models can require significant amounts of high-quality labeled graphs that are expensive collect. When individual institutes do not possess sufficient graph data, federated learning (FL) becomes a handy solution graph
for them to collaboratively obtain powerful graph models without directly sharing their data. However, existing FL frameworks for graph data do not consider the realistic setting of personalized FI. with heterogeneous data, where each client aims to leverage the data of certain other clients to boost ils own model performance. In this work, inspired by graph structure learning, we propose to learn a dynamic client network that tracks the graph data similarity across clients to guide model sharing along FL. Specifically, we rely on the marginal parameters local GNNs to dynamically learn the client network, and refer a set fundamental graph propertics to guide its learning. Extensive experiments on three real-word weal-world graph datasets demonstrate the consistent effectiveness of our two major proposed modules, which also mutually verify the effectiveness of each other.
1 Introduction
Federated Learning (FL) has gained widespread popularity as a machine learning paradigm that enables distributed model training without sharing local data samples McMahan al. (2017); Li et al. (2020). A significant challenge that limits the performance of FL data heterogeneity across clients. As diverse local data collected by different clients in various scenarios often adhere to non-identical distributions [Zhao] et al. (2018) Zhu et al. (2021). simply aggregating knowledge from clients with heterogeneous data disrupt the model training and impair the model's performance local tasks, rather than enhancing them. Recently, more studies have applied FL to various graph learning scenarios, such as node classification with distributed subgraphs Zhang et al. (2021); Chen et al. (202 : Yang et al. (2024) and distributed knowledge graph completion Chen et. al. (2021b); Zhang et al. (2022) However, these techniques do not adequately address cross-client graph data heterogeneity which can widely occur roal-world sccnarios.
To gain deeper insight into the relation between data heterogeneity and FL efficacy, conduct synthetic experiments the molecules dataset NCII by simulating different levels of heterogeneity. In these exper- iments, all clients are partitioned into two groups, where clients within the same group share a consistent label distribution. For the homogeneous setting where two groups have the same distribution (see Figure [(a)], , the advantage FedAvg McMahan et al.) (2017) significantly expands as we distribute the data to more clients and increase the data scarcity. However, for the modcrately heterogeneous setting where the difference between two groups acceptable (sce Figure [(b]], FedAvg surpasses Self- helf-training only when local data extremely scarce. For the highly heterogeneous setting where cross-group divergence continues to

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0.35
holir
0.710
0.5
6.72
0.32
6,700
0025
Namber
03 Nambor
(a) homogeneous
(b) moderately heterogeneous
(c) highly heterogeneous
Figure 1: Experimental analysis on the influence of data heterogeneity over FL on a real-world graph
dataset (NCI1 Morris al. (2020))- Clients within the same group share consistent label distributions while the heterogeneity between groups grows as the setting changes from homogeneous to highly heterogeneous.
grow (see Figure [(c)), FedAvg significantly undermines self-training instead of enhancing it. Our model performs well across all settings by properly handling different degrees of heterogeneity.
To properly address data heterogeneity among clients, personalized FL Li et al. (2021): Deng et al. (2020)
has been proposed to learn client-specific models. Existing methods typically comprise two main components Chen al.] (2022ap: knowledge sharing and model personalization. The first component aims construct global models through local model aggregation, while the second one focuses on optimizing local models under the guidance of global models. Current methods primarily emphasize model personalization while overlooking the importance of effective knowledgg-sharing, Such implementation may fail to recognize diverse dependencies among different clients. In a complex setting where the data distributions of clients vary from each other, uniform aggregation across all clients may result in a low-quality global model, causing the degradation of local model performance. To design a more effective knowlodge-sharing mechanism, it is beneficial to reveal the latent relationships between clients. As powerful tool for modeling the complex relationships among different entities, graphs have been used in many scenarios. Under the guidance of a relationship network with links between similar clients, we strategically perform knowledge sharing. This approach allows clients lo selectively benefit from knowledge consistent with their own, while miligating the influence of incongruous information from disparate clients, thus enhancing the overall performance of FL.
However, the lack of supervision makes quantifying the relationship among clients challenging. For graph classification, relationships among clients are even more difficult to capture due to the complexity of graph data, which involves multi-sourced heterogeneity from node features, topological structures and the depen- dency between them. In this work, we propose novel Graph Personalized Federated Learning framework (a.k.a. GPFL) by integrating an unsupervised client network learning model and GNN-based model ag- gregator into FL for graph classification. Specifically, in each communication round, we extract marginal parameters from local models to capture evolving client features and refer to combination of fundamental graph properties and functional embedding to dynamically initialize the client network. A network recon- structor is then utilized to refine the client network based on the client features and the initial network. Finally, we conduct GNN-based model aggregation using the reconstructed client network. Following are the contributions of this paper.
We design client features using marginal parameters, ensuring the capturing of evolving client char- acteristics along FL.
We guide client network learning with a dynamic combination of fundamental graph properties and functional embedding. Additionally, rule-based feature selector tailored to identify pivotal properties across diverse domains.
We develop graph reconstructor that refines the client network leveraging the initial network and client features. Furthermore, our GNN-based model aggregator for FL enhances knowledge sharing, capitalizing the underlying network relationships for improved graph classification.
2
Related Work
Federated Learning with Graph Driven by the growing research interest in Federated Learning (FL) and the advancements of Graph Neural Network (GNN) techniques, increasing work signifying the intersec-
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tion of these two pivotal domains is emerging, which can be divided into two categories: graph federated learning (GFT.) and federated graph (earning(GTT) The former category aims to leverage the latent graph relationship among clients Chen et al. (2017 2022a) to address the heterogeneity among clients through graph-guided knowledge sharing. In this field, the critical problem is to cstablish proper graph structure among clients. While Lalitha et al. (2019) follows preliminary graph structures, Caldarola et al. (2021) establishes clusters for similar clients. FGL, on the other hand, concerns the local task over graph datasets.
Current FGL studies can be further categorized into anter-graph and intra-graph FGL. Works in the former
category focus graph-level local tasks such graph classification Xie et al. (001]): |: Tao et al. (0022) He
ct al. (2021). knowledge graph completion Chen et al. (202b)) recommendation based on decentra lized user-
item graphs Wu et al. (002I). However, in the latter setting, clients own subgraphs of the entire global graph and Uhere exists structural links between local graphs. So the key is to recover lost positional information
through different ways, i.e, missing neighbor generation Zhang et al. 2021 link-type aware collaboration
Xic et al. (202)), community discovery Back ct al. (2023a).
Though existing works have studied GFL and FGI., the intersection field where local clients own heteroge- neous graph datasets remains rarely explored. The various types of heterogeneity in different graph topologies and features are the main problems for constructing a reasonable graph structure among clients. [Chen et al.) (0211a) designs a self-supervised FL framework to capture the heterogeneity among clients but only considers basic graph structure instead of high-order graph topology. Xie et al. (2021) analyzes the non-IID graph property over cross-domain graph datasets including cluster coefficient and shortest path length etc, but only performs knowledge sharing in cluster manner. None of them consider the unique challenge of heterogeneous graph data and addresses the challenge under the guidance of properly designed client network.
Graph Structure Learning Graph Neural Network (GNN) is a powerful tool for exploiting graph- structured data. However, its efficacy heavily depends on the quality of graph structure, which can be impaired by misleading links. To mitigate these limitations, Graph Structure Learning (GSL) has been proposed to optimize graph structure and representations simultaneously. For instance, GLCN [Jiang et al. (2019) constructs graph structure basod on node feature similarity. GAE Kipf Welling (2016) initially embeds raw graphs into latent spaces, refining the graph structure based on embeddings.
Recently, there have been many works focusing on further enhancing the quality of graph structures through incorporating external constraints i.e. knowledge distillation Wu et al. (2022). graph family preliminaries Balcan & Sharma (2021); Pu et al. (2021). supervised information ion corresponding to certain downstream
tasks Fatemi et al. [2021): : Wang et al. 2021). Furthermore, for unstructured data, including images Han
et al. (022), molecules Yu & Gao (2022), GSL can also uncover the latent graph relationship. In this way,
GSL facilitates the application of GNN to learn superior representations by considering the interrelationships among data samples rather than treating them separately. However, existing GFT. works rely inflexible peeric-baseed or direct optimization methods to extract the latent client network, overlooking the potential of GSL in learning informative client relationships.
3 Methodology
3.1 Problem Formulation
Inspired by the insights gained from the synthetic experiment and existing graph-based FI. works Chen ct al. (2022a), we propose a novel Graph Personalized Federated Learning (GPFL) framework, which is a pioneering client-network-basedd personalized FL framework tailored for graph applications.
the design of client features Xc based on marginal parameters derived from local parameters to capture the evolving characteristics of cach client, 2. the graph property guidance for initializing property-based client network An 3. the client network update component for refining the property-based client network Ag by performing a weighted average with a similarity network Ag considering the functional embedding of each local model over a set of random graphs to generate a dynamic initial network A, for communication round t, and 4. the knowledge sharing component where the learned client. network Á is reconstructed from designed client. features X and initial
Figure 2 shows overview of GPFL. It consists of four main parts: 1.
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Client i
Server
Graph Property Guidance
Client Network Update
initial network A,
Pi
Gi
property features
P
property network Ag
G11
random graphs
embedding network Ag
similarity embeddings
GNon (0f)
6
GN GNN serser
R2
R2
Giz
A0द
compute marginal
Wij
0c+1
parameters
8
Xc
learned network À
Knowledge sharing
Client Feature Design
Figure 2: Overview of GPFL. Knowledge sharing is performed under the guidance of the client network, which is reconstructed from marginal parameters. The initialization of this network is guided by fundamental graph properties and functional embeddings to ensure consistent federated collaboration.
client network A, and then the weighted aggregation of local models is conducted under its guidance. The detailed pseudo-code is presented in Algorithm !
Assume there are clients {C1, C2.... ..., C+} with corresponding local graph datasets {91, G2, .... 9& Each local dataset Ga contains set of graph (Gn, Gi2,--), where Gi = (Vij, Eij, Xij. Uhy) Gi is graph with node set Vij, an edge set Eij, node feature set Xij and the graph label Vij. For each client C₁, its local task is to train an individual graph classification model G. GNNoo parameterized by A,:
0, = arggin |9
Σ
Ntocal Niocat Geyz Vij).
(1)
where / is the loss function for the local task.
During FL, at communication round t, cach client follows Eq to compute 0% which is close to the real solution for the local task. The local updates A 0 0f are then uploaded to the server for aggregation:
0++1 0f + AGGR() A0 wxy)).
(2)
JEN())
where of and A are the parameter and update for all client i. W W [wa]] is the knowledge-sharing weight matrix between clients in communication round t. N(i) is the neighborhood of client i and AGGR is the aggregation function. Our goal to optimize the personalized FL loss L under iteratively gradient sharing:
min ((1 W) = (E((G;; 0:)],
1
The knowledge-sharing matrix W is gained by combining the normalized client graph and the identity matrix T together: and summing it with the identity matrix T,
W -I + (1 -1- (1-2 Normalize(A),
where y is the hyperparameter used maintain balance between accepting external knowledge and fitting local data. The discrete client network Á is constructed the server with simple but effective structure

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Algorithm Graph Personalized Federated Learning
Inputs:
Clients (C1, ...; Cx h, Local datasets (9i, 92, ..., Ga Initial local models {lf. .... 0%) Random graph set IR, Initial client network Au, N iterations for training GN Neerver Outputs:
Final local models (0.'
1: for communication round = T-1,...,--1 do
2: for each client C, do
3: 0 L-call Update(G(; 0f), Ee; + GNNNioolll 0
end for
5:
Xe, + Flatten(0) [[ 8j))
6:
Ag + Ec A: t- 3+ + Ac-1 + (1 B) AE
7:
for = 0,1,...,N-1
8:
Ze + GNNoerver (Xc, A.), Å - 10 (t) h)
9:
Leerver t- BL, H (ā:)) B., [log(1 - a.s)] [ppaaeeGNNNeevvonnnnal
10:
11:
end for
12: W 7d + (1 Normalzzzzzz))
13: for each client C. do
14: 05+1 + + AGGR A0J, my))
15: end for
16:
end for
2016) denoted by GN server- To establish Å, we first compute Ze, the latent embedding of clients, using GN N Neeverr based on client features and the input client network:
learning model graph auto-encoder (GAE) Kipf & Welling
Ze = GN (xcNeeerrr(XeA)) Ax),
(5)
where Xe is the features needed for client network learning and A₁ is the input network starts from the initial client network As and updated through t communication rounds. Then discrete client network Å is derived by filtering the inner product of Ze.
À = I[softmaz h)
(6)
Here the softmar and threshold employed to cut out weak connections, which can assist improving the efficiency of knowledge sharing. Theoretical analysis regarding aggregation efficiency in Section 3.4
In the following sections, we will specify how to obtain client features Xe, the initial client network Au, the updated input client. network A,, and the training process of GN Ngerver
3.2 Client Network Learning
To learn an informative client network, we propose to design client features Xc revealing the essence of local tasks and guide the learning process by constructing a property-based client network Ag. In communication round t, we first combine the property guidance with functional embedding by mixing last round initial client network A,- with the similarity network Ar based on local model embeddings over random graphs to get initial client network A, and then feed Xc and A, into a two-layer graph auto-encoder GN GNN Neerver to get the final network Å for knowledge sharing.
Client feature design. The local model parameter is common choice for client features Chen & Zhang (2022) for its abundant information about the client. However, simply using model parameters may not be effective in FL scenarios with heavy data heterogeneity due to the similar natures of all graph classification tasks You et al. (2020). To study the impact of taking vanilla local parameters as client features under highly heterogencous sottings, we design an experiment following the same setting in Figure [(c] where clients are divided into two groups and across-group clients exhibit significantly heterogeneous distributions compared to intra-group clients. As Figure shows, in heavily heterogeneous scenarios, the local parameters are
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marirall parameters
100
0
4.75
4.50
5
5-
0.5
10
10-
500
-0.00
16
15
10
15
Figure 3: Similarity of local parameters and marginal parameters under high heterogeneity.
still too similar to be considered as client features due to the inherent similarities of their local tasks. As a result, constructing client relationships with vanilla local parameters is not promising in heterogeneous settings.
To address this problem, Xic al. (2021) uses local gradients instead construct client clusters (a particular kind of graph relationship). However, when it shows better results in heterogeneous selting, the gradient keeps fluctuating and can not give stable results. To circumvent the aforementioned issues related to vanilla parameters and gradients, we employ the difference between local paramcters and the uniform aggregated global model, termed marginal parameters, for instructing the construction of the dynamic client network,
k
Xc. = Flatten((; - where
Here, Xc, refers the feature of client This approach diverges from typical normalization as it maintains the scale of each parameter that is closely related to the importance of the parameters. As shown in Figure the heatmap of marginal parameters, compared with raw parameters, shows a clear pattern indicating the group relationship among clients, i.e., the similarity of clients within groups is high while across groups is low. The marginal parameters, as client features, are not only more expressive than vanilla parameters but also more stable than gradients since their convergence is ensured by the convergence local models, which makes beneficial for learning a high-quality client network.
Client network update. As local models keep evolving across the communcatiin rounds, always starting with the property-based network Ao may not be adequate, regardless of how sophisticated the initialization strategy is or even with the most powerful graph encoders, since Ao cannot track the dynamics of evolving local models along FL. To resolve this issue, designed client network updating mechanism to ensure that the client network is up-to-date for feeding into the graph Iearner. Since we have alrcady taken the local parameters as input. features, we consider the functional embedding here since it provides idnal perspective on the local model. To achieve this, we first generate random graphs using Erdós Rényi methods [Paul [1959] Gilbert (1959)) ) as a global dataset R. We then obtain the functional embodding of cach client by aggregating the embedding of each graph in and compute the cosine similarity between each pair of functional embeddings to form embedding similarity network Ag. In every communication round (t > 0), we update the initial client network A, with the following equation:
A = 3 Ar-1 + (1 (1-3) AF,
(8)
where 3 is the hyperparameter used for maintaining balance between preserving the existing relationship between clients constructed in the last communication round and adjusting to relationship given by the embedding similarity network. By incrementally incorporating functional embedding into the initial property guidance, we ensure the dynamic capture of the inter-client relationships.
Client network reconstruction. To combine client features Xę and the updated client network At, we train a graph autoencoder(GAAe Kipf & Welling (2016), denoted as G.N.ervvrr to reconstruct A,, aiming at climinating unnocessary client connections while amplifying the critical ones. As in the FL sctting, it is challenging obtain supervised information at the server without compromising local data privacy. We train G server in unsupervised manner by N iterations each communication round, leveraging the

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regularization term from
Ying al. 2019
server
E
(a:;))
E 1,7
[ogg(1 - -diy]l
(9)
where dzj sigmoid( Zeg represents the probability that client i and client should be connected and H is the entropy function. The first expectation penalizes for uncertain edge, i.e, dz around 0.5, while the second one stresses the sparsity of the client network. As Xe and A, have captured the central information of cach client, G.N would be able to eliminate disruptive links and construct a more coherent collaboration network.
3.3 Graph Property Guidance
While our client feature design and client. nelwork updating mechanism can effectively excavate the inter- connections among clients and dynamically construct expressive client relationship networks even based on random initial network (uniformly sample each entry from [0, IJ), relying solely on these two components may be suboptimal for overlooking the prior topology knowledge for clients. Therefore, to incorporate the guidance of fundamental graph properties into the learning process, we proposed a property-guided initializa- tion that can leverage the inherent topological characteristics of clients, thus laying more solid foundation for client relationship capture.
We first search for a set PP of fundamental graph properties, including network entropy Xu et al. (2023)
density, average degree, degree variance, scale-free exponent, and average closeness centrality. These graph properties are computationally straightforward yet strong in expressing essential information about the corresponding graph samples. Specifically, network entropy, defined through random walk Cover (1999); Burda et al. (2009); Spptzer (2013), is a potent way to mcasure the information quantity of the graph, as a special type of entropy rale and an important property for distributions. The network entropy can be efficiently derived in the case that the graph is connected (ubiquitous in real-world scenarios) with the formula,
Pentropy
|E| Σ de log
(10)
The four features, density, average degree, degree variance, and scale-free exponent, theoretically proved closely related to network entropy in in et al. (2023), are important features rogarding the degree distribution which is a key component of graph topology. Apart from them, We also use the average closeness centrality, i.c., average shortest distance among vertices, for a high-order measurement of graph topology.
Then construct the initial client network with the identified property set P. Each property is viewed function P G + u, that embeds graph samples with single scalar. Therefore, by incorporating all properties, the intrinsic topological characteristics of each graph G can be demonstrated with a fcature vector PG = P E P, which can be further aggregated to form the client-level property feature pc, for client C, Finally, the initial client network based on property set IP is constructed with cosine similarity, Ap = {cos(pc..Pc)) )c
However, as single property can hold different significance for graphs from different domains due to their varying nature, indiscriminately using all properties in all cases may obscure the key information. Thus, further introduce rule- based feature selector to select core properties ! specific to the current domain from all candidates P by iteratively removing insignificant properties. Firstly, we construct the initial client network Ar, (Po = P) with all properties following the process stated above. After that, we persistently manipulate one of the properties to minimize the gap between Ar, and functional embedding network Ag enabling us to select pertinent properties tailored to the current scenario, which described as follows:
p' (I) - -All2)
(11)
PP++1 PA (P').
(12)
The selection process ends when further removal cannot reduce the distance, or a minimal sot of properties is reached. Then we construct property-bar -bsse client network A, with the selected property set P Pt. ensuring solid starting point for subsequent client network updates and GNN-based reconstructions.
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3.4 Aggregation Efficiency Analysis
To further improve the efficiency of aggregation (formalized in 2q shown in Eq consider discretizing client network with threshold ht instead of directly using the dense network. Theoretical analysis regarding the efficiency of aggregation for both dense and discrete client networks is as follows.
Assume that for each client i(i = 1, 1,2....,) k), its local model 0, contains parameters and its degree is de (the number of j such that i i and client and client j are linked within the client network). The time cost of addition and multiplication in Eq are Ta and Tm. respectively.
For aggregation with dense elient network, the case where all d, 1(i 1, k), we would naturally have dense weight matrix W. Consequently, to update local parameters, each client has to first compute weighted gradients Wxy from all clients j(j = 1.......k) k), sum them up, which takes kF multiplication and (k: F) addition, and then combine the aggregated gradients Σ Wiy with local paramcters 6; which needs another addition. So in this case, the aggregation each client would cost kF multiplication and addition. Since we have clients, the overall time cost
Teeuse = FTF + T.))
(13)
Then considering discrete client network Å. Note that the mixup in Equ4 would not introduce any additional link between clients since adding an identity matrix only strengthens the self-loop of each client. So the weight matrix W resulting from our discrete client network can be viewed as a sparse matrix, where each client only aggregates gradients from its neighbors the client network and itself. In analogy to the dense case, we would have the aggregation cost of each client is (d, + 1)F addition and multiplication, where the extra F addition and multiplication are used to aggregate the gradient of itself. So we have:
T Tdiserete
+ 1)F +Tm)
1=1 -2M + FT. +Tm),
(14)
where M Σ the number of edges between different clients in Å. And the dense network is special where M = 1). So we have T /Tapars 12/(2M + k). Empirically, have k2 12/(2M + k) 1.7 through our experiments. It suggests that discretization can improve the aggregation efficiency by 70%.
3.5 Overall Complexity Analysis
We analyze the computational complexity of cach component in GPFL per commmication round. Following Sed3.4. k denotes the number of clients, F the number of parameters each local model, and E the dimension of functional embedding. The GNN NeNserrer is a 2-layer GAE trained for iterations, with hidden dimensions do di. The size of the random graph set R and E, N, do, di are fixed constants across all settings.
Client feature design. As shown in E the complexity of calculating marginal parameters O(KF).
Client network update. As the size of IR and embedding dimension E are constants, obtain the functional embedding would lakes O(F) for each client and O(kF) for all k clients. Then, calculate the similarity matrix Ag and update dense client network Ar to A, cost O(k?), resulting in an overall complexity of O(KF + +*²).
Client network reconstruction. formalized as:
The process of encoding Xe and A into latent embedding Ze can be
Ze A (Ax(A.Wo))WW
(15)
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where Wo E RPdd and W1 E Rxxd, In the first layer, Xe is first mapped to do dimension, which costs OkFF) since do is constant. Then, aggregation through A, takes O(k²), yielding total complexity of O +kF). Similarly, the second layer costs O(kdo = = takes O(k²). Consequently, the time cost for reconstructing A is O(k? + kF). After that, calculate the reconstruction loss in Eq 9 takes O..2). The above process repeated for N iterations each communication round. Since N is a constant, the overall complexity should be O + kF).
O(k)). Then the decode process, as shown in Eq
Aggregation. As demonstrated in See 3.4 considering that M 2 k. the complexity is O(MF).
Combining all components, the overall time cost should be O(k² + MF). As local model size F typically dominates the number of clients k, the aggregation becomes the primary computation bottleneck. Such observation underscores the necessity of our aggregation optimization in See 3.4
3.6 Discuss on GPFL
As we locus on constructing the client nelwork a self-supervision manner, only with structural prior formalized by regularization terms, the local data are not sufficiently exploited. Meanwhile, privacy and efficiency problems are not extensively explored in this work. Detailed discussions on the limitations of this work concerning these three problems are listed below.
Semi-Surpervised Learning manner for refining client network One limitation of our model is that we need a hyperparameter a to balance between adopting external gradients from other clients or believing in the knowledge contained in local gradients. Fortunately, [Zhang el. al. (2023) provides a feasible way learn client-specific a, in supervised manner, where we can construct a local model parametrized by a in the following formula:
(1- - a.) +
wiy A09),
(16)
where of and Adt have the same definition in Section 3.1. Then we can train these local models parametrized by a; over local datasets and iteratively optimize a with gradient descent over local loss functions to reach an ideal result. Although simply adding this component will cause performance drop rather than an improvement, let alone significant. time costs for this second-round local training towards the convergence of a, within single communication round, it's still promising way further refine the client network in semi-supervised lcarning manner which can be explored in future work.
Data Privacy In our setting of FL over graphs, the global graph reconstruction task does not require any type of inter-client or client-server data transmission. For the functional embedding step, instead of building global dataset by sampling representative local graphs, we employ random graphs, which shield our GPFL from the data leakage problem. However, do not consider how to deal with malicious attacks in this work. In the future, we can introduce advanced privacy protection techniques to ensure the safety.
Efficiency In this work, we focus less on the efficient implementation of our framework, and the current training process takes longer time than some baseline methods we compare e.g. FedAvg, GCFL. ensure the convergence of the client network, although as shown in Figure D the time cost of constructing the client network is almost independent of the scale of local datasets and will become less significant the scale continues to grow. In the future, could further improve the efficiency of GPFL by adopting the carly-stop strategy in the learning process and only performing adaptive learning over clients with uncertain relationships in each communication round.
4 Experiments
4.1
Experimental Settings
Datasets. We utilize the three most widely used graph classification benchmark datasets from two domains
Morris et al. (2020), including two molecules datasets (NCT1, Yeast) and bioinformatics dataset. (PRO-

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TEINS). Among them, NCI1 and PROTEINS are relatively small, containing about four and one thousand graphs separately, while Yeast is large dataset containing nearly 80,000 graphs. However, considering the severe label distribution skew existing in the raw Yeast dataset, we conduct downsampling to create a uniform subset containing 20,000 graphs. This approach is taken because designing effective split methods control helerogeneity becomes challenging when the raw dataset is already lopsided. The data details are as follows Table 1j.
Table 1: The statistics of datasets.
Dataset
Statistics
igraphs
fnodes
avg. fedges
classes
NCI1
4110
29.87
32.30
2
Yeast
79601
21.54
22.84
PROTEINS
1113
39.06
72.82
2
Yeast (sampled)
19136
22.77
24.22
2
Research questions. To comprehensively evaluate the effectiveness and contribution of our proposed framework, we formulate four rescarch questions as follows that will guide our empirical investigations:
RQL: How does GPFL compare to other widely adopted FL frameworks in graph classification lasks?
RQ2: How do the proposed client network learning framework and network initialization mecha- nisms individually contribute to the overall performance?
RQ3: What does the inferred client network reveal, and how do the networks learned with different combinations of components differ from each other?
RQ4: How do the proposed client network learning framework and graph initialization mechanisms individually contribute to the overall time cost?
We design label heterogeneity settings following a practical data split mechanism Wang et al. 22000 Lee
et al. (2021): ; Luo et al. (2021), which controlled by the Dirichlet distribution Dir(a). The setting becomes 0.5, 1, 5 to represent strong heterogeneity,
heterogeneous as the value of a decreases. We consider moderate heterogeneity, and weak heterogeneity in real-world scenarios, respectively. These settings are combined with varying levels of data scarcity, represented by client numbers k 15, 20, and 25, yielding a total of nine distinct combinations.
Compared methods. We employ self-train the initial baseline to assess whether FL can enhance client performance. In this baseline, each client starts from the same initial model downloaded from the server and conducts independent local training without collaboration. For FL basclincs, we employ basic FL algorithms Avd McMahan et al. (201)), FedProx Li et al. (2000), and five widely adopted personalized FL. algorithms. Among those personalized methods, SCAFFOLD Karimireddy et al. (2020) is based on
gradient adjustments, GCFL Xie et al. (2021) based on clustering, FedStar Tan et al. (2023) adopts a
decoupled sharing strategy, FED-PUB Back et al. (2023b) and FedSelect Tamirisa ct al. (2024) construct masks to perform selective parameter sharing, and FedAMP Huang et al. 2021) and pFdd @FeeGrraph Ye et. al. (0023) also follow graph-basod aggregation manner. For the graph classification model, we employ GIN Graph Isomorphism Network) Xu et al. (2019), simple yet powerful GNN for graph-level tasks. We fix the architecture and eyper-parameten of the local model for all baselines in all experiment settings to control the experiment.
Evaluation metrics. We measure the performance different FL algorithms using the average accuracy of all local models evaluated on the local test datasots and report the accuracy achieved in the last commu- nication rounds as a reference for all methods. All experiments are run with a five-fold pross-validation for three repetitions under fixed random seed 0.
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Table 2: Average accuracy on NCIL, Yeast, and PROTEINS datasets under multiple clients and different values of a. is the parameter of the Dirichlet distribution. The heterogeneity among clients increases when the a decreases.
Datroet(Sefivera)
(CT)
NCT1
NCT1(15)
skew rale
0.5
--
0.5
welf zoln
0.7706(0.012
0.7120(0.01))
(8001(00010)
0.7925/00008;
0,7250/0015:
0.6001
(..22(00114)
(.7261000114)
0.2005/0.012)
FalAvg
0. (29)
014)
1.6474 0255
016383(0018)
0.05
0.639/000199
0.8819/0.119
FedProx
1.575410.022 022)
(L676200.117)
0.643900.220
(161
0.657
0.3379(0.088)
0.0022000009
SoaBood
0.7012/0 022)
0.8287(0.025)
0.807900.013)
0.760210.015;
0.897210.020)
0.898200.0290
0.7843(0.007)
0.02296.017)
0.822/0.021)
GCFL
U.73xGj0 0201
(17979(00019)
(1222)00025)
(17048
(1771)(00117)
0.7142(00013)
0.8037(0.01.)
0.7045(0.114
0.7185000117
FediSter
0.7771 007)
0,7067(0.0113 13
0. 0.0627(0.013)
0:7708/0.011:
0.7307/0.011 11
0.6850/0.011
0.2536/0.005
0.7144(0.014
0.7065(0.016)
pFallGupph
0.7068)0.011)
(.609100.000)
0.6823(000011
0.7901 (0.05)
0.7118(0011
0.6573(0.012)
0.7597(0.0003
0.70930.0004
0.884500013)
FedAMP
0. 0.764700 015)
0. 0,700300 013)
0. 0.8555000015 015)
0,7882200 000:
017189:0013:
016:38
18/000001100
0.7101000000
FRISPUR
0.7788(0.009)
0. (07
0.0662(00006)
0.7966/0 008:
0.7052/0.006;
(.6781(0.011
0.51 59/0.007)
0.7024(0.005)
0 (688910.008
TedSelect
0. 0657
0.8 1.8811600000
0.6445(0.00)
0.7081(00005)
0.691300.005
0,6352/0.006;
0.7835/0.005)
0.8022000003
0509000.111
GPPL
0. 7865(0.012)
0.7378(0.010)
0.6041(0.009)
0.8109(0.010)
0.7.89(0.014)
0.7185(0.010)
0.8241(0.012)
0.7309(0.012)
0.7273
(25
Yeurt (20)
(eset(
self troin
0.766200000)
0.7171(00007)
0.88L6(0.007)
0.801000.05;
0.7530000005
0.6780000006;
0.5155/0.000
0.7127(0.007
0.8899/0.007)
FallAg
(.0245(00000)
(.6557((0.00))
(00
0.65
(..0))(0.007))
00.016)
0.667O(0.004)
0.5615/0.008
FedProx
ILR236jO.00 008)
ILG55500 (US)
0.0226400.000
(0614/0.8177)
SoaBoodd
U.756300.000 006)
U.715410.006
1.674370.0099
0.799950.004 004)
0.7046/O.000 0065
(0.075/0.007)
0.8075(0.005)
0.7065/0.005)
0.679500.007)
GCFL
0.7767(0.010)
0.726400 004)
0.856000.000 006)
0.7965/000005 0105
0.7132/0.000 006;
0.65355000005
0.8.57(0.005)
0.7778/0.007)
0.6037(0.000 0.008)
FedStar
0.7722(0.004)
D. 0,70220(00000 006)
(.0532(00006)
0,7810000000
066877000055
00005
0.506:/0.005)
0:601 000005
0.8725(0.006)
pFultruphh
0.7800(0 004)
0.721 5(2 00S)
0. 0.084600.000 007)
0.70555/00085
0.7052100000 006;
0.6782(0.006;
0.8114(0.005)
032153000004)
O 0.6879
RdJAMP
(.7837(0.006)
0,718440 006)
0.676110.008
(0.00))))
0.7023(00006)
0.6710(0.006)
0.5126(0.007)
0.7115/0.005)
0.684400.004)
FED-PUB
0.7673(0 002)
0.0021 004)
0.035600 004)
0.783360 003;
0.6706/0 002:
0.6406/0.003
0.7977(0.002)
0.6074(0.003)
06610)0.0004
D. 0.700)(000002)
0.0738(0.0005
0.6252(0.002) 002)
0.7067(0.001)
0.675770.000)
0.6381 (0.002)
0.7874(0.00)
(0.064(00000)
O 0.6185(0.002)
GPFL
0.7 0.7911(0.004)
0.7272(0.005)
0.6914(0.006)
0.8020(0.00D) 003))
(.7210(0.003)
0.6887(0.007)
0.8203(0.004)
0.7202(0.006)
(9.000)0008)
Dataac((xlleess)
PROTEINS(25)
PROTEINS(20)
PROTEINS(LS)
skow rde
0.5
0.5
5
0.5
5
sell zaiin
(L7570(0.012)
I.. (.778
I.BSS310.222 (226)
(170019000233
0.7198(00025)
(L7062(0000))
0. 0.722T(0.015)
0.7303/0.1133
0.722)(0.0112)
0.7123(0.025)
01177)
0.7087(0.008)
0.710000.003
0:7
0.7185/0.031)
0.7197(0.027)
0.209%(0.017)
RedPhas
0.7192(0 (25)
0.70
0.7047700.0113
0.7310000089)
0.7194(0.0244
0.7192(0.03)
(..800
0.705-(0.019)
Soalood
(7520)00014)
(.712800006)
(.7116(00012)
(.7.48((0022)
1.7.811(000229
(.7269(0.020)
0.7200(0.112)
0.7219(0.120)
0.7101 (0.088)
GCFL
0.7430(0.088
0,722910 (26)
0.8956(00022
0.697300.005)
0.7382(0.020)
0.7805/0.013)
0.7333000288)
0.7353(0.019
FedStar
0.7081 022)
0. 1.888400 028)
0.6391(00011) 001)
0:7488:00000
0,6835/00026
0.688770.088
0.748100015)
0.71990.02))
0.6072(0.025)
pridGraph
0.725-400 025)
034479(0.004)
0.05-0(00020)
0.7089/0:111
0.6885000025
0.69:6/0.025;
0.7567(0.017)
0.6096/0.059)
0.71 16)00.0)
RP
0.7467(0.017)
0.7542(00019)
0.0529(00880 o3n;
0.7525(0.025)
0.7145/0.045)
0.7626/0.016
0.7251 (0.06)
0 0.7211(0.0233
FRI-PUB
(.7007(0.015))
0.738900.006 0063
0.7)
0.7728(0.009)
(.7431(0.021)
(0.06)
0.788000.221
0.751010.025
0.74830.024)
RedSclees
(.763110.012)
1.7136(0.016)
(.8870(00022)
0.7499(0.016)
0.7321(0.018)
(.6859(0.030)
0.7519(0.15)
0.7015/0.012
0. 0.72180.019)
GPFL
0.7 0.7460(0.0228) 0.7787(0.015)
0.7155(0.029)
0.7680/0.050
(..401
(0.001)
0.8050(0.008)
0.7000(0.020)
0.7500(0.024)
Paramcter settings. We utilize three-layer GINs with a hidden size of 64 as local models. Local training uses batch size of 128, the Adam Kingma & Ba 20044) optimizer with the learning rate of 1e-3 and the weight decay of 5e -4 All FL methods are trained for 200 communication rounds with 1 local epoch in each communication round. For GPFL, we generate 20 random graphs with 30 nodes to compute functional embedding. The graph lcarner is trained for 100 epochs during each communication round. And the hyperparameters 7 in Eq and ,3 in Eq [ are set to 0.95, 0.95 across all settings, respectively. All codes and data can be found in https:
com/
4.2 Overall Performance (RQ1)
As can be observed from Table 2 our proposed framework can significantly improve the performance of local graph classification tasks. As the degree of heterogeneity intensifies (decreasing a), the effectiveness of FedAvg drops accordingly. Specifically, in relatively homogeneous settings (large a) with a lack of data (large k), FedAvg achieves comparable performance with or even holds an advantage over self-training. Conversely, in heterogeneous settings (small a) with relatively sufficient local data (small k), self-train demonstrates superior performance compared to FedAvg. GPFL outperforms both approaches across these settings by considering heterogeneity and providing local clients with network- knowledge sharing, which enables similar clients to share common knowledge while preventing them from being influenced by heterogencous users. For all datasets with all combinations of a and k, our GPFL framework achieves 1.57% - 8.03% performance gain over self-train and FedAvg on average. While personalized FL baselines SCAFFOLD, GCFL, FodStar, FED-PUB, and FodSeloct demonstrate docent performance, they cannot compote with our approach due to their inflexible knovledge-sharing mechanisms. Furthermore, even though FedAmp and pFedGraph also employ graph-based knowledge sharing, their expressiveness is limited as they rely on
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random
1.0
5-
4.594
10-
10
8375
gipastyrleam
15
15
20
0.6
8675
10
10
property
property-leamm
1.59
0.4
4035
NeT 2ia-1
Nen 200-1
Permios Bras
Toaa ira-1
Yonk- M8-1
10-
10
15-
15-
20
20
Experiment Scking
0.0
10
Figure 4: Ablation Study of GPFL.
Figure Client Network Visualization on NCI1 dataset with 25 clients and 0.5.
1620
2000
aclf-arii
sclf-tain
seli-triin
raadoms
4200
rusdons
1200
random
property
poopenty
1000
property
910
randone
property-laam
2010
pooperyy Hlemm
600
property-Lem
403
200
Oge 15
a Rus
k ao
25
ke-25 3-3
1t
20 D to15 gus
a
S
4-15 a-03
ke gu
te 0-133
a-1
2- 2--0
Expetiment Seaing
Experiment Settin
Experimant
(a) NCTI
(b) Yeast
(c) PROTEINS
Figure 6: Run time analysis property-based initialization and network learning.
vanilla parameters and their deviation from the initial parameters, which may not efficiently capture the characteristics of each client. In contrast, our approach surpasses them by explicitly modeling the client relationship as a network and applying marginal parameters and the client network to guide more precise knowledge sharing among related clients.
4.3 Ablation Studies (RQ2)
We conduct ablation studies to evaluate the effectiveness of each component in our model, following the same experiment setting used in Section 4.2 (see Figure for complete results), as depicted in Figure
Random Initialization v.s. Property-based initialization To evaluate the impact of graph property guidance incorporated in the initialization process, we use our GPFL framework without learning and updal- ing; instead, we assume that the relationship between clients is fixed, either as a random (uniformly sample each weight from [0,1], denoted as "random" " in Figure 4h or a property-based (denoted as "property" in Fig- ure relationship. That is, at all rounds, all clients follow the same network given in the initialization step for knowledge sharing. random relationship network fails in all cases. The property-based initialization, capable of capturing client relationships through fundamental properties, outperforms random initialization even without adaptively graph learning; however, it is slightly inferior to GPFL.
Fixed initialization v.s. Adaptive learning We also examine the impact of our adaptive learning strategy including iterative network update and learning with client features. To achieve this, we evaluate the performance adopting the learning strategy under random and property-based initialization, denoted "random+leare and ppropert++eaad separately. can be observed that our learning strategy effective even with random initialization as it excavates latent relationships with marginal parameters and functional
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Published in Transactions on Machine Learning Research (08/2025)
embedding. Nevertheless, learning with property- based initialization still outperforms as the model starts from meaningful client network.
4.4 Client Network Visualizations (RQ3)
Figure illustrates the comparison of the average client network generated using the four different. methods listed in Section 4.3. Compared the random client network, there are certain connections between the property-based client network and the learned client network, demonstrated by relative intensities. For example, in the property- baaeed network, clients 6, and show strong connections with each other, a pattern that is also observed in the learned network. Given that the network learned from random initialization is derived without any property preliminaries, relying solely on local parameters and functional embedding, this observed similarily suggests that fundamental properties of graph samples can, to some extent, reflect the inherent characteristics of clients. Moreover, regardless of whether the initialization is random- based or property-basod, we consistently obtain similar lcarned networks. This finding further demonstrates the robustness of GPFL.
4.5 Runtime Analysis (RQ4)
To measure the time efficiency of GPFL and the time cost of each component within it, we further conduct a runtime analysis on the three datasets with all settings. As shown in Figure G our property-based initializa- tion incurs only a 5% increase in runtime compared to random initialization, as we only consider fundamental properties of graph samples that can be computed efficiently, while this slight sacrifice in runtime signifi- initialization can
cantly enhances performance. And in real-world scenarios, the efficiency of property- be further improved by precomputing and storing the property values of each graph. Furthermore, GPFL. only considers certain client properties, the time cost of learning only grows linearly with the number of clients and is almost independent of local dataset size. As demonstrated in Figure G while GPFL might entail heavier time costs for small-scale datasets like PROTEINS compared with vanilla self-train, its com- munication cost becomes acceptable when applicd to larger datasets like Yeast which are more common in real scenarios.
sakker
sake:
nakken Haazs
080
Somt
prapery-boot
odt
o Adde
bottact
todd IJ
Led
2o
4- mmxl
Beck
(a) NCI1
(b) Yeast
(c) PROTEINS
Figure 7: Full results of ablation studies.
5
Conclusion
This work focuses on FI. on graph classification with local distribution heterogeneity. Specifically, we study the problem of uniform knowledge sharing in the setting where each local client owns graphs sampled from non-IID distributions. To address this problem, propose client- new-erk-wwwwweeeeee personalized federated graph learning framework (GPFL) that performs GNN-based knowledge sharing based on dynamic client network. The client network is first dynamically initialized under the guidance of fundamental propertics and functional embedding and then further refined through reconstruction leveraging marginal parameters during training to ensure its effectiveness. The extensive experimental results and in-depth analysis demonstrate the effectiveness of GPFL. Morcover, we discuss the limitations of GPFL, including the lack of supervision information further enhance the client network and the absence of optimization in terms of privacy and efficiency, which can be explored in future work.
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16


Reviews:
[{"review_id": "gZka1wdlgD", "reviewer": "Reviewer_Qgqt", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "**Strengths**\n\n1. Problem Significance: Tackles challenges in federated graph learning—personalization under graph-structured non-IID data—with clear motivation from synthetic experiments (Figure 1).\n\n2. Innovative Methodology: Marginal parameters effectively capture evolving client characteristics (Figure 3), resolving limitations of vanilla parameters/gradients; Graph property-guided initialization (e.g., entropy, centrality) provides a principled prior for client relationships; Functional embeddings from random graphs enable dynamic network updates without compromising privacy.\n\n3. Rigorous Evaluation: Extensive experiments across 27 settings (datasets × clients × heterogeneity) show consistent gains (1.57–8.03% over baselines). Ablations (Figure 4) and visualizations (Figure 5) reinforce design choices.\n\n**Weaknesses**\n- Hyperparameter Sensitivity: Critical hyperparameters (e.g., γ, β, λ) are fixed across all experiments. Sensitivity analysis is missing.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper proposes GPFL, a novel framework for personalized federated learning (FL) on graph data. Key contributions include:\n\n1. Dynamic Client Network Learning: Introduces an unsupervised method to learn a client similarity network using (a) marginal parameters (local-global model deviations) as client features, and (b) fundamental graph properties (e.g., entropy, density) for network initialization.\n\n2. GNN-Based Aggregation: Leverages the client network to guide weighted model aggregation via a graph auto-encoder (GAE), enabling personalized knowledge sharing.\n\n3. Heterogeneity Handling: Addresses non-IID graph data by adaptively linking clients with Graph Property Guidance, outperforming FedAvg and clustering-based methods in highly heterogeneous settings.\n\n4. Comprehensive Evaluation: Demonstrates SOTA results on three graph datasets (NCI1, Yeast, PROTEINS) under varying heterogeneity levels (Dirichlet-α) and client counts. Ablations validate the utility of each component.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "1. The phrase *\"To further improve the efficiency of aggregation (formalized in Eq. (2))\"* is misleading, as Eq. (2) does not pertain to the message aggregation process.\n\n2. The term *\"marginal parameters\"* appears without explanation until Eq. (8) on page 5. Consider introducing and defining this concept earlier to avoid reader confusion.\n\n3. Although the paper analyzes aggregation efficiency theoretically, it lacks empirical measurements. Discretization operations often produce non-contiguous memory accesses, which can impair tensor operation performance. Please include experiments or benchmarks to verify and quantify this effect.", "broader_impact_concerns": "N/A", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "kr6IAaQ0YU", "reviewer": "Reviewer_dbah", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "**Pros**\n\n- The manuscript models client features using marginal parameters to capture evolving client characteristics throughout the federated learning process.\n- It leverages fundamental graph properties and functional embeddings for client network learning and introduces a graph reconstructor to enhance the network structure.\n- Comprehensive evaluations are conducted to validate the effectiveness of the proposed method.\n\n**Cons**\n\n- As stated in the Introduction, the authors claim to design a graph reconstructor to refine the client network. However, subsequent sections lack any detailed description of this component. The authors should provide a comprehensive explanation of the graph reconstructor.\n- Figure 2 fails to clearly illustrate the logical relationship between client feature design and knowledge sharing. It is unclear how the various components interact to enable personalized model learning. The authors are encouraged to include a pseudo-algorithm to clarify the training process.\n- In Equation (6), the hyperparameter $h$ is used to prune weak connections. However, no sensitivity analysis is provided to assess its impact on performance. Additionally, the influence of the number of clients on the method's performance is not evaluated.\n- In Table 2, the authors use FedAvg and FedProx as baselines. However, these traditional aggregation methods are designed for global model learning. The manuscript does not evaluate their performance in the context of personalized client model learning, which should be addressed.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This manuscript addresses the challenge of graph classification in settings where high-quality labeled graph data is scarce. This manuscript proposes a novel method inspired by graph structure learning that dynamically constructs a client network based on graph data similarity. This network guides selective model sharing among clients. The approach leverages the marginal parameters of local GNNs and incorporates fundamental graph properties in its design. Experimental results on three real-world datasets validate the effectiveness and mutual reinforcement of the proposed modules.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "Please refer to the \"weaknesses\" part.", "broader_impact_concerns": "None", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "5IHH9UeMO4", "reviewer": "Reviewer_E7hw", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "1. The problem tackled in this paper is challenging in federated learning with graphs.\n2. The performance of the proposed framework is promising.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper presents a federated learning framework for graph classification tasks. The proposed framework can dynamically learn the similarities between clients based on graph structural features and GNN marginal parameters. Experimental results demonstrate the effectiveness of the proposed framework.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "1. The motivation of the paper can be presented in a clear way. To me, the motivation part in the 3rd and 4th paragraphs of the Introduction is vague. The authors are suggested to use a proper example with specific explanations to show why this GPFL is proposed.\n2. For related work, graph/network structure learning for generated federated learning has been investigated. Authors are suggested to survey papers published in top conferences/journals since 2023 and distinguish them from the proposed method.\n3. There is no solid theoretical analysis validating the performance of the proposed GPFL.\n4. More test datasets can be selected for experiments.\n5. More baselines that have been published in the last two years can be selected to compare with the proposed framework.6. Model complexity should be clearly analyzed.\n6. The model complexity should be clearly analyzed.", "broader_impact_concerns": "NIL.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "0nindIYS41", "reviewer": "Reviewer_LwR7", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n1. The paper is well-written and clearly structured.\n2. The paper targets a challenging problem in graph federated learning with heterogeneous data.\n3. Detailed experiments are provided to support the effectiveness of the proposed framework.\n\nWeaknesses:\n1. One concern is the unsupervised way to learn the client network, since the data is heterogeneous in the client side, I am a bit concerned will the structural learning model can learn the client network effectively under this setting. This may need more justification and experiments.\n2. It is not clear how to choose the hyperparameter $h$ as the threshold. It would be better to provide hyperparameter analysis, and provide guidelines for hyperparameter selection.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper considers graph federated learning for graph-level classification task with heterogeneous data at the client side. The main contribution of this study is to propose a novel design of client features by using graph-guided properties and the marginal parameters. Second contribution is a client network learning method for knowledge sharing. Overall this approach seem novel to me, and the client feature design and the use of random graph model for functional embedding seem rational.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "1. Add more analysis and discussion on the structural learning model under data heterogeneity.\n\n2. Add hyperparameter sensitivity analysis on $h$.", "broader_impact_concerns": "N/A", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Decision: Accept (poster)