FedHERO: A Federated Learning Approach for Node Classification Task on Heterophilic Graphs
Authors: Zihan Chen
Xingbo Fu
Yushun Dong
Jundong Li
Cong Shen
Venue: Accepted by TMLR ()

Abstract: Graph neural networks (GNNs) have shown significant success in modeling graph data, and Federated Graph Learning (FGL) empowers clients to collaboratively train GNNs in a distributed manner while preserving data privacy. However, FGL faces unique challenges when the general neighbor distribution pattern of nodes varies significantly across clients. Specifically, FGL methods usually require that the graph data owned by all clients is homophilic to ensure similar neighbor distribution patterns of nodes. Such an assumption ensures that the learned knowledge is consistent across the local models from all clients. Therefore, these local models can be properly aggregated as a global model without undermining the overall performance. Nevertheless, when the neighbor distribution patterns of nodes vary across different clients (e.g., when clients hold graphs with different levels of heterophily), their local models may gain different and even conflict knowledge from their node-level predictive tasks. Consequently, aggregating these local models usually leads to catastrophic performance deterioration on the global model. To address this challenge, we propose FedHERO, an FGL framework designed to harness and share insights from heterophilic graphs effectively. At the heart of FedHERO is a dual-channel GNN equipped with a structure learner, engineered to discern the structural knowledge encoded in the local graphs. With this specialized component, FedHERO enables the local model for each client to identify and learn patterns that are universally applicable across graphs with different patterns of node neighbor distributions. FedHERO not only enhances the performance of individual client models by leveraging both local and shared structural insights but also sets a new precedent in this field to effectively handle graph data with various node neighbor distribution patterns. We conduct extensive experiments to validate the superior performance of FedHERO against existing alternatives.

FedHERO: A Federated Learning Approach for Node Clas- sification Task on Heterophilic Graphs
Zihan Chen
brfira@vinginia.edu
Deportment of Electrical and Computer Engineering University of Virginia
Xingbo Fu
afBao@virginia. edu
Department Electrical and Computer Engineering University of Virginia
Yushun Dong
yd2 edu
Department of Computer Science Florida State University
Jundong
Sundong@virginen edu
Department of Electrical and Computer Engineering University of Virginia
Cong Shen
cong @nvinngiii edu
Department of Electrical and Computer Engineering University of Virginia
Abstract
Graph neural networks (GNNs) have shown significant success in modeling graph data, and Federated Graph Learning (FGL) empowers clients to collaboratively train GNNs in dis- tributed manner while preserving data privacy. However, FGL faces unique challenges when the general neighbor distribution pattern of nodes varies significantly across clients. Specif- ically, FGL methods usually require that the graph data owned by all clients is homophilic to ensure similar neighbor distribution patterns of nodes. Such assumption ensures that the learned knowledge is consistent across the local models from all clients. Therefore, these local models can be properly aggregated overall performance. Nevertheless, when the neighbor distribution patterns of nodes vary across different clients (e.g., when clients hold graphs with different levels of heterophily), their local models may gain different and even conflict knowledge from their node-level pre- dictive tasks. Consequently, aggregating these local models usually leads to catastrophic performance deterioration HERO, an FGL framework designed to harness and share insights from heterophilic graphs effectively. At the heart of FEDHERO is dual-channel GNN equipped with structure learner, engineered to discern the structural knowledge encoded in the local graphs. With this specialized component, FEDHERO enables the local model for each client to identify and learn patterns that are universally applicable across graphs with different patterns of node neighbor distributions. FEDHERO not only enhances the performance of individual client models by leveraging both local and shared structural insights but also sets new precodent in this field to effectively handle graph data with various node neighbor distribu- lion patterns. We conduct extensive experiments to validate the superior performance of FEDHERO against existing alternatives.
a global model without undermining the
the global model. To address this challenge, propose FED-

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1 Introduction
Graph Neural Network (GNN) aims to extract informative patterns from graphs {Xia al. 2021 Wu
et al. 2020b; Zhou et al., 2020 Scarselli et al. 2008 Xu et al. 2018a). However, graph data may contain sensitive information about the involved individuals (e.g., a user's race in social network (Dwork el al., 2012 Beutel et al. 2017)). As a consequence, sharing graph data across different stakeholders is raising concorns duc to the potential risk of privacy Ieakage, which further prevents training GNNs in a centralized
manner [Cong& & Mahdavi, 2022: Dai et al. 2022: Mei et al., 2019 Zhu & Zhu 2020). To properly handle the above-mentioned problems, Federated Graph Learning (FGL) has emerged as a popular collaborative
learning framework, which enables participants (clients) to derive insights from distributed graph sources
while upholding stringent privacy safeguards (Liu et al.] 2022a Lou et al.] 2021 Zhu et al.) 2022 Zhang et al. 2022 Peng et al. 2021 Chen et. al. 2021bp. A typical scenario of FGL is that each client. possesses a single graph (local graph) and seeks to collaboratively train a global GNN model for certain tasks (e.g.,
node classification tasks (Xiao et al.] 2022 Bhagat et al.) 2011h) without sharing the raw graph data. In
such scenarios, current FGL approaches implicitly rely on the assumption of homophilic local graphs (Zhu et al.] 2020: Ma et al.] 2021 i.c., nodes within a client's graph are more likely to form connections with other nodes of the same class (Ma et al., 2019; Tang et al., 2009b). Specifically, when clients hold homophilic graphs, most of the neighbors of each node will have the same class as this center node (Ying et al. 2018 The GNNs trained
different clients will thus capture similar tendency, and aggregating these GNNs usually makes the global model in FGL better learn such a tendency and benefit the generalization ability of the global model (Baek et. al.) 2023
Zhang el al. 2021).
Nevertheless, a critical issue regarding the above- mentioned assumption is that it overlooks the preva- lence of heterophilic graphs (Pandit el. al.] 2007
Low
Moderate
Hligh
Zheng et al. 2022 2023 Bo et al.] 202 Yang et al.
Bank A
Bank B
2021 Chien et al. 2020 Liu et al. 2023a where nodes belonging to different classes tend to be con- nected. For instance, in financial transaction net- works, nodes denote bank clients, where node labels are their credit risk and edges represent the finan- cial interactions between them. Such network can be heterophilic, and we show an example in Fig- ure [ Specifically, a 'Moderate Risk' customer in Bank A may transact with multiple 'Low Risk' in- dividuals, whereas in Bank B, the 'Moderate Risk' customer engages primarily with 'High Risk' coun- terparts. When training GNNs to predict customer risk, Bank A's GNN learns the connection between 'Moderate Risk' and 'Low Risk,' while Bank B's GNN captures the connection between 'Moderate Risk' and 'High Risk. Directly aggregation models could lead to poor performance in predicting 'Moderate Risk' customers, as they fail to establish a consistent pattern that generalizes well across both banks. Consequently, this mismatch can result in performance degradation for FGL algorithms.
A
Naighbar
Neighber distribution
distribution
Figure 1:
An example of financial transaction net- works in two banks. The edges in the figure represent transaction records. Due to the diverse customer fi- nancial habits in distinct networks, customers (nodes) within the same risk classification (label) across differ- ent banks have diverse transactional relationship pat- terns (ncighbor distribution).
To properly handle the challenge discussed above, in this paper, we introduce FEDHERO, a novel framework for Federated Learning on Heterophilic Graphs. FEDHERO is equipped with a carefully designed dual- channel GNN model, including the global channel and the local channel. The dual-channel design aims to aggregate GNNs that have learned similar patterns to facilitate knowledge sharing. To ensure each client obtains GNN model aligned with others, we introduce a shared structure learning model that generates latent graphs across clients based on common patterns. By learning from and sharing the knowledge from these latent graphs, GNNs in the global channel capture similar tendencies, enhancing their overall performance. Mcanwhile, the local channel operates directly on the original graph. With such a design, FEDHERO facilitates the sharing of common knowledge across clients while leveraging the unique structural information in each client's 's local graph to enhance overall model performance. This approach offers two key
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advantages: (1) The global channel, trained on the latent graph, reduces reliance the original neighbor distribution. The GNN models trained on different clients could capture similar tendencies from the shared structure learning model, and aggregating these GNNs could exploit FGL's potential. (2) Retaining the locally trained GNN on the original graph preserves sensitive information, cnhancing privacy protection. We summarize the contributions our paper below.
Problem Formulation. To the best knowlodge, we take an initial stop to formulate and handle the challenge arising from the implicit heterophilic assumption of FGL.
Algorithmic Design. We introduce an innovative FGL framework, named FEDHERO, which em- powers clients to acquire global structure learning models while preserving graph-specific structural insights the local level.
Empirical Evaluation. We perform comprehensive experiments across four real-world graph datasets and three synthetic datasets. The results demonstrate that FEDHERO consistently out- performs existing FGL alternatives significantly.
2 PRELIMINARIES
Notations. Let 9 - (V, be a graph containing N nodes V and & C V x is the edge set. We define X E Nxd as the feature matrix, where X2 F2 represents the attributes of node v. The initial graph structure can be represented in adjacency matrix A = N where duv indicates the presence of an edge between node u and and 0 otherwise. Y E R.VCC' denotes the label matrix, where y. represents the label vector for node u, and C' is the number of classes. GNNs operate by representing nodes based on information from both their neighborhoods and their own attributes, which can be expressed as follows:
z = AGG((E Vu s.t. aue = 1))),
(1)
where zi. is the embedding of the node v at 1-th layer. The operation AGG aggregates the embeddings of v's neighbors, while UPD updates the representation of node using its embedding from the previous layer and the aggregated embeddings from its neighbors. Initially, 2. is set as X.-
Federated Learning. The objective of clients in FL is to jointly train models using local data. Let's consider M data owners, each possessing data exclusively accessible to them, denoted as D. = (1), where X; represents the data instances and V/ is the corresponding labels. N; signifies the number of data samples held by client and N = E, N₂ denotes the total number of data samples available. L; and w; are the loss function and model parameters of client i, respectively. The FL. process typically encompasses the following steps: (i) At r-th round, the server selects a subset of clients that participate in the training process. These clients receive the global model from the last round W, and initialize the local model parameters / +- W. (ii) Each selected client updates its local model using its own local data to minimize the task loss: wf <- = - v/ VV(ww")) (iii) The server aggregates the updated local models to obtain an updated global Ni
model: 1T+1 = E. N
" +1 This process continues iteratively until convergence is achieved.
Preliminary Study. To highlight the unique challenges posed by varying neighbor distribution patterns across clients, we conduct a preliminary study comparing the performance of local training models with the global model produced by AvD Table I contrasts results on heterophilic datasets (Rozemberzzki et al. 2021 (Squirrel and Chameleon) with those homophilic datasets (PubMed (Namata et al. 2012) and Citeseer (Sen et al. 2008)). ). On homophilic graphs, the global model generally shows better performance. In contrast, for heterophilic graphs, the aggregated global model underperforms relative to local training models. This discrepancy arises because clients with heterophilic graphs are more likely to exhibit diverse neighbor distribution patterns, leading locally trained GNNs to capture varied tendencies. As a result, the global model struggles to aggregate and generalize this knowledge, resulting in poor prodictions. This pre- liminary experiment underscores the impact of distinct neighbor distribution patterns on FGL performance, reinforcing the need to address the challenges identified in our study.
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Table 1: Performances of the locally trained model and FEDAVG's global model on four datasets.
Squirrel
Chamelcon
PubMed
Citeseer
Datasets
heterophilic
homophilie
LoCAL
#2.92:1..4 28.55+0.445
07.45:1.49
84.47-0.47
67.8910.54
AVD
38.65-22.19
87.08:10.01
72.41+0.22
Problem Sctup. In the FGL system, we assume that M clients hold M graphs and aim to collaboratively train node classification models. In particular, client owns the graph G; (V,, and A; denotes the corresponding adjacency matrix of graph 9;
We aim to train a universal structure learner 9L paramcterized by d across local graphs. This learner should capture the universally applicable patterns across graphs (2.. The trained structure learner is expected to generate effective graph structures that enhance the downstream classification performance of local GNN classifiers. Formally, the goal of training gt alongside the local models fi can be expressed as an optimization problem:
M Σ C. A.).
min 8,00 SU
(2)
where gr. takes the node feature X, and adjacency matrix A, of the local graph as input generate a new graph structure, and the local model fo predicts the node classes from the new model structure and the original graph data.
3 Proposed Framework: FedHERO
We aim to address the issue of distinet neighbor distribution patterns, particularly for heterophilic graphs. In this context, clients possess heterophilic graphs in which the neighbor distribution patterns of nodes vary across different clients. As discussed in Section D this variability can result in diverse aggregation effects. Models trained on graphs with distinct neighbor distributions exhibit limited generalization ability.
To address this challenge, we present FEDHERO, as illustrated in Figure 2 First, we outline the implemen- tation of structure learning and its initialization. We then demonstrate how FEDHERO integrates the global graph structure pattern and local structural information, detailing the joint optimization process involving structure learning and personalized task models. Lastly, explore the mechanism for sharing structural knowledge within FEDHERO.
3.1 Graph Structure Learning in FedHERO
Graph structure learning endeavors to comprchend the messago-flow pattern throughout the graph (Xia al. 2021b. Nevertheless, in FL scenarios where data is diversely distributed and privacy concerns are paramount, directly aggregating all data to train a comprehensive structure learning model becomes unfeasible. To tackle this challenge, we implement structure learning model for each client, which can learn structural knowledge from local data. By sharing the learned knowledge with other clients, the entire FGL system can acquire a unified, globally optimized structural representation that captures universally applicable patterns across diverse graphs.
The objective of the structure learning model is generate relevant latent structures that facilitate effective message passing based the original graph. A common approach considers representing the weight of an odge between two nodes as a distance mcasure between two end nodes (Zhao et al. 2021b Kazi et al. 2022: Chen et al. 2020). We follow this idea and employ one-layer GNN to derive node representations Z from the original graph. The structure learning model can be represented by learning a metric function o(:-)) of pair of representations: ăuo = p(z,, where z, is the learned embodding of node u produced by GNN. The metric function <(---) can assume various forms like cosine distance (Nguyen & Bail 2010) and RBF kernel [i et al. 2018b). In this study, we employ the multi-head attention mechanism as the metric
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Clsst
I globall
Yo
Graph learerr !
GNNSD
Fiocet
I-d
CONN
smooth
BAvE
X
MLPS0
GNN loc
Clieet
gtobal
Original graph
I-thlayer
MLPSc
Sucet
The framework of FEDHERO. Blue boxes represent models in the flocal channel, which are trained locally and personalized for each client. Yellow boxes denote models in the ggotat channel, shared among clients to train a structure learner for mutual benefit. On the right side of the figure, the model aggregation scheme in FEDHERO is depicted.
Figure 2:
function, following the approach outlined by Chen et al. 22020
o Zo)
cos( wh O Zuo wh. ② Ze).
(3)
NH
where -) is cosine similarity, and @ denotes the Hadamard product. By consolidating the outputs NH heads and using w/ wI to scale the node embeddings individually, the structure learning model can poten- tially identify connections between similar dissimilar nodes and exhibit the necessary expressive power to handle graphs with heterophily. First, aggregating outputs of different heads enhance the model's expressiveness in capturing the underlying influence between nodes from various perspectives. Additionally, the weight vectors w). and w are introduced to learn element wise scaling of input vectors, i.c., node repre- sentations. Moreover, the use of two independent weight vectors w and w/, allows for potential alignment or misalignment, enabling the model to connect both similar and dissimilar nodes. It's important to high- light that FEDHERO can be integrated with various metric functions and even various structure learning methods. Further empirical results are illustrated in Section 4.4
To construct the latent graph À NNN, we implement post-processing step to create ANN graph, wherein each node connects to up to k neighbors, i.e.,
āijz if ā.j is top-k clement in (āzglí e [n]].
A.
(4)
0. otherwise.
This design choice is based the differentiability of the top-k function, which facilitates the computation of parameter gradients and subsequent model updates in FEDHERO. Additionally, explore alternative method for latent graph generation. Such method treats each edge in the latent graph as a Bernoulli random variable. Here, each latent edge Aij is sampled from a Bernoulli distribution with parameter āij (Wu et al. 2020a; Elinas et al. 2020 Zhao et al. 2023 comparison these methods and the impact of varying values provided in Appendix
3.2 Optimization of the Dual-channel Model
the local models primarily employ multiple GNNs in sequence. These models initiate the process of generating node representations directly from raw features. However, as Tan et al. (2023) pointed out, directly constructing and sharing these local models across diverse clients can siguificantly compromise personalized performance due to fealure and representation space misalignment. To address this challenge, divide the local model into two channels: folobal and flocal- The global learner fytohal takes the original input graph and refines the latent graph structure. Through cooperation with other clients, fgiobal detects patterns of universal relevance across heterophilic graphs. On the other hand, the local task learner flocat extracts valuable client-specific information from
In existing FGL frameworks (Zhang et al.) 2021 Back et al. 2023
5

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raw node features and structures within the local graph. This information includes biased structures diverse feature distributions tailored for follow-up tasks.
In a client's local graph G = (V,E), we initiate the process by utilizing a Multi-Layer Perception (MLP) fo to extract information from the node feature matrix X into node embeddings Z Next, we feed the node embeddings zo; the latent graph A, and the original graph structure A into an I-layer GNN. The middle part of Figure depicts how FEDHERR leverages information from both the local graph structure A and the structure A from the structure learner to obtain node representations. In the fglobat channel (models in yellow boxes in Figure 2). the I-th layer of the GNN (denoted as f/) utilizes the node embeddings from the previous layer z and the latent graph À to generate hidden node embeddings that reveal patterns that hold universally across different graphs, denoted as H'. While feature propagation on the A could potentially yield enhanced node embeddings that align with global patterns, it is important to note that the original graph structures also contain valuable information, such as effective inductive bias (Bronstein et al. 2017). Therefore, we leverage the information within A. It is combined with the output from the last layer, Z- and fed into the I-th layer of the GNN (denoted as flae) within the flocel channel (models in blue boxes in Figure 2 This process generates hidden node embeddings that adhere to the massage-passiigg patterns within the local graph, resulting E These embeddings play a crucial role in computing the layer-wise updates for node representations:
Z'= 2==((EE' o.E' + (1-a))) o)HH
where a is an activation function and a is trading prper-parameter that controls the concentration weight imput structures. Additionally, integrating the outputs from both the fglobal and flocal channels can enhance training stability. This is achieved by mitigating the influence of substantial variations in latent structures encountered during the training process within the fglobat channel.
Recent studies show that merging intermediate node representations from mopt enables the GNN to integrate nodes of the same class (Zhu et al.j 2020 Abu-El-Haija et al.] 2019). In addition, encod- ing the features of the ego node separately from the aggregated neighbor representations enhances node embedding learning (Zhu et al., 2020 Suresh et al.) 2021; Yan et al. 2022) Thus, merge the inter- mediate node representations generated by each layer of the dual-channel GNNs with the ego feature X: z = COMB(X, Z",... "e.....Z'' )... The COMB function can be implemented in several ways, including max- pooling, concatenation, or L.SMMattention (Xu et al. 2018b). In our approach, we specifically use con- catenation for the COMB function. This choice is based on the observation that concatenation consistently outperforms other methods in similar contexts (Xu et al., 2018b Zhu et al.. 2020).
In the classification stage, the prediction of the node class is based its final embedding:
Y (f
(6)
where the classify layer Je gives the C' dimension prediction.
Alongside the classification loss, we incorporate a regularization term to constrain À
Lemooth Σ AmwlIx - x0 + ||
(7)
0,0
where || 1|x is the Frobenius norm. The first term in Eq. evaluates the smoothness of the latent graph, operating under the assumption that nodes with smoother features more likely to be connected. The second term in Eq. 7 serves the purpose of preventing excessively large node degrees. The hyperparameters X and govern the magnitude of the regularization effects. Hence, in conjunction with the cross-entropy loss Lee, we fine-tune tune the local model using the following loss function:
Liotal = Lee (Ý, Y) + Lemooth-
(8)
Minimizing the loss function in Eq. 88, the generated latent structure leveraged to generate node embed- dings, providing supplementary information for representation learning.
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3.3
Model Aggregation in FedHERO
The right side of Figure illustrates the process of clients sharing local models and receiving updated models from the server. The model aggregation process in FEDHERO resembles that of FEDAVG (MeMahan et al., 2017). However, in the FEDHERO framework, the server only receives and aggregates models from the Iglobal channel of clients instead of the whole model. This sharing mechanism offers two key advantages for FEDHERO. First, the structure learning model in the global channel generates latent graphs from node embeddings with relatively low dependence on the original graph structure. By sharing this model among clients, the global channel GNNs learn similar patterns from the generated latent graphs. Aggregating these aligned models enhances the effectiveness of FGL, leading to improved overall performance. Second, retaining the model flocal-Whie which focuses on learning the message passing pattern within the local graph-ar as private and training it locally allows the local model to capture client-specifie information, ultimately contributing to subsequent tasks. Let w/ denote the parameters of the fglobal in client i. The server does the aggregation: " = E. N w where N, represents the number of nodes in the client i's graph, and N denotes the total number of nodes in the graph data of all clients. Subsequently, the server transmits Wy to the clients. The clients then update model in the falobat channel with wy and commence local training for the ensuing round.
In FEDHERO, the information in the flocel channel, including the final classifier layer fer is not shared. This separation distinguishes between global and personalized information within the local graph. In Section 4.5 we evaluated the impact of sharing different parts of the model. This empirical examination underscored the efficacy of maintaining the flocal channel in private, further emphasizing the effectiveness of bifurcating the GNN into two distinct channels.
3.4 Computational and Communication Overhead
We analyze the additional computational and communication overhead introduced by the dual-channel design in FEDHERO and compare with current FGL methods, providing insights into its scalability and efficiency in various FT. environments.
Let M denote the total number of clients, E represent the number of local training epochs, and L signify the number of layers in the model architecture. For simplicity, let d denote the larger dimension between the node feature dimension dz and the embedding feature dimension dhidden- Nlink, fd dag. and dew regard method-specifie parameters. In Table 2 we compute the additional overhead caused by the FGL algorithms compared to FEDAvG (McMahan et al. 2017). Regarding communication overhead, since a relatively small NH (e.g. NH 4) enables the structure learner to perform effectively, the additional cost is comparable with other FGL methods like FEDLIT. As for computational overhead, the primary increase in computational load arises from dual-channel GNN. From Table 2
we can observe that the computation cost of FEDHERO aligns with the FGL methods that scale linearly with the size of node and edge sets. Therefore, FEDHERO's design allows it to handle large-scale datasets effectively without introducing much computation burden. Appendix E we further report the practical metrics including running time and memory usage, showing that FEDHERO scales well on large datasets and is comparable with FGL baselines.
Table 2: Additional computational and communication over- head of FGL methods compared with FEDAVG, calculated per client per round.
Methods
Computation cost. ((M + MlogM)/E)
Communication overhead
GCFL
Xie et al.
2021
O(1)
FEDLIT
Xie et al.
2023
(naadld + [V|d2 + 2n dI/E)
( Ld2)
FEDPuB
Back et al.
2023
OLLa + Md/EE) ((LLd(d)) +|E))
FEDSTAR
Tan et al.
2023
O(1)
FEDSAGE
Zhang et al.
2021
O(VI((" +Lf))
D(VVd+Ld'
F FRDHERO
O(d(([)]+ + +18) + Vnd
O O(Nnd + d))

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4 EXPERIMENTS
4.1 Experimental Settings
Datasets. We carry out experiments using well-known heterophily datasets such as Squirrel and Chameleon derived from Wikipedia datasets (Rozemberczki et al. 2021), along with the Actor dataset (Tang et al. 2009a) and the Flickr dataset (Zeng et al. 2019). Given these datasets' inherent incompatibility with the FGL framework, we adapt them into a federated context using two prevalent graph partitioning methods: the METIS algorithm Karypis & Kumar 1997 and the Louvain algorithm (Blondel et al.) 2008). This approach enables us to create synthett federated graph learning datasets. As detailed in Appendix A the graph partitioning process preserves the hetcrophilic propertics of the graphs. Additionally, Appendix demonstrates significant differences in the neighbor distributions of same-class nodes across clients. This highlights the challenges in FGL that discussed in the Introduction. We follow the common FGL proto- col (Baek et al., 2023 Zhang et al. 2021) with non-overlapping clients for fair comparison with prior work. We note that FEDHERO does not rely on this assumption, since no component in FEDHERO relies on unique nodes among subgraphs, cross-client neighborhoods, or graph stitching. For further details on this process and the overlapping scenario, please refer to Appendix and C respectively.
We also include three graph datasets: syn-cora (Zhu et al., 2020), iece-fraud (Howard et al. 2019), and credit (Yeh & Lien 2009]. These datasets naturally lend themselves to subdivision into multiple subgraphs (o.g.; distinct subgraphs within the ieco-fraud dataset correspond to different product transaction rocords), and we denote them as real-world datasets. The description of the dalasets is summarized in Appendix A
Hyper-Parameter Settings. The architecture of the GNN models consists of a feature projection layer, two graph convolutional layers, and a classifier layer. We employ Adam optimizer (Kingma & Ba 2014) with a learning rale of 0.005. We apply a consistent hyprparammeeer setting in our main results. Specifically, we set a 0.2, μ == 0.1, 20, and Nz 4. In the supplementary material, we provide an analysis of hyperparameters, indicating that optimizing these values could lead to further improvements in performance. The training process involves 200 communication rounds, with each local training epoch lasting one iteration. The nodes are randomly distributed into five groups. For each experiment, one group is chosen as the test set, while three of the remaining groups are utilized for training and one for validation. We perform five experiments on each dataset and report the models' average performance. For the iece-frand and credit datasets, we present the mean test Area Under the Curve (AUC), accounting for the imbalanced labels. For the remaining datasots, we use mean test accuracy across clients for evaluation. All methodologics are implemented using PyTorch 1.8 and executed on NVIDIA RTX A6000 GPUs. Our code can be found in the supplementary material.
Basclines. We comprehensively compare FEDHERO against five bascline methods in federated graph learning. These baselines encompass strategies that focus on (i) promoting collaboration among clients with similar graph distributions (GCFL (Xie et al. 2021) and FEDPUB [Back et al. 2023 ), (ii) sharing structural
insights (FEDSTAR (Tan et al. 2023)). , (iii) producing missing edges between subgraphs (FEDSAGE (Zhang ct al. 2021)), and (iv) discerning and modeling mossagc-passing for latent link types (FEDLIT (Xie et al.,
2023
To ensure the completeness of our experiments, we also include the standard FL method FE-
DAvG MMcMahan et al. 2017).
4.2
Evaluation on Semi-synthetic Datasets
We present the node classification results four semi-syuthetic heterophilic datasets. The average test accuracy and its standard deviation are summarized in Table 3. The results indicate that FEDHERO consistently outperforms all the baseline methods by a significant margin. This is because the global channel in FEDHERO has less dependence on the local graph structure, with the GNN falobal being updated on the latent graph. By sharing the structure learning model across clients, FEDHERO ensures that the latent graphs generated by different clients exhibit similar neighbor distribution patterns. This allows the aggregation of consistent information from the global channel, ultimately enhancing the performance.
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Table 3: Performance of FEDHERO and baselines on semi-synthetic heterophilic datasets. Bold fonts
indicate the best performances among all mothods, while underlines denote the next best results across all methods. M denotes the number of clients.
Squirrel
Chamelcon
Actor
Flickr
Datasets
METIS
METIS
METIS
METIS
Louvain
Louvain
Louvain
Louvain
M 5 M-7 M-9
M
M-5
M-7
M
M-7
M
M 30 M
M 50
31.32
31.44 31.33
32.92
43.77
44.34
45.15
47.45
29.27
28.75
28.37
26.14
45.03
44.98
45.37
45.02
LocAL
(11
(40.11) (40000)
(41.94)
(#1107)
(43.16)
(41.37)
(40.49)
(40.00)
(4:030)
(40.34)
(4:0990)
(40.13)
(4:0.36)
(40.37)
(40.26)
29.67
28.28
27.18
28.55
42.27
39.08
45.09
38.65
31.90
31.45
31.40
31.14
42.45
42.40
42.30
42.56
FEDAvG
(+1.84)
(40.64) (#1.37)
(+0.45)
(+22339)
(+1.15)
(43.24)
(42.19)
(+1.02)
(#0.72)
(#0.322
(#11.0)
(+0:2)
(40016)
(40.39)
(40.39)
29.52
29.38
29.12
32.87
42.36
46.40
45.71
47.16
28.50
26.92
26.95
26.92
47.47
46.64
46.77
46.99
FEDPuB
(20.86) (d:1.04) (#:0.56)
(::1.9))
(2:1.50)
(d:1.20)
14: 1.60)
(#22.03)
(+0.84)
(2:0.90)
(::11 12:
(5)
(=0.76)
(2: 28)
(4:0.39)
(4:0.85)
31.74
32.60 33.53
36.84
50.60
50.42
50.72
51.32
28.58
27.13
27.18
27.43
49.35
49.15
49.08
49.03
FEDSTAR
(10.73) (d: (.01))) (200011
(1:0.90)
(2:0.84)
(1: 14) (1:1
(4:1.26)
(10.74)
(1:044))
(::0.40)
(2:1.10)
(100118)
(2:0.62)
(1:0.25)
(1:0.45)
31.40
30.04 28.98
30.42
45.12
43.47
40.30
38.73
31.39
31.63
31.41
31.63
47.65
47,41
46.88
47.37
GCFL
(+2.09) (4:1/25) (300.33)
(4:2/28)
(+:1.4)
(+22001) (+22853)
(43.77)
(+0.94)
(+1122) (+11
(#:1.29)
(#00.22)
(#:0.24)
(++0.00)
(+0.399
30.01
28.22 28.22 27.42
32.76
40.10
34.36
35.97
36.67
32.23
31.74
32.16
32.85
48.18
48.35
48.56
48.49
FEDLIT
(+2.46) (#:2.00) (#2.42)
(4:3.66)
(++4.45)
(++4.38) (4:3.00)
(+6.06)
(+1.07)
(=00882 (+1111))
(=1.71)
(=10000)
(+:0366)
(+0.44)
(#00.52)
33.30
33.07
33.10
35.17
50.93
48.72 49.17
45.51
33.75
32.73
33.30
33.57
45.75
45.45
44.74
50.37
FEDSAGE
(10 63) (10088) (1.1.02)
(12.13)
(1.1.77)
(122.1) (12260))
(111.66
(11.02)
(1:0.87) (100.80
(111.83)
(100 23) (1.0.28) (1.0.36)
(1.0.56)
FedHERO 36.63 36.08 37.83
38.00
53.93
54.06 52.65
55.63
35.25
34.60 34.32
34.54
50.51 50.33 49.96
50.45
(10.95) (10.87) (11.02)
(1.0.92)
(1.0.88) (100.66 (11133)
(.12.00)
(10.29) (11.03) (10.68)
(1.0.80)
(10.32) (1.0255 (10.31)
(10.25)
We also observed that FEDAVG often underperforms compared to local training in many experiments. This suggests that heterophilic graphs are more likely to exhibit distinct neighbor distribution patterns across them, which can negatively impact FEDAVG's performance. Notably, FEDPuB and GCFL demonstrate superior overall performance compared to FEDAVG. Both encourage clients to collaborate with those who have similar model gradients or outputs. During optimization, the GNN learns to capture graph information, including neighbor distribution patterns. Therefore, similar model gradients or outputs indicate similar neighbor distribution patterns or tendencies captured by the model. As previously discussed, aggregating models with similar tendencies enhances the performance of the aggregated model.
In our investigation of FEDHERO's performance with heterophilic data, we also observed significant improve- ments in datasets characterized by high heterophily, particularly in the Squirrel and Chameleon datasets. These datasets have homophily ratios of 0.22 and 0.25, respectively, as reported in (Mao et al., 2023 with lower ratios indicating greater heterophily. In comparison to Flickr (homophily ratio: 0.32 Kim & Oh 2022 FEDHERO's enhancements are more pronouneed. For example, under Louvain partitioning, FED- HERO demonstrates improvements of 4.31%, 1.16%, and 0.08% on the Chameleon, Squirrel, and Flickr datasets, respectively, when compared to the pest-performing baseline. We believe this phenomenon occurs because, as heterophilic ratio increases, the differences in node neighbor distribution patterns across clients' local graphs become more pronounced, posing greater challenges to existing FGL methods.
4.3 Evaluation on Real-world Datasets
3 provides a comprehensive overview of the evaluation results across real-world datasets
Figure
in FGL settings. FEDHERO consistently outper- forms all FGL baselines on ieee-fraud and credit datasets. The similar performance between our method and other FGL baselines ieee-fraud and credit datasets may be attributed to distinct class features that are easily distinguishable (e.g.,
Local
FedPub FedStar
GCFL
FodSage
FedAvg
FedLit
FodHERO
Average Performance
80-
75
70
a linear regression model can yield satisfactory re- sults) HHowadd al. 2019) or the low dimension-
65
ality of features (Yeh & Lien] 2009). The superior performance of FEDSAGE on the syn-cora dataset
syn-cora
iccc-fraud
credit
Figure Performance of FEDHERO and basclines on three real-world datasets.
9

---

may be attributed to GraphSage's utilization of hybrid design, incorporating elements of both ego- embedding and neighbor embedding. Similar findings are also observed in (Zhu et al. 2020
Notably, FEDPUB and FEDSTAR face challenges in achieving strong performance on the syn-cora dataset. The syn-cora dataset consists of random graphs where nodes of different classes have the same expected degree, and different graphs share the same degree distribution (Abu-El-Haija et al. 2019 Zhu et al., 2020). The suboptimal performance of FEDSTAR also demonstrates that relying solely structural information from the adjacency matrix, while overlooking distinctions between nodes connected by edge, is insufi- cient for handling heterophilic graphs. Thus, structure embeddings in FEDSTAR don't contain distinguishable information across classes. Sharing the structure knowledge doesn't benefit training GNNs for node classifi- cation. On the other hand, FEDPUB assumes graphs in clients have community structures, and it leverages the community information. However, the assumption does not hold syn-cora where random graphs are generated independently.
4.4 FedHERO with Different Structure Learning Methods
In this section, we explore the adaptability of FEDHERO to various structure learning tcchniques. For example, we substitute the similarity function with an attention-based structure learner, denoted FEDHEROatt, and with Graph Attention Networks (GAT) (Veličković et al. (018)), denoted FEDHEROgat. Another variant, FEDHEROCOS, uses cosine distance as the similarity function. We further examine FEDHERO with more complicated graph learning methods, including GLCN (Jiang et al. 2019). GAug (Zhao et al. 2021b). We replace the structure learning model in FEDHERO with these methods. The experiments are performed on the Squirrel and Chameleon datasets, and the results are presented in Table From the results, we observe the following:
The original FEDHERO, integrated with multi-head weighted attention, consistently outperforms its variants. This superior performance can be attributed to the ability of multi-head weighted attention to capture a wide range of influences between nodes effectively, making it particularly effective for heterophilic graphs.
Among basic variants, FEDHEROcos shows slightly better performance than the other two variants, likely because avoids additional model parameters, thus reducing the risk of overfitting. Addition- ally, unlike FEDHEROgat, FEDHHEROcos considers the entire subgraph for edge generation, which mitigates the impact of heterophilic graphs the GNN aggregation mechanism LLi et al. 2022 Yang et al. 2022
Table 4: Performance of FEDHERO with different graph structure learning methods.
Squirrel
Chameleon
Variants
METIS M
Louvain
METIS M-7
Louvain
FEDHERO FEDHERO, att
34.65-10.69
37.83=1.78
51.36-2.72
52.39
34.92+1.00
36.80+1.49
51.71+1.88
54.28++.66 1.22
FEDHERO, got
34.83-10.81
37.1241.16
51.45-1.73
53.26:12.43
PEDHERO-GIAN
35.11+1.11
37.25+0.85
52.18-3.63
52.544.2.29
FRoHERO+GAug FEDHERO
36.65++1.33
37.63+1.00
52.44=2.67
54.57+22.42
37.83+1.02
38.00+0.92
52.65+1.33
55.63-12.00
4.5 FedHERO with Various Sharing Mechanisms
We conduct an analysis of various FEDHERO variants involving the sharing of different. components of the local model, including all model parameters, task model parameters, and none (denoted as FEDHEROar FEDHERO, gen; and FEDHERO, none: respectively). Additionally, we consider whether to incorporate a structure-task model decoupled scheme. For variants without the Dual- Channel (DC), we remove the GNN in the Slocat channel and feed the learned adjacency matrix and the original matrix into the same GNN.
gen;
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Table 5: Performance of FEDHERO when sharing different modules with server.
Squirrel
Chameleon
Variants
DC
METIS M=7
Louvain
METIS M-7
Louvain
FEDHERO, Home
32.53=0.66
36.85=0.85
48.48=1.12
48.30+1.50
FEDHERO,g
29.37+1.18
32.84+0..2
44.09+-2.84
44.12++1.98
FEDHERO, home
34.14=1.335
36.25+2.96
50.62=1.54
52.03::1.70
FEDHERO all
32.04+1577
34.08=2.14
45.38=1.64
46.39+3.03
FEDHERO gon FEDHERO
28.05-+0.65
31.13+1.57
1..27
43.70+1..8
37.83+1.00
38.00=1.92
52.65:11.33
55.63=2.00
In Table we observe that the structure-task model decoupling schome consistently outperforms the model without it, indicating that independently learning the struct knowledge enhances FEDHERO's perfor- mance across various scenarios. Furthermore, sharing all parameters or the task model results performance degradation compared to pure local training. This observation underscores that sharing local task model information across heterophily graphs harms FEDHERO's performance, since the original graphs have dif- ferent node neighbor distribution patterns and aggregating of models that capture distinct tendencies would lead to performance degradation for the global model.
4.6 Convergence Analysis
We conduct experiments to compare the convergence speed of FEDHERO with other FGL baselines on differ- ent datasets. The results, as presented in Figure demonstrate that FEDHERO exhibits faster convergence compared to most basclines that of FEDSTAR, since both two methods employ a dual-channel GNN in the client's model. We conclude that FEDHERO does not require more steps to converge compared to existing methods, though it introduces additional parameters, which underscores the efficiency of FEDHERO.
both datasets. Notably, FEDHERO's convergence speed is comparable to
Local
FedPub
GCFL
FedSage
FedSage
Fedtvgg
FedPab
FedAvg
FedSar
FedLit
FeaHERO
Better
Clasification Ave un Chancioo
LIA Accuracy an Actor
50
Better
35-
Toat 88
40
20
30
30-
15
40
20
20-
10
Better
Rerter
25
35
150
200
200
11A Accuracy on Chameleon
Classfication, Age on Squirrel
Training Round
Training Round
Figure 5: (Left. Link inference attack (LIA) accu- racies on FEDHERO and FGL baseline methods. (Right) Performance of FEDHERO and FGL base- line methods on noisy graph datasets.
Figure 4: Convergence analysis of FEDHERO and basclines on (left) Squirrel and (right) Chamelcon datasets.
4.7 Empirical Privacy Preservation Evidence in FedHERO
FEDHERO only transmits the components in the fylobal channel to the server. This subset contains fewer parameters, thus reducing the volume of sensitive information transmitted. We provide empirical privacy evidence by evaluating resistance to link inference altacks (LIA) (Gong & Liu (018)) that infer the underlying graph structure from the learned node representations. The LIA attack accuracies on two datasets are presented Figure 5 (left)). In general, LIA struggles accurately predict the graph structure due to the inherent heterophilic characteristies of the graphs. We can observe that FEDHERO offers better privacy protection compared to the FGL baseline approaches by sharing only portion of the model, and make I.IA
11

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even harder to predict. We leave the certified guarantees (e.g., differential privacy guarantees) and other empirical attack evaluations (egg, membership inference) for future work.
4.8 Robustness Study of FedHERO
We assess the robustness of FEDHERO by introducing noise to the graph, flipping each edge with a proba- bility of 0.1. As shown in Figure 5 (right), while baseline FGL methods experience significant performance degradation under such conditions, FEDHERO maintains its effectiveness. This resilience is due to FED- HERO's unique design: unlike other FGI. methods that rely heavily on the original graph structure, FRD- HERO shares a global structure learner and performs message passing on a generated latent graph. This approach reduces the impact of noise on the original graph's 's structure, enhancing FEDHERO's adaptability to noisy environments. Additionally, FEDHERO exhibits reduced reliance on the local graph structure, demonstrating its ability to address the performance deterioration brought by varying neighbor distribution patterns and effectively handle heterophilic graphs.
5
Related Work
Graph Structure Learning. Graph Neural Networks (GNNs) have emerged a potent tool for analyzing
graph-structured data and have found wide applications in various domains (Zhao et al. 2021a; Wu et al.
2019
Kipf & Welling, 2016
Zhu ct al. 2019 Liu ct al., 2020 Fan ct al. 2019 Luan et al.,
2022 Yuan et al.
2022
Dwivedi et al., 2023 Shlomi et al.] 2020 Wang et al. 2024). In order to overcome the limitations of
GNNs in effectively propagating features within observed structures, recent efforts have aimed at simultane-
ous learning of graph structures alongside the GNN model (Jin et al.] 2020 Liu et al.] 2022b Li ct al.) 2024
Liu et al.
2023b Wu et al. 2022). At the heart of graph structure learning lies an encoding function respon-
sible for modeling optimal graph structures, often represented by edge weights (Luo et al., 2021 Kreuzer
et al. 2021 Sun et al. 2022 Wang et al.) 2020 Gasteiger et al. 2019 Yu et al. 2021). These edge weights can be defined through pairwise distances or Icarnable parameters. For example, GAUGM (Zhao et al.
2021bb calculates edge weights by taking the inner product of node embeddings, introducing no additional parameters. Franceschi et al. (2019) treat each edge as a Bernoulli random variable and optimize graph structures with the GNN. IDGL (Chen et al. (220),, to make full use of information from observed struc- tures for structure learning, employs a multi-head self-attention network to represent pairwise relationships between nodes, while Li et al. (L. et al., 2018a) adopt a metric learning approach based on the Radial Basis Function (RBF) kernel for a similar goal. Moreover, DGM (azi al. 2022 utilizes the Cumbel-Top- trick to sample edges from Gaussian distribution and incorporates reinforcement learning, rewarding edges that contribute to correct classifications and penalizing those leading to misclassifications. Additionally, Zhang ctt al. (2019) present a probabílistic framework that views the input graph as a random sample from a col- lection modeled by a parametric random graph model. However, while these methods have shown promise, they assume that training and testing nodes originate from the same graph, and they primarily consider a single graph. In contrast, Zhao et al. (2023) address graph structure learning in a cross-graph setting and propose a comprehensive framework for learning shared structure learner that can generalize to target graphs without necessitating re-training.
Federated Graph Learning. Federated Learning (FL) is a paradigm that facilitates model training across
decentralized clients while safeguarding privacy (Li et al. 2020 Liu et al. 2024 Gafni et al. 2022 Wang
et al.
2023 Ye et al.
2023 Lei et al. 2023). As the field of FI. evolves, a new specialized branch has
emerged to address the unique challenges of graph data, known as Federated Graph Learning (FGL) Liu
et al.
2022a
Fu et al. 2024b). This branch can be categorized into graph-level and node-level methods Fu
et al. 2024a
Graph-level FGL methods consider scenarios where each client possesses multiple graph data, as seen in domains like molecular structures. Like traditional FL, it mainly focuses on the issue of non-independent and identically distribution (non-IID) issues across clients (Xie et al. 2021 He et al.) 2021 Tan et al.) 2023) Zheng et al., 2021 Chen et al.] 2221aa Fu et al. (025). On the other hand, nodo-level FGL assumes that each client holds a single graph, with the objective of addressing node classification tasks. In this variant, each client usually possesses a subgraph of the larger graph, introducing a scenario where there are missing links
12

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between subgraphs. To address this issue, Zhang et al. introduced FEDSAGE (Zhang et al. 2021 which involves collaboratively learning missing neighbor generator across clients. However, FEDS AGE could raise privacy concerns. In contrast, [Bakk et al. (2023) utilize random graphs as inputs to compute similarities between clients' GNNss subsoquently employing these similaritics for weighted averaging on the server side. Additionally, Xie et al. (2023) focus on detecting latent link-types during FGL and differentiating message- passing through various types of links using multiple convolution channels. In this study, we address a specific challenge in node-level FGL, namely the distinction in node neighbor distributions across clients, Our approach involves sharing structure learning model among clients, enabling the learning of message- paassagggsssingggg patterns across the graphs. By leveraging this information, we aim to enhance the predictive performance of the local models.
6 Conclusion
The heterophilic patterns of graphs can result in variations in the distribution of node neighbors among different graphs, leading to performance deterioration for current FGL algorithms. The FEDHERO frame- work effectively addresses the challenge of varying neighbor distribution patterns, resolving it by sharing structure learners across clients. The structure learner would generate latent graphs with similar tendencies for different clients. Clients' GNNs that capture these tendencies could be aggregated and shared among clients to harness FGL's ability. By decoupling the structural learning model from the local classification model, effectively capture and make available structural insights for global sharing. Additionally, proposed framework mainlains the capacity for personalization based on local graph structure and node features, Experimental results affirm that FEDHERO consistently surpasses state-of-the-an methods across various datasots.
Acknowledgments
This work was supported in part by the National Science Foundation (NSF) under grants 2313110, 2143559, IIS 2006844, IIS-2144209, 2S2222376,, CNS-2154962, BCS- 2228542, and CMMI-2411248; the Office of Naval Resoarch (ONR) under grant N0001 4241136; and the Commonwealth Cyber Initiative (CCT) under grant VV-1Q24-011.
13

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A Experiment Setups
In our experiments, we utilize seven distinct benchmark datasets, the specifics of which are outlined in Table 6 This table provides detailed statistics for each dataset, including the number of nodes, edges, classes, and node feature dimensions. Additionally, we describe the process of partitioning the original graphs into multiple subgraphs to create semi-synthetic federated graph learning datasets.
For graph partitioning, employ well-established algorithms commonly used in federated graph learning. Specifically, we utilize the METIS algorithm (Karypis & Kumar 1997) and the Louvain algorithm (Blondel ct al. 2008 With METIS, we ensure an even distribution of nodes across subsets, with each subset representing a client's data in a federated learning context. Using Louvain, we follow the methodology of Back et al. 2023) and (Zhang et al. 2021). We initially partition the graph and select subgraphs containing a minimum of 50 nodes. The smaller subgraphs are then randomly merged into these larger ones to guarantee adequate training data. For example, if Louvain results in 20 subgraphs but only have over 50 nodes, we consolidate the remaining 15 subgraphs into these 5, effectively simulating federated learning scenario with clients.
We further provide the description of real-world datasets. The syn-cora dataset Zhuu el al. 2020 generates nodes and edges based on the expected homophily ratio within the graph, with feature vectors of nodes in each class derived by sampling from the corresponding class in the Cora datasct (Yang et al.) 2016). The ieco-frand dataset comprises transaction records for products, with edges determined by the proximity of transaction occurrences. The objective is predict fraudulent transactions (Howard et al. 2019). Meanwhile, the credit dataset has 30,000 nodes, each representing an individual, and their connections are determined by the similarity of their spending and payment patterns @Ych & Lien 2009 The objective is to predict whether individual will default on their credit card payment or not.
Table 6: Dataset statistics
Dataset Squirrel
Chamelcon
Actor
Flickr
syn-cora
ieco-fraud
credit
Nodes
5,201
2,277
7,600
89,250
14,900
144,233
30,000
Edges
198,493
31,421
15,009
899,756
29,674
28,053,7U
1,436,858
Features 2,089
2,235
932
500
1433
371
13
Classes
5
2
We follow the previous work (Mao et al., 2023) to compute the homophily ratios of both the original graphs and the averaged homophily ratios of partitioned graphs. As in Table 7 the partitioned graphs exhibit comparable homophily ratios when compared to the original graphs. It means that the partitioning process does not compromise the heterophilic property of the graphs.
Table 7: Homophily ratio of different partitioning methods.
Dataset
Squirrel
Chamelcon
Actor
Flickr
METIS
0.22-10.02
0.26::0.05 0.2740.06 0.25
0.17+0.02 0.1940.04
0.33-10.04
Louvain
0.21
0.32+0.04
Origin 0.22
0.22
0.32
B Neighbor node distributions of clients in two datasets
In this section, we also give an example in two real-world datascts: Squirrel and Chamelcon (Rozemberzzki et al. 2021). In these datasets, nodes correspond lo web pages, and edges represent hyperlinks between them. To simulate the FL scenario, we apply the community detection algorithm METIS (Karypis & Kumar 1997) to partition these graphs, and variations in the structures of the resulting subgraphs also arisc. As illustrated in Figure 0 we compare the neighbor distributions of two clients in two datasets, respectively. (The neighbor distributions across all clients refer to Figure 7 Each bar illustrates, for specific class of nodes, the
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Squirrel
Chameleon
50%
70%
Ratio of connectios
Client
Ratio of connectios
Client
Client
Client 2
50%-
30%
30%
10%
10%
5-5
5-1
5-2
5-3
5-4
1-1
1-2
1-3
1-4
1-5
(a) connections of class nodes
(b) connections of class nodes
Figure 6: Neighbor node distributions of two clients in two datasets respectively. Each bar represents the ratio of edges connecting nodes of one class to the total mumber of edges with nodes of that class as an endpoint. For example, in Figure (a), the orange bar at '5-1' indicates the proportion of edges from class 5 class 1 nodes relative to total edges originating from class 5 nodes in client
ratio of edges connecting them to other types of nodes of one type to the total number of edges serving this class node as an endpoint. For instance, in Figure G (a), the orange bar with the x-axis '5-1' signifies the proportion of edges linking class 5 nodes to class 1 nodes in relation to the overall number of edges originating from class nodes. The results indicate distinct neighbor distributions among different clients. For instance, in the Chameleon dataset, almost 70% of edges originating from class nodes are intra-class connections in client 1, implying class nodes tend to establish hyperlinks with similar web pages. Conversely, less than 10% of the neighbors of class 1 nodes nodes in the same class in client 2, indicating preference for establishing hyperlinks with diverse web pages. To safeguard data privacy, the structural details of subgraphs cannot be directly shared between clients. Consequently, this leads to distinct message- passing patterns of information transfer between these subgraphs. Traditional FL methods like FEDAVG (McMahan et al. 2017) simply aggregate GNN models, potentially hindering the global model's ability to account for the aggregation discrepancies among various subgraphs effectively.
Client
Client
Client
Client
Client
0.5
Ratio of connectos
0.3
0.1
s 5
5 4
5.
4
(a) Neighbor distribution of class 5 nodes Squirrel
Client
Client
Client 3
Client
Client
0.7
Ratio of connectios
0.5
0.1
シランン
(b) Neighbor distribution of class nodes Chameloon
Figure 7: Neighbor node distributions of clients in two datasets split by METIS.
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C
Case study
In this section, we present a series of case studies designed to further illustrate the practical applications and effectiveness of FEDHERO under diverse conditions. These case studies encompass range of scenarios, each highlighting different aspects of our approach.
C.1 Overlapping subgraphs scenario
Despite the commonality of the non-overlapping node assumption, some research investigates scenarios with overlapping nodes. We have followed the data partitioning approach from (Baek et al. 2023 in our exper- iments, focusing on the Flickr and Actor datasets. The results, as illustrated in Table S show FEDHERO consistently outperforming most baselines across these datasets. This indicates its robust capability to man- age overlapping scenarios effectively. We theorize that overlapping subgraphs provide client subgraphs with additional connections, hinting at the potential for developing FL algorithus specifically designed to cater overlapping environments.
Table 8: Results on the overlapping subgraphs scenario.
Method
LOCAL
AVD
FEDPUB
FEDSTAR
GCFL
FEDLIT
FEDSACE
FEDIIERO
Flickr
55.00:2.22
55.3440.69 32.30
55.92=0.42 55.50:t0.31 28.67:10.99
56.47:0.21
56.64=0.50
56. 0..70-0.42
56.74:10.30
Actor
32.46-+0338
27.98=0.77
42.48+1.23
42.50=0.66
41.57=0.89
43.46::1.11
C.2 Latent graph generation
In graph structure learning, there are various methods for generating latent graphs. In our ap- proach, we define ر(z as the learned edge weight between nodes u and v, and subsequently ap- ply post-processing step form ANN graph (where each node is connected to up k neighbors) as the latent graph. This choice is informed by the differentiability of the top k function, which aids in calculating parameter gradients and updating the model in FEDHERO. We also examine the influence of another preva- lent latent graph generation method (Wu et al.) 2020a; Elinas et al. 2020 Zhao et al.) 2023). This method treats cach edge in the latent graph as a Bernoulli random variable, resulting edge distri- butions represented by a product of N N indepen- dent Bernoulli variables.
Squirrel
Chameleon
42
58
Acc
40
56
38
54
52
Table 9 presents analysis of FEDHERO's per- formance when employing the Bernoulli sampling method for latent graph generation during infer- ence. Using ā(t,)) as a Bernoulli parameter in- troduces greater variance, potentially leading to less stable model performance. Despite this, FED- HERO still surpasses most baselines, as evidenced by the comparative results in Table 3 Our experi- ments also suggest that an asymmetric latent graph may impact model performance. Investigating op- timal strategies for utilizing the Bernoulli sampling method in latent graph generation offers promis- ing direction for future research and development in our work.
50
50
Actor
Flickr
36
52
35
Acc
34
51
33
50
50
k 50
k
Figure 8: The sensitivity study of hyperparameter k. The star point in the figure corresponds to the default result reported in the main text.
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Table 9: Results on the different latent graph generation.
Squirrel
Chameleon
Datasets
METIS M-7
Louvain
METIS M-7
Louvain
Bernoulli
33.62+1.81 36.08 0.87
36.97=4.43 38.00+00.22
48.82+3.52 55.63+ 52.65+1.33
51.59+2.99
top k
To assess the impact of the node degree k in the latent graph, we conducted tests with h: set to 5, 10, 20, and 50. Generally, a larger value results in a denser latent graph. The outcomes of these tests are illustrated in Figure [ When these findings are combined with the baseline methods' performance from Table 2 in the main paper, we can deduce the following:
Across varying values of k FEDHERO consistently outperforms all the baseline methods.
For datasets with smaller average node degree, such Actor and Flickr, selecting relatively smaller & value is advantageous. Conversely, for datasets with larger average node degree, like Squirrel and Chameleon, opting for a larger & value is preferable.
These insights provide valuable guidance for choosing appropriate & values based on the characteristics of the dataset, thereby optimizing the performance of FEDHERO.
C.3
Federated graph learning baselines
We provide detailed explanations of the federated graph learning basclines employed in our experiments. These include:
GCFL Xie et al. 2021j: It incorporates a gradient sequence-basee based clustering mechanism using dynamic time warping. This mechanism enables multiple data owners with non-lID structured graphs and diverse features collaboratively train robust graph ncural networks.
FEDSTAR (Tan et al, 2023): ; It relies on structural embeddings and feature-structure decou- pled graph neural network lo address non-IID data challenges through shared structural knowledge. Within the FL framework, it exclusively exchanges the structure encoder. This allows clients to collectively learn global structural knowledge while maintaining personalized learning of node rep- resentations based on their features.
FEDLIT (Xie et al. 2023): It lackles the variability in link characteristios within graphs, where ostensibly uniform links may convey varying degrees of similarity or significance. dynamically identifies latent link types through an EM-basod clustoring algorithm during federated learning and adapts message-passingg strategies using multiple convolution channels tailored to different link types.
FEDPUB (Baek et al. 2023): It leverages functional embeddings of the local GNNs with random graphs as inputs to calculate similarities between them. These similarities are then employed for weighted averaging during server-side aggregation. Additionally, the method learns personalizod sparse mask at each client, allowing for the selection and update of only the subset of aggregated parameters relevant. to the specific subgraph.
FEDSAGe ZZhang et al. 2021): introduces NeighGen, an innovative missing neighbor generator integrated with federated training procodures. This endeavor geared towards achieving a universal node classification model within distributed subgraph framework, eliminating the need for direct data sharing.
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Squirrel
Chamclcon
Squirrel
Chamelcon
40
40-
59
58
Acc
56
Acc
56
54
52
50
0.1 0.2 0.4
0.1
0.2 0.3 0.5
0.0
0.2 0.4
0.1
0.2
0.4 0.5
Actor
Flickr
Actor
Flickr
51
Acc
52
32
50
30
48
48
0.0
0.1
0.2
0.3
0.4
0.5
0.0
0.1
0.2
0.3
0.4 0.5
0.0
0.1 0.2
0.3
0.4
0.5
0.0
0.1
0.2
0.3
0.4
0.5
À
À
M
(a) Sensitivity study of
(b) Sensitivity study of
Squirrel
Chameleon
Squirrel
Chamelcon
38
57
58
55
Acc
56
34
53
36
54
51
32
34
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
2
8
10
2
8
10
Actor
Flickr
Actor
Flickr
36
51
36
34-
Acc
50
Acc
52
32
49
32-
51
48
30-
30
0.4
0.2
0.6
2
8
10
2
8
10
NH
NH
(c) Sensitivity study of a
(d) Sensitivity study of NE
Figure 9: Performance FEDHERO with different hyperparameter settings. The star point in the figure corresponds to the default result reported in the main text.
Influence of Hyperparameters in FedHERO
D.1 Hyperparameter Settings.
The architecture of the GNN models consists of feature projection layer, two graph convolutional layers, and classifier layer. We employ Adam optimizer (Kingma & Ba 2014 with a learning rate of 0.005. We apply consistent hyperparameter setting in our main results. Specifically, we set a = 0.2, X 0.1, k = 20, and NH = 4. The training process involves 200 communication rounds, with each local training epoch lasting ittraaioon The nodes are randomly distributed into five groups. For each experiment, one group chosen as the test set, while the remaining groups are utilized for training and validation. We perform five experiments on each dataset and report the modcls' average performance. For the ieco-frand and credit. datasets, we present the mean test Area Under the Curve (AUC), accounting for the imbalanced labels. For the remaining datasets,
mean test accuracy across clients for evaluation.
In an idcal scenario, a grid scarch for hyperparameter optimization would be conducted to determine the optimal combination for each set of experiments. It's noleworthy that our experimental results consistently demonstrate the superior performance of FEDHERO compared to all baseline methods, even without hy- perparameter tuning. Additionally, we conducted an investigation into the impact of these hyperparameters under the Louvain data partitioning method to provide recommended values for these aggregation and smoothing hyperparameters and their potential impact. The results illustrated in Figure g
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Chameleon
Squirrel
Method
Time (s)
GPU | (MB)
Time (s)
GPU (MB)
FEDLIT
35.74
899.16
69.31
3994.69
FEDSTAR
10.87
663.10 10
20.17
1020.89
FEDHERO
11.62
601.76
20.83
948.50
Table 10: Average wall-clock training time and peak GPU memory (lower is better) under the Louvain split for 200 rounds on single RTX A6000.
D.2 Influence of Smoothing Hyperparameters and μ
No distinct trend related to the intrinsic nature of the data was observed for À and However, it is noteworthy that removing regularization on structures (i.e., setting À or to 0) resulted in more pronounced performance degradation. In fact, the regularization loss plays a constructive role in offering guidance for structure learning, as highlighted prior work (Zhao et al. 2023 Conversely, increasing À or l a certain value proved beneficial in enhancing the performance of FEDHERO. However, further increases had negalive impact the model's focus on the classification task, leading to decline in performance.
D.3 Influence of Aggregation Hyperparameters
For the Squirrel, Chameleon, and Actor datasets, optimal results were observed at a = 0.2, while a = 0.4 exhibited the best performance for the Flickr dataset, as illustrated in Figure [cc. This variation in optimal a values is attributed to the homophily ratios of the datasots. According Mao al. (2023) and Kim & Oh ),022,, the homophily ratios for Squirrel, Chameleon, and Actor 0.22, 0.25, and 0.22, respectively. In contrast, Flickr has higher homophily ratio of 0.32. Given Flickr's relatively elevated homophily ratio, employing a larger to increase the proportion of local models proves beneficial, effectively leveraging the structural information within the subgraph. Conversely, for datasets with lower homophily ratios, superior performance achieved by placing more emphasis on the homophily properties introduced by the global structure learner. In summary, we posit that, for graph data with a larger homophily ratio (indicating lower heterophily), higher values of a can be advantageous.
D.4 Influence of the Number of Heads Nи
Figure [d), we investigate FEDHERO's performance under varying values of Nu. We observe that increas- ing Nи up to a certain point enhances FEDHEROOs performance. This improvement can be attributed to the aggregation of multi-hoad results, bolstering the model's ability to capture underlying influences between nodes from diverse perspectives.
However, beyond certain threshold, further increases in No do not yield additional performance improve- ments. This phenomenon could be attributed to factors such the saturation of connections between nodes, potential overfitting concerns, and the increased time and computing resources required with larger N
E Practical Scalability: Runtime and Memory
In this section, we complement the memory and running time analysis (Table 2 wall-clock training time and peak GPU memory-on Chameleon and Squirrel under the Louvain split for 200 communication rounds, using single NVIDIA RTX A6000. Each configuration is repeated five times, and we report the average cost.
with practical metrics-
From Table 10 we can observe that FEDHERO matches FEDSTAR in runtime (within 3 7%) while using less memory on both datasets (9% lower on Chameleon; 7% lower on Squirrel). Compared to FEDLIT FEDHERO is 67-70% faster and reduces memory by 33% (Chameleon) and 76% (Squirrel). These empirical results align with the analysis in Table indicating that FEDHERO comparable with FGL baselines and scales well in practice.
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F Comparative Analysis with FedStar
In this section, we compare FEDHERO with FEDSTAR. Both decouple learning into a feature channel and a structure-fouused channel to mitigate feature heterogeneity. FEDHERO, however, targets the harder heterophily regime ShereFEDSTARR static structure embeddings fail and adds (i) a learnable latent-graph generator and (ii) per-layer dual-channel integration, as explained below:
Problem setting. FEDSTAR addresses cross-domain FGL under feature heterogeneity. In contrast, FEDHERO formally studies heterophily in FGL for the first time, where neighbor label distributions can be divergent or contradictory; under strong heterophily, FEDSTAR's assumptions break and its performance degrades.
Structure information embedding. FEDSTAR uses static, hand-crafted structural embeddings (degree, RWSE) without modifying the adjacency. FEDHERO learns task-aligned latent graph via multi-head attention metric, dynamically reconstructing edges to suppress misleading cross-class links and enable robust cross-client aggregation.
Channel interaction. FEDSTAR'S structure-to-fettt teatuuu flow is essentially one-way. FEDHERO performs per-layer dual-channel integration between global (latent) and local (original) channels, stabilizing training and balancing global alignment with local bias.
Empirical evidence. On strongly heterophilic datasets (homophily S 0.25), FEDHERO sig- nificantly outperforms FEDSTAR. On syn-cora, where degree distributions are identical across classes Zhu et al. (2020), FEDHERO achieves ~20% accuracy gain: static degree/ RRWSE fea- tures cannot distinguish nodes with similar degrees but different label contexts, whereas the learned latent graph can.
In summary, while both methods separate global and local channels, FEDHERO's focus on heterophily, dynamic structure learning, and layer-wise dual-channel integration are substantive advances that drive its superior performance heterophilic graphs in federated settings.
27


Reviews:
[{"review_id": "Zwas32aHPO", "reviewer": "Reviewer_mXFF", "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. The proposed dual-channel design balances global knowledge sharing with local personalization.\n2. Empirical results show consistent gains in accuracy and demonstrate robustness to noise.\n\n\nWeaknesses:\n\n1. The idea of splitting a model into a global channel and a local channel is already present in FedStar (Tan et al., 2023) and other personalized FL frameworks. The authors do not convincingly argue what is fundamentally new here, apart from incorporating a structure learner.\n\n\n2. The proposed structure learner (multi-head attention similarity + kNN) appears to be a straightforward adaptation of IDGL (Chen et al., 2020) to a federated context. The paper offers limited substantial theoretical or algorithmic innovation in graph structure learning.\n\n3. The experiments are not sufficiently convincing. While they motivate heterophily as a problem, the specific setting (different levels of heterophily across clients) is not strongly supported by real federated heterophilic graph datasets—most are synthetic partitions of existing graphs. Specifically, the “heterophilic” setting is largely created via METIS/Louvain partitioning of homophilic graphs, which may not faithfully represent truly heterogeneous-client scenarios in real FGL. Moreover, only a few small “real” datasets are used (e.g., ieee-fraud, credit). These are not compelling for GNN-specific claims.\n\n4. The hyperparameter settings are overly simplistic. For example, the authors use the same constant learning rate across different settings.\n\n5. The privacy argument is neither quantitative nor convincing. The authors merely claim that the proposed method could provide stricter privacy protection, but this is not supported by formal privacy analysis. Typically, to claim improved privacy, one should use empirical privacy attack evaluations (e.g., membership inference attacks) or formal theoretical tools such as differential privacy. Even though sharing only part of the model may yield some privacy benefits, a quantitative assessment of the privacy of the proposed algorithm is essential for a research paper. Without such analysis, privacy should not be presented as a key selling point.", "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 FedHERO, a federated graph learning framework designed to handle heterophilic graphs, where connected nodes often have different labels. FedHERO employs a dual-channel GNN: the global channel uses a shared structure learner to generate latent graphs that capture universal structural patterns across clients, while the local channel operates on each client’s original graph to retain personalized information. Experiments are conducted on both semi-synthetic and real-world datasets.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "1. Please provide a clearer and more compelling explanation of the fundamental novelty in your proposed dual-channel design compared to FedStar (Tan et al., 2023) and other personalized FL frameworks. In particular, clarify why the incorporation of a structure learner represents a substantive innovation rather than an incremental adaptation.\n\n\n2. The proposed structure learner appears to be a direct adaptation of IDGL (Chen et al., 2020) to a federated setting. We recommend that you either (a) introduce non-trivial theoretical or algorithmic improvements, or (b) provide a rigorous analysis explaining why this adaptation is both challenging and significant in the context of federated learning.\n\n\n3. Please provide stronger empirical evidence that the heterophily setting in your experiments faithfully reflects real-world federated heterophilic graph scenarios. Consider incorporating additional real-world heterogeneous-client datasets beyond ieee-fraud and credit, ideally with varying and quantified heterophily levels. If synthetic partitions are used, please include a detailed justification of how these partitions reflect realistic data distributions. For reference, here are examples of benchmark datasets in federated learning: [A], [B] (other benchmarks may also be suitable for the revision).\n[A] https://arxiv.org/abs/2007.13518\n[B] https://arxiv.org/abs/2104.07145\n\n\n4. Please avoid using the same constant learning rate and other fixed hyperparameters across all experiments without justification. We suggest including more detailed hyperparameter tuning methods, such as grid search. At a minimum, include sensitivity analyses to demonstrate how different hyperparameter settings influence model performance, particularly in heterogeneous and noisy environments.\n\n\n5. Since privacy protection is a key claimed advantage, please support this claim with formal methods (e.g., differential privacy guarantees) or empirical attack evaluations (e.g., membership inference, attribute inference). Clearly quantify the privacy benefits of sharing only partial model components. If such analyses cannot be provided, the privacy-related claims should be substantially downplayed.", "broader_impact_concerns": "This work has the potential for broader impact, which is not currently discussed in the paper.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "hn22voaTyt", "reviewer": "Reviewer_hcAc", "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- Relevant and Well-Defined Problem: The paper successfully identifies and formulates a practical and important problem in FGL. The assumption that client graphs are homophilic is often violated in real-world scenarios, and addressing the challenge of varying neighbor distributions across clients is a valuable contribution to the field. \n- Novel Dual-Channel Architecture: The proposed FedHERO architecture is an intuitive and clever solution. The decoupling of the model into a shared global channel that learns from a generated, more uniform latent graph and a private local channel that retains client-specific information is an effective design for balancing generalization and personalization. \n- Thorough Experimental Evaluation: The empirical validation is comprehensive. The authors use a variety of datasets with different characteristics, employ multiple graph partitioning methods, and compare FedHERO against a strong and relevant set of recent FGL baselines. The inclusion of extensive ablation studies on sharing mechanisms, structure learning methods, and hyperparameters further strengthens the paper's claims. \n\n\n**Weaknesses**\n- Incremental Novelty Over Baselines: The proposed method has considerable conceptual overlap with the FedStar baseline, particularly the idea of decoupling the GNN and sharing only a structure-focused component.  Although the paper includes a direct comparison, the novelty of FedHERO can be seen as more incremental than transformative, which slightly diminishes the paper's impact.", "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 addresses challenge in Federated Graph Learning (FGL) where the performance of Graph Neural Network (GNN) models deteriorates when clients' local graphs exhibit varying degrees of heterophily. The authors propose FedHERO to handle this issue. FedHERO proposes a dual-channel GNN architecture for each client. A global channel operates on a latent graph generated by a shared structure learner, aiming to capture universally applicable patterns that can be aggregated across clients. A separate local channel operates on the original client graph to learn personalized, client-specific patterns. The authors conduct extensive experiments on several semi-synthetic and real-world datasets, demonstrating that FedHERO generally outperforms existing FGL baselines, particularly on graphs with high heterophily.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "I would recommend acceptance of this paper without necessary changes.", "broader_impact_concerns": "N/A", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "U2yn4OW2YG", "reviewer": "Reviewer_7zGn", "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. Authors performs comprehensive experiments across four real-world graph datasets and three synthetic datasets. The results demonstrate that FedHERO consistently outperforms existing FGL alternatives significantly.\n2. FedHERO introduces a dual-channel GNN: a global channel whose parameters are aggregated across clients, and a local channel kept private. By letting the global channel operate on a shared latent graph while the local channel works on the original graph, the design simultaneously extracts universally useful message-passing patterns and preserves client-specific nuances without forcing them into the aggregation.\n\nWeaknesses：\n\n1. The dual-channel “feature + structure” split and the idea of aggregating only the structure branch already appear in FedStar; the authors themselves devote Appendix E to explaining the overlap. The remaining differences (heterophily framing, attention-based metric) feel incremental. As a result, the novelty of FedHero relative to FedStar and other dual-channel FGL frameworks remains unclear. Furthermore, the authors does not articulate a technical difference big enough to justify “first to tackle heterophily in FGL”.\n\n2. Equation (4) defines the latent-edge selector as a binary top-k function and claims this design is “based on the differentiability of the top-k function” ﻿. In reality, top-k is non-differentiable; practical graph-structure-learning papers resort to continuous relaxations. The paper supplies neither a surrogate nor a gradient derivation, creating doubts about whether the reported implementation matches the description.\n\n3. The main text explicitly “assumes no overlapping nodes are shared across data owners” ﻿, but Appendix C evaluates an “overlapping subgraphs scenario” with no algorithmic change except re-running the code ﻿. This raises two issues: the stated assumptions are violated, and it is unclear why FedHERO should work under overlap if its aggregation analysis relies on disjoint subgraphs. A rigorous exposition should either drop the assumption or adapt the method/analysis.\n\n4. Table 2 only lists Big-O complexities and argues FedHERO’s dual-channel cost is “comparable” ﻿, yet no wall-clock time, GPU memory, or transmitted-bytes measurements are reported. For a federated system, such metrics are central; omitting them weakens the argument that the method scales to large client fleets.\n\n5. Symbols such as H, Z, and “UPD/AGG” sometimes change meaning between Sections 3.1 and 3.3. Explicitly list dimensions at first use, and adopt a single bold/italic style for matrices and vectors.", "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": "The paper proposes FedHERO, a federated graph learning framework for node classification in settings where clients possess heterophilic graphs. Unlike conventional federated graph learning (FGL) approaches that rely on homophily assumptions and suffer performance degradation under varying neighbor-label patterns, FedHERO employs a dual-channel GNN architecture for each client. The global channel processes a latent graph generated by a shared structure learner, while the local channel operates on the client’s original graph. By only aggregating and sharing global-channel weights, FedHERO enables collaborative learning of transferable message-passing patterns across clients while retaining graph-specific information locally. Experimental results show that FedHERO consistently outperforms existing methods across diverse datasets.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "1. The dual-channel “feature + structure” split and the idea of aggregating only the structure branch already appear in FedStar; the authors themselves devote Appendix E to explaining the overlap. The remaining differences (heterophily framing, attention-based metric) feel incremental. As a result, the novelty of FedHero relative to FedStar and other dual-channel FGL frameworks remains unclear. Furthermore, the authors does not articulate a technical difference big enough to justify “first to tackle heterophily in FGL”.\n\n2. Equation (4) defines the latent-edge selector as a binary top-k function and claims this design is “based on the differentiability of the top-k function” ﻿. In reality, top-k is non-differentiable; practical graph-structure-learning papers resort to continuous relaxations. The paper supplies neither a surrogate nor a gradient derivation, creating doubts about whether the reported implementation matches the description.\n\n3. The main text explicitly “assumes no overlapping nodes are shared across data owners” ﻿, but Appendix C evaluates an “overlapping subgraphs scenario” with no algorithmic change except re-running the code ﻿. This raises two issues: the stated assumptions are violated, and it is unclear why FedHERO should work under overlap if its aggregation analysis relies on disjoint subgraphs. A rigorous exposition should either drop the assumption or adapt the method/analysis.\n\n4. Table 2 only lists Big-O complexities and argues FedHERO’s dual-channel cost is “comparable” ﻿, yet no wall-clock time, GPU memory, or transmitted-bytes measurements are reported. For a federated system, such metrics are central; omitting them weakens the argument that the method scales to large client fleets.\n\n5. Symbols such as H, Z, and “UPD/AGG” sometimes change meaning between Sections 3.1 and 3.3. Explicitly list dimensions at first use, and adopt a single bold/italic style for matrices and vectors.", "broader_impact_concerns": "NA", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Decision: Accept (poster)