MOTION: Multi-Sculpt Evolutionary Coarsening for Federated Continual Graph Learning
Authors: Guancheng Wan
Fengyuan Ran
Ruikang Zhang
Wenke Huang
Xuankun Rong
Guibin Zhang
Yuxin Wu
Bo Du
Mang Ye
Venue: NeurIPS 2025 poster ()
Keywords: Federated Learning
Graph Learning
Continual Learning
Primary area: social_and_economic_aspects_of_machine_learning

Abstract: Graph neural networks (GNNs) have achieved remarkable success in various domains but typically rely on centralized, static graphs, which limits their applicability in distributed, evolving environments. To address this limitation, we define the task of Federated Continual Graph Learning (FCGL), a paradigm for incremental learning on dynamic graphs distributed across decentralized clients. Existing methods, however, neither preserve graph topology during task transitions nor mitigate parameter conflicts in server‐side aggregation. To overcome these challenges, we introduce **MOTION**, a generalizable FCGL framework that integrates two complementary modules: the Graph Topology‐preserving Multi‐Sculpt Coarsening (G‐TMSC) module, which maintains the structural integrity of past graphs through a multi‐expert, similarity‐guided fusion process, and the Graph‐Aware Evolving Parameter Adaptive Engine (G‐EPAE) module, which refines global model updates by leveraging a topology‐sensitive compatibility matrix. Extensive experiments on real‐world datasets show that our approach improves average accuracy (AA) by an average of 30\% $\uparrow$ over the FedAvg baseline across five datasets while maintaining a negative $\downarrow$ average forgetting (AF) rate, significantly enhancing generalization and robustness under FCGL settings. The code is available for anonymous access at https://anonymous.4open.science/r/MOTION.

MOTION: Multi-Sculpt Evolutionary Coarsening for Federated Continual Graph Learning
Guancheng Wan't, Fengyuan Ran Ruikang Zhang Wenke Huang', Xuankun Rong', Guibin Zhang", Yuxin Wu', Bo Du Mang Ye Wuhan University TTongii University RReminn University of China {guanchengwan, yemang)@vhu.edu.. edu.cn
Abstract
Graph neural networks (GNNs) have achieved remarkable success in various do- mains but typically rely on centralized, static graphs, which limits their applicability in distributed, evolving environments. To address this limitation, we define the task of Federated Continual Graph Learning (FCGL), a paradigm for incremen- tal learning on dynamic graphs distributed across decentralized clients. Existing methods, however, neither preserve graph topology during task transitions nor mitigate parameter conflicts in server-side aggregation. To overcome these chal- lenges, we introduce MOTION, a generalizable FCGL framework that integrates two complementary modules: the Graph Topology presserviig Multi-Seuu Multi-Sculpt Coarsening (G-TMSC) module, which maintains the structural integrity of past graphs through multi-expert, similarity-gen gutided fusion process, and the Graph-Aware Evolving Parameter Adaptive Engine (G-EPAE) module, which refines global model updates by leveraging topology-sensitivy compatibility matrix. Extensive experiments on real-world datasets show that our approach improves average accuracy (AA) by an average of 30% over the FedAvg baseline across five datasets while maintaining a negative + average forgetting (AF) rate, significantly enhancing generalization and robustness under FCGL settings. The code is available for anonymous access at htttts://ggthtiie httphuu..oooooaooooaaaoaooooeooe /ttp///aanneengg////OOOOO
1 Introduction
Graph neural networks (GNNs) 27 65
provide a powerful framework for exploiting relational information in graph-structured data for various learning tasks. Their ability model complex interdependencies between entities has driven notable progress in domains such as recommendation systems 44, social network analysis 45 and digital marketing optimization [19]. However, existing
graph learning methods [72] 63 (68] assume centralized data storage, where a single institution collects and manages the evolving graph, which often fails in real-world scenarios. To address these limitations, researchers have integrated federated learning frameworks with GNNs to develop FGL enables efficient learning on distributed graph data and supports knowledge extraction across decentralized sources.
Federated Graph Learning (FGL) 14
40 52
Graph-structured data in modern systems is inherently dynamic, with continuously adding nodes and Moreover, storing or accessing exten- sive historical node profiles and topologies is impractical due to client-side storage limits, edge device constraints, and limited database resources. These constraints prevent edge devices from maintaining complete history of the evolving graph. Consequently, graph models must incrementally incorporate
edges reflecting changing structures and behaviors [1 25 69
"Coffrst authors with equal contributions. Author order was determined alphabetically, with each author reserving the right listed first. Corresponding authors.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

---

new classes into growing graph distributed across decentralized clients. We refer to this process as Federated Continual Graph Learning (FCGL), which addresses storage and edge device limita- tions. Existing FGL methods 7 62 assume shared graph data across clients, and current continual
75 focus on static or locally evolving graphs within a single client. The core difficulty unique to FCGL lies in the interplay between local CL limitations and federated aggregation challenges, amplified by client heterogeneity in both data and temporal evolution. Therefore, we define the FCGL task as constructing global model that generalizes ef- fectively to distributed graphs in an incremental learning framework. A key research question emerges:
graph learning (CGL.) approaches 70
How can we design an FGL. framework tailored for continuously evolving streaming data?
Existing CGL methods mainly address node- or class- incremental scenarios 669
74 13] and often
struggle to preserve the inherent graph topology [ 67 [5]] that is, the structural properties of each local graph such as node centrality and subgraph patterns. In addition, methods such as memory 9 must work under the constraint that clients only have partial and changing graph views with limited resources. As a result, preserving topological integrity, namely the consistent maintenance of these structural properties across tasks during continual updates, remains difficult. This difficulty arises because similarity metrics [48] 57) or criteria [26] 3 computed locally often fail capture important global relational patterns. This limitation raises a critical question: 1) How can we effectively preserve the topological information of previous tasks under FCL constraints?
replay 77 58 42 parameter regularization 30 g 57
In the FGL setting, client-specific updates re- flect heterogeneous objectives and graph struc- tures (34 76 60), which can lead to conflict ing parameter updates during aggregation. Stan- dard averaging strategies (36) may dilute task- specific knowledge and destabilize the global model, reducing its ability to accommodate new tasks without forgetting previous ones. Al- though several advanced aggregation methods, such as clustered FL 43), attentive aggrega- tion (23), and weight regularization [.. have been proposed mitigate client heterogeneity, they still fail to resolve the fundamental issue of update conflicts when task distributions or graph structures diverge substantially [22) 20). This observation leads to a second question: II) How can we capture and leverage correla- tions between the existing parameters of the global model and the client-updated param- eters when learning new tasks?
Local Update
Task T-1
Global Aggregation
heterogeneity
a
Task To
predict
Aggregation
Forgetting!!
Conflict!!!
Figure I: Problem Illustration. We describe the chal- lenges FCGL encounters. Local updates cause catas- trophic forgetting, while global aggregation ereates pa- rameter conflicts.
To address these challenges, we present the first comprehensive study of FCGL. We propose the Multi- Sculpp Ex ExOuTTONyryy Coarsening (MOTION) framework for FCGL.. To address Problem [J] we develop Graph Topology-preserving Multi-Sculpt Coarsening (G-TMSC). This method mitigates forgetting by preserving the key topological structures of previous task graphs. Inspired by a multi- expert paradigm, we introduce scoring mechanism that computes node similarity and importance to guide the coarsening process. This mechanism enhances both feature and topology replay, allowing clients to retain critical information from earlier tasks. On the server side, to address Problem [I] propose the Graph-Aware Evolving Parameter Adaptive Engine (G-EPAE). Each client generates topology-senan sensitive parameter increments that reflect local graph evolution. The server constructs graph compatibility matrix to measure the alignment between these increments and the global model across parameter dimensions. Aggregation rates then adjusted dynamically so that increments with high compatibility receive greater weight to capture essential patterns while those with low compatibility down-weighted to reduce conflicts. All adjusted increments are integrated into the global model without fine-tuning dynamically. This approach achieves balanced evolution that adapts new structures while preserving historical knowledge securely.
Our principal contributions are summarized as follows:

---

Problem Identification. We formally characterize the main challenges in FCGL: maintaining graph-topological integrity and preserving tusk-relevant information during CL, while avoiding conflicts in knowledge transfer to ensure robust global generalization.
Practical Solution. We design client-side G-TMSC guided by learned similarity scores to merge new and historical subgraphs, and we develop server-side G-EPAE that dynamically adjusts aggregation weights to reduce interference and improve coherence.
Experimental Validation. We conduct comprehensive experiments multiple benchmark graph datasets to demonstrate that MOTION outperforms existing methods under FCGL settings.
2 Preliminaries
2.1 Notations
Continual Learning. CL involves updating a model sequentially on a series of tasks, where each task introduces new information while requiring the retention of knowledge from previous tasks, The primary objective is to mitigate catastrophic forgetting, in which the model's performance on earlier tasks deteriorates as learns new ones. Formally, the model encounter sequence task-specific datasets D, (X,, Y.), where X, denotes the input data and Y, the corresponding labels for task The model parameters 0 are updated by balancing the acquisition of new information with the preservation of prior knowledge. This trade-off can be expressed as:
Pioul (0) P(())) +R(()),
(1)
where Po) represents the update term for task t, R(0) serves as a regularization term that preserves knowledge from previously learned tasks, and the hyperparameter À modulates the trade-off between learning new tasks and reducing catastrophic forgetting.
In practice, only the data from the current task Dr is accessible during training. Therefore, the objective at step T is formulated as:
(T) - (0) + ATR(())
which highlights the central challenge in CL. namely achieving high performance the current task while preserving knowledge acquired from earlier tasks through regularization.
Problem Formulation. In the FCGL. framework, a central server coordinates distributed learning across K clients, denoted C = [CI..... CK). Each client C₁ maintains an evolving graph G = (Vg (V) for task t, with adjacency matrix Af. Each node U; Vi has an associated feature vector 2.. and label k.,. The goal is learn new tasks incrementally while preserving prior knowledge to ensure the stability of the global model. To this end, each client l trains local model Fog with parameters og and periodically transmits its updates to the central server. The global model parameters & are optimized by minimizing the weighted sum of local losses:
K
No. N
min
L)()),
where N₁ = -VV the number of nodes in the graph of client k at task N, >k= Nt is the total number of nodes across all clients at task t, and (d) denotes the expected loss over G under the global model parameters c. FCGL unifies FCL and CGL by enabling incremental task learning and knowledge preservation while protecting data privacy through distributed model aggregation.
2.2 Motivation
This paper systematically examines the challenges of maximizing the generalization performance of the global model in FCGL. Traditional FCL and CGL methods, such as Experience Replay (75 and Gradient Episodic Memory 333, were designed for image-based tasks and do not deliver comparable performance graph-structured data. These methods suffer from three main shortcomings. First,
they cannot effectively capture graph topological information [56] 32 54 Second, they require
excessive storage [58 (5) for node replay buffers. Third, they introduce severe parameter conflicts
3

---

during aggregation, as heterogeneous local updates push the global model in divergent directions [55 53 49). By relying on simple empirical node replay, these methods ignore the structural relationships that encode critical topological patterns. This increases misalignment between client and server, destabilizes training, and accelerates catastrophic forgetting. As shown in Figure [ nodes exhibit substantial heterogeneity in connectivity patterns and neighborhood distributions. Therefore, local training in FCGL must minimize storage requirements while preserving graph topology and node information to support incremental learning without loss of prior knowledge. We formalize this objective as:
(0% M arg min
Σ Bu (Fog (z), + X Lrea (0%s Gk Gh:t1t) s.t.
|M S
B, (4)
61 ME
where l the per-sample classification loss, Leet enforces new-task learning and forgetting, and B bounds each client's replay memory capacity.
replay, balances
After local training effectively mitigates knowledge forgetting, we subsequently integrate client- trained parameters into the global model F' during the server-side aggregation phase, ensuring a conflict-free aggregation process that faithfully preserves the knowledge previously acquired:
K
Σ Eggwey (T(F(())) Foz (i+))
arg mii
(5)
where Re produces replay samples for client k, and (::)) measures the discrepancy between global and local model outputs. This approach ensures retention of previously accumulated knowledge.
Based on these objectives, we therefore comprehensively outline the systematically derived key design principles for generalizable FCGL pipeline:
Generalizable FCGL Design Principles: Storage Efficiency: preserve critical topological structures and key node information while reducing memory requirements; Knowledge Re- tention: track changes graph topology and node information across tasks without losing previously learned knowledge; Knowledge Integration: aggregate client updates into the global model with minimal conflicts to ensure effective knowledge transfer and mitigate forgetting.
In the subsequent sections, we describe how our approach effectively implements these design principles. Specifically, we minimize client-side storage, prevent catastrophic knowledge loss, and seamlessly integrate updates into the global model with reduced parameter conflicts.
3 Methodology
3.1 Framework Overview
In this section, we briefly present an overview of our framework. On the client side, we apply G-TMSC to accurately preserve the critical topological structures from previous task graphs. G-TMSC uses a expei- scoring mechanism to estimate node similarity precisely and guide structural fusion. On the server side, we employ G-EPAE to mitigate confficts in the task space during aggregation. G-EPAE adjusts parameter aggregation rates dynamically based on graph compatibility matrix that measures the alignment between client updates and the global model. Moreover, diagrammatic representation of the framework provided in Figure 2
3.2 Graph
Multi-Sculpt Coarsening (G-TMSC)
Dynamic Graph Merging. To integrate graph data across successive tasks, we introduce Dynamic Graph Merging, which constructs progressively evolving knowledge graph. For client k at task t, let G = (V2 EE) ) be the local graph. Each node E VV is assigned a unique global identifier by fusing its semantic feature 2f with the task identifier task;;
2 Fuse( k.1 lask;);
66
where Fuse(.) denotes a task-aware embedding fusion module. All global identifiers are stored in centralized node mapping table Ig to ensure consistent entity referencing across tasks. To prevent

---

Graph Topology-preservingg Multi Multi-Sculpt Coorsening 4+
Graph Aware Evolving Parameter
Adaptive Engine
Merged Graph
Ingut Gruph
Task
Task
Dynamic Merging
hhop
Nada Factures
Con cimilarity
Global
Task
Task
Brash
Coarsening
Expert- 1
Companibllit
Magnittua
Companent
Matrix
Companent
Expert-k
Coorsened
Graph
Muliti- Expert
Figure 2: Architecture illustration of MOTION. (a) The left part shows the Graph Sculpt Coarseing (G-TMSC) on the client side. (b) The right part presents Graph-Aware Evolving Parameter Adaptive Engine (G-EPAE) on the server side.
identity drift across tasks, maintain two mappings: many-to-one mapping M -ecarse-voriginal from merged to original nodes, and a one-to-one mapping Morigiual--coarse for traceability. This dual mapping supports dynamic node aggregation while preserving entity fidelity.
At initialization (t = 1), we construct a base graph using the node and edge mappings of G For each subsequent task &. = 2..... T, we apply an incremental merging strategy: unseen nodes vy & Io are identified by global hashing and assigned embeddings ě,. This selective update avoids exponential growth in computation from naive accumulation of all previous graphs and improves scalability. Thus, each client k refines its evolving graph G capturing long-range dependencies via coarsening and mapping, and progressively unifies knowledge across tasks.
For edges Fi. we transform the local adjacency matrix A into unified matrix A defined by - (1. 1,, if (u;, U2) E E and Us By E Ic.
(t, = (0 otherwise,
which preserves structural integrity while reducing redundant computation overhead. Therefore, task-specific representations are continuously integrated with explicit preservation of graph topology and node semantics, ensuring historical knowledge retention and new information assimilation.
Multi-Sculpt Coarsening. Sculpting in graph coarsening refers to the precise selective removal of non-essential or peripheral elements to preserve the fundamental core structural integrity of graph. Inspired by the Mixture-of-Experts (MoE) paradigm, our approach employs a collaborative multi-expert framework in which each expert specifically applies distinct evaluation criterion, such as topological centrality, local substructure decomposition, and semantic similarity. By integrating these expert assessments, the Multi-Sculpp Coarsening framework systematically prunes extraneous redundant nodes and suppresses noise, thereby significantly reducing storage and computational demands while preserving semantic fidelity and essential graph properties.
First, we compute diverse set of topological features for each node. Degree centrality quantifies immediate connectivity: Degree(u;) = Engev; (i,jj, while betweenness centrality identifies
all.4 (6,9) The clustering coefficient further measures community
critical bridges: BC(v:) = Enfight
compactness via C(v)) = k, (I where (:(k.)) is the number of triangles through v; and k; =
2T.(h.()
Degree(v;). Additionally, global metrics such eigenvector centrality and closeness centrality
further enrich the feature set. To model diffusion, we apply PageRank:
1-d d
PR(v;)
PR(1;) = No
+ d Σ
(8)
Dogreo(v,))
5

---

with damping factor d and neighborhood (w:).. We also derive degree- based heterogeneity and community index to capture neighborhood diversity and cohesion.
For fine-grained analysis, we decompose the graph into 1-hop and 2-hop subgraphs. We compute the average degree kaub Vautal EveV.... ky and measure subgraph diameter D Subgraph clustering coefficients and densities further characterize community cohesiveness. comprehensively represent each node, we introduce position-awan degree embedding scheme employing multi-frequency sinusoidal encodings to capture structural variations:
sin (c/1000000)//)) k even.
PF (d) (ccosdd11000)) (c0000//0000///))) k odd,
where d the node degree and F the embedding dimension.
In our proposed framework, the similarity assessment module employs statistical metrics. Maximum mean discrepancy (MMD) detects distributional shifts:
MMD*(XX,)) = Σ ((x,) Σ p(1))
(10)
while Mahalanobis distance identifies statistical outliers via (x)( v(x 1) TE nt) We subsequently compute Pearson correlation and cosine similarity metric via CosSim v) T vll to capture both functional and semantic alignments.
a.y
Based these features, implement multi-expert decision mechanism where each expert specializes in a distinct feature domain. Employing a sparse activation strategy selects the top-K K experts dynamically, and introduces controlled random noise perturbation along with the coefficient of variation squared CV² = Sor to ensure balanced and equitable expert utilization. Subsequently, we aggregate experts' normalized importance scores to prioritize nodes for preservation, then map removed nodes to their semantically closest preserved counterparts minimize information loss.
To merge features in the coarsened graph, we apply simple yet robust arithmetic averaging at both the raw feature and respective latent representation levels:
Tmerged
Ti.
Danerged
h;s
(11)
n
ensuring unbiased aggregation and retention of semantic and structural integrity.
Finally, we introduce reservoir sampling-based dynamic memory mechanism that blends selected nodes from historical tasks with new samples. This mechanism mitigates gradient shocks, stabilizes convergence, and enhances robustness by regulating the mixing ratio between past and new nodes.
3.3 Graph-Aware Evolving Parameter Adaptive Engine (G-EPAE)
Graph Compatibility Matrix. Upon completion of local training, each client & E transmits its sensiiv-ee parameter increment: A = 0* - Φb where & denotes the current global parameters of F This increment implicitly captures structural changes in the local graph G = (V. Fi)), since GNN parameter updates reflect variations in the adjacency matrix A through neighborhood aggregation.
updated parameters 6 to the central server. The server then computes
To integrate these heterogeneous updates, we introduce a graph compatibility matrix M; E ddd that quantifies the alignment between local and global update dynamics. Unlike traditional aggregation methods (e.g., FedAvg), which weight updates solely by data volume, our matrix incorporates both directional consistency and relative magnitude of each client's 's update:
M
A@
A
(12)
where denotes the Hadamard product. The directional component is obtained by L2 normalization:
A@k
A@k L
(13)
AA
1

---

which isolates the update direction from its scale. The magnitude component is defined as:
|| 12
A maR
(14)
Ejec | 1
providing a normalized importance score that emphasizes clients with larger topological contributions.
By incorporating Mg into the aggregation process, we enable topology-awas and contribution- sensitive update mechanism. The directional component A dir ensures that the global model aligns more closely with structurally consistent client updates, which reduces the cancellation effect caused by conflicting update directions. At the same time, the magnitude component A0th maag emphasizes clients whose updates reflect more substantial topological shifts their local graphs. The Hadamard combination then produces compatibility matrix that softly reweights each update. This conflict- aware integration retains essential task-specific knowledge and improves global model stability.
Elastic Regulation Fusion. Building on compatibility-guider aggregation principle, we introduce an elastic regulation fusion mechanism to further enhance both adaptability and long-term stability in global model synchronization for FCGL. This mechanism applies a dynamic gating function g (M&) to appropriately scale aggregation weights nonlinearly:
(xp( M& T,
0
1 MR.
otherwise,
(15)
where т is the compatibility threshold, E (0, is linear decay factor, and dr regulates the contribution of each local update A to the global model. To suppress instability from incompatible updates, we introduce an adaptive regularization term:
R()) / A| 1|2
Add ( M2 <T)
(16)
which selectively truncates gradients of poor compatibility parameters. The global model is then updated by integrating the filtered and scaled local updates:
K
Ao
ag Agh
(17)
This update enables Fg to assimilate emerging structural patterns from clients while preserving representations learned previous tasks. From mathematical perspective, the fusion strategy performs adaptive filtering in parameter space: tensor level aggregation is jointly governed by directional alignment via normalized updates A and compatibility driven scaling ag,, allowing fine-graine fine-grained, client specific fusion across both parameter dimensions and client axes.
The proposed method offers two primary benefits in FCGL, First, it enhances the responsiveness of the model to dynamic topological changes through M4-guided integration. Second, it ensures minimal conflict during parameter evolution across tasks. These benefits collectively enable robust and scalable continual learning in dynamic graph environments.
4 Experiment
In this section, we comprehensively evaluate MOTION through four axes: Q1 (Superiority), Q2 (Resilience), Q3 (Effectivenesss, Q4 (Sensitivity).
4.1 Experimental Setup
Datasets.
To effectively evaluate the performance of our approach, employed five benchmark graph datasets of various scales and distributions, including Cora [35], CiteSeer [16], PubMed [5].
Amazon-Photo, and Coauthor-CS 44 Detailed descriptions and dataset splits are provided in
Appendix C.I Moreover, implementation details and parameter settings are given in Appendix C.6
Counterparts. We compare MOTION against the following representative baselines covering classical
FL. FGL., FCL, and CGL methods: (1) FedAvg [ASTATS17] (36) (2) FedDe (CVPR22) [15), (3)
FedDyn [ICLR21] 2. (4) FedSSL [ICCA124] (1). (5)
[50] (6) FedTTp
[ICML.24) 4 (7)SEA-ER [CoLLAs224]
and (8) FedPowde [NeurIPS24] Detailed
descriptions are provided in Appendix C.2
7

---

Table 1: Comparison with the state-of-the-art methods five node-classffication Average Accuracy (AA) (%) and Average Forgetting (AF) (%) for our downstream tasks. Green indicate improvements over the FedAvg baseline, while red denote performance declines. Meanwhile, denotes an increase in the value, whereas & denotes decrease. The best and second results are highlighted with bold and underline, respectively.
datasets. We report
Cooa
CheeSeer
PubMed
Photo
Counther
Cussgory
Methods
AA
AF
.AA
AFF
it
AF J
AA1
AF
A.A
AF
FadAvg [ASTATSI7]
23.57
96.90
10.07
00.01
33.33
30.42
18.45
54.74
12.15
65.78
PedDe (OVPI22)
25.0
2..12puu
y0,00
18
42.22,2232
10742
FedDyn ([CLR21]
18.00 66
71.00 9177
13:00
67,82
26.0
36.32
8.19 (me
FedSSL [[CAI144]
20.14
15.50
20.4
20,340011
20.08
12.30 rou00
9.70
7:28
14.77am
FGL
FolSSP [NcurPPS34]
95.76- 3.
96.00 24400
-8ppsss
88.4
11.66ecee
10.22,
PedTpp (ICML24)
15.88
27.07
10.02-55
3.00
29.70
28.22 2633
12.15
58 20:000
SEA ER (CoLLAs224)
2005
69 17
$1.38
47 m:
S0770-22
13:2.11.0
48.90
48
6.98
82,02
PCL
FedPowde [Pe44PP524
19005
102
00.57
50.80
10.30
64.00
FOGL
NOTTOM
62.00
88.3 9.54 oin
49
(8
78 no 50 yon 15 24.177
00
22 26
-11 62
4.2 Superiority
To address Q1, we analyze the superior performance of MOTION on node classification across multiple real-world graph datasets. The overall Average Accuracy (AA1) and Average Forgetting (AF() results
summarized in Table Here, AA + Eド= "T AF + プーー
maxie(L..... (t.j (T
where 7 is the total number of tasks and 04,j is the performance of the global model on task j after training on task i. From these experiments, we derive three key observations.
Obs. MOTION consistently achieves the highest accuracy on all evaluated datasets, demonstrating notably higher AA and negative AF values. Negative AF indicates not only preservation but also reinforcement of prior knowledge. On Amazon-Photo, MOTION outperforms the second-best baseline, FedTPP, by 48.34 48.34% in AA and yields negative AF, highlighting its strong capabilities for knowledge consolidation and conffict mitígation. The G-TMSC module preserves critical topological patterns, and the G-EPAE module reduces parameter conflicts between clients and server. Together, these components enable MOTION to capture fine- fine-grained structural knowledge across heterogeneous tasks.
Obs. @ Traditional FL and FGL methods tend to overfit the current task, which leads to catastrophic forgetting and prevents clients from retaining prior knowledge. Moreover, the server encounters significant difficulty in resolving parameter confficts, resulting in substantial performance degradation.
Obs. 0 Both FCL and CGL approaches struggle under the FCGL paradigm. CGL methods cannot resolve server-side parameter conflicts, and FCL techniques fail to capture essential topological structures. Among the baselines, FedTPP and FedPowde deliver the next-best AA; however, FedTPP still exhibits high AF due to aggregation-induced conflicts, and FedPowde's weaker structural modeling leads to lower AA and increased forgetting. Consequently, neither method supports efficient, continuous knowledge sharing across heterogeneous clients.
4.3 Resilience
To address Q2, we evaluate MOTION on the Cora and CiteSeer datasets. We vary the Dirichlet concentration parameter a from to 9 to control data heterogeneity and assess performance with 2 to clients. Figure 3 shows that MOTION achieves robust gains across all client scales and a values. On CiteSeer, MOTION outperforms FedAvg by an average of 29.1 % and exceeds the strongest competing baseline by at least 18.1 %. These findings confirm that MOTION adapts effectively to diverse FCGL. scenarios and maintains stable performance under severe client heterogeneity.
8

---

sgha
sigha
alpho
apha
0.6
0:1
0.5
0:4
0.0
apha
alpha algha
alpha
alpha
alpha alpna
aipha
alara
alona
algna
aloha
aggha
aigha
algra.
dlhha
ran (tertpo)
FAPT
Nan, Diertswd
PAP 2 TUP (RORtSH FUPE clorse
(a) Analysis on Cora
(b) Analysis on CiteSeer
Figure 3: Resilience study of hyperparameters Reduction Rate and Experts Selected with datasets for further analysis.
including Cora and CiteSeer. Please refer to Sec.
(b) Detailed data display
4.45
Cora
CiteSoer
Method
40
AAA
A.F
AAA
AF
w/o Mul. Ex.
56.62
-5.69
40.58
18.27
Para.-Al
2.16
20
w/o Gra--Co
25.43
24.18
27.54
18.49
Mil-Ex
Wio Para -Vl
wib Goa--oo
NOTION
(a) Figure of effective study
MOTION
64.57
-8.87
48.45
-0.15
Figure 4: Effectiveness study of G-TMSC and G-EPAE on Cora and CiteSeer. For an in-depth study, Sec.
4.4 Effectiveness
To address Q3, conduct ablation study evaluate the contributions of key components on both client and server sides. In Figure 4 we first isolate the effects of the Graph-Coarsening mechanism (w/o Gra.CCo.) and the Multi-Expert strategy (w/o Mul.-Ex.). Removing the Graph- Coarsening mechanism alone causes a significant performance decrease, and further exclusion of the Multi-Expert strategy amplifies this decline. These results demonstrate that both components are crucial for capturing diverse structural patterns and mitigating knowledge forgetting. We then assess the Parameter-Ae Alligmment mechanism (w/o Para.-Al.) within the G-EPAE module. Its absence intensifies server parameter conflicts and increases update drift, confirming its essential role in harmonizing model updates and enabling continuous knowledge accumulation during FCGL.
4.5 Sensitivity
To investigate hyperparameter sensitivity for Q4, we conduct a systematic study on MOTION. As shown in Figure we examine two key parameters: the graph reduction rate and the number of selected experts s. We vary from I to 0.9 in increments of 0.2 and adjust from 2 to 10 in steps of The results show that model performance varies modestly across this parameter range, indicating strong robustness. On Cora, AA and AF exhibit variances of 0.49 and 1.84, respectively. On CiteSeer, the variances are 0.70 for AA and 0.44 for AF. balance compression and information retention, we set r-0.5 and = 3, which promotes effective multi-expert collaboration while minimizing storage.
0.6
0.4
super (eleCAcii)
0.6
ropart cepttdndded
5
3.4
0.0
0.2
iupert selecrcci
0.4
0.2
eelecedd
-0.2
sceni intecven1
0.3
0.5
0.1
0.7
0.1
0.5 Recurtion Rate
0.5
0.5
Redurtion Babe
Recurtion Rate
Reduction Baca
Analysis CiteSeer Figure 5: Sensitivity Study of hyperparameters Reduction Rate and Experts Selected. Please refer to Sec. 4.5 for further analysis.
(a) Analysis on Cora

---

5 Conclusion
In this paper, we propose MOTION, a unified FCGL framework that simultaneously preserves historical graph structures and mitigates aggregation conflicts in decentralized, evolving environments. On the client side, our G-TMSC module integrates multiple structural metrics through multi-sculpt scheme inspired by MOE, in which each expert applies a distinct evaluation criterion and the results are fused via similarity-guiderr merging. On the server side, our G-EPAE module adjusts aggregation weights based on sopology-sensitvv compatibility matrix to align heterogeneous client updates while maintaining task-specific knowledge. Extensive experiments on five real world graph benchmarks demonstrate that MOTION consistently outperforms state-of-thh-ar baselines in both generalization performance and robustness catastrophic forgetting. Comprehensive empirical evaluations across diverse datasets validate the robustness and efficacy of MOTION.
Acknowledgement
This work is supported by National Natural Science Foundation of China under Grant (62361 166629, 62225113, 623B2080), the Major Project of Science and Technology Innovation of Hubei Province (2024BCA003, 2025BEA002), and the Innovative Research Group Project of Hubei Province under Grants 2024AFA017. The supercomputing system the Supercomputing Center of Wuhan University supported the numerical calculations in this paper.
References
[1] D. Acar, Y. Zhao, R. Navarro, M. Mattina, Whatmough, and V. Saligrama. Federated learning based on dynamic regularization. In International Conference on Learning Representations (ICLR), 2021.
[2] D. A. E. Acar, Y. Zhao, R. Matas, M. Mattina, Whatmough, and V. Saligrama. Federated learning based on dynamic regularization, In ICLR, 2021.
[3] K. Ahrabian, Y. Xu, Y. Zhang, J. Wu, Y. Wang, and M. Coates. Structure aware experience replay for incremental learning in graph-based recommender systems. In Proceedings the 30th ACM International Conference on Information & Knowledge Management, pages 2832-2836. 2021.
[4] X. Cai, C. Huang, L. Xia, and X. Ren. Lightgel: Simple yet effective graph contrastive learning for recommendation. arXiv preprint arXiv:2302.0819), 2023.
[5] K. Canese and S. Weis. Pubmed: the bibliographic database. The NCBI handbook, 2(1), 2013.
[6] A. Carta, A. Cossu, F. Errica, and D. Bacciu. Catastrophic forgetting in deep graph networks:
an introductory benchmark for graph elassification. arXiv preprint arXiv:2103. /750, 2021.
[7] F. Chen, P. Li, T. Miyazaki, and C. Wu. Fedgraph: Federated graph learning with intelligent sampling. IEEE Transactions on Parallel and Distributed Systems, 3375):177--1786, 2021.
[8] X. Chen, J. Wang. and K. Xie. Trafficstream: streaming traffic flow forecasting framework based on graph neural networks and continual learning. arXiv preprint arXiv:2106.06277 2021.
[9] D. Daza, M. Cochez, and P. Groth. Inductive entity representations from text via link prediction. In Proceedings of the Web Conference 2021, pages 198-808, 2021.
[10] J. Dong, L. Wang, Z. Fang, G. Sun, S. Xu, X. Wang, and Q. Zhu. Federated class-incremental learning. In Proceedings of the IEEE/CVF conference computer vision and pattern recogni- tion, pages 10164-10173, 2022.
[11] M. Du, S. Wu, Q. Wang, D. Chen, P. Jiang, and A. Mohaisen. Graphshield: Dynamic large graphs for secure queries with forward privacy. IEEE Transactions on Knowledge and Data Engineering, 34(7):3295-3308, 2020.
[12) G. Febrinanto, F. Xia, K. Moore, C. Thapa, and C. Aggarwal. Graph lifelong learning: survey, IEEE Computational Intelligence Magazine, 18(1):32-51, 2023.
10

---

[13] Y. Feng, H. You, Z. Zhang. R. Ji, and Y. Gao. Hypergraph neural networks. In Proceedings of the AAAI conference on artificial intelligence, volume 33, pages
2019.
[14] X. Fu, B. Zhang, Y. Dong, C. Chen, and J. Li. Federated graph machine learning: survey of concepts, techniques, and applications. arXiv preprini arXiv:2207.11812, 2022.
[15] L. Gao, H. Fu, L. Li, Y. Chen, M. Xu, and C.-Z. Xu. Fedde: Federated learning with non-iid data via local drift decoupling and correction. In CVPR, 2022.
[16] C. L. Giles, K. D. Bollacker, and S. Lawrence. Citeseer: An automatic citation indexing system. In Proceedings of the third ACM conference Digital libraries, pages 89-98, 1998.
[17] S. M. Hendryx. D. R. KC, B. Walls, and C. T. Morrison. Federated reconnaissance: Efficient, distributed, class- flass-incemmenal learning. arXiv preprint arXiv:2109.00155, 2021.
[18] K. Hu, M. Lu, Y. Li, S. Gong, J. Wu, F. Zhou, S. Jiang, and Y. Yang. A federated incremental learning algorithm based on dual attention mechanism. Applied Sciences, 12(19): 2022.
[19] W. Hu, M. Fey, M. Zitnik, Y. Dong, H. Ren, B. Liu, M. Catasta, and J. Leskovec. Open graph 2020.
benchmark: Datasets for machine learning on graphs. NeurlPS,
[20] W. Huang, G. Wan, M. Ye, and B. Du. Federated graph semantic and structural learning. In Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence, pages 33338888, 2023.
[21] W. Huang, G. Wan, M. Ye, and B. Du. Federated graph semantic and structural learning. arXiv preprint arXiv:2406.1888 18937, 2024.
[22] W. Huang, M. Ye, Z. Shi, and B. Du Generalizable heterogeneous federated cross-correlation and instance similarity learning. 2023.
[23] Y. Ji, X. Chen, Y. Wang, T. Yang, M. Xu, D. Jin, and Y. L. Wang. Learning private aggregation for federated learning via attentive message passing. In Proceedings of the 39th International Conference on Machine Learning (ICML), 2022.
[24] W. Jiang, X. Li, and J. Zhang. Graph continual learning: Challenges and benchmarks. In Proceedings of the 38th International Conference on Machine Learning (ICMI), 2021.
[25] W. Ju, S. Yi, Y. Wang, Z. Xiao, Z. Mao, H. Li, Y. Gu, Y. Qin, N. Yin, S. Wang, et al. A survey of graph neural networks in real world: Imbalance, noise, privacy and ood challenges. arXiv preprint 240::2403.04468,, 2024.
[26] S. Kim, S. Yun, and J. Kang. Dygrain: An incremental learning framework for dynamic graphs. In IJCAI, pages 3157-3163, 2022.
[27] T. N. Kipf and M. Welling. Semi-supervised classification with graph convolutional networks. In ICLR, 2017.
[28] X. Li, K. Huang, W. Yang, S. Wang, and Z. Zhang. On the convergence of fedavg on non-iid data. arXiv preprint arXiv:1907.00 1907.02189 2019.
[29] X. Li, Y. Zhu, B. Pang, G. Yan. Y. Yan, Z. Li, Z. Wu, W. Zhang, R.H.. Li, and G. Wang. OpenFGL: A Comprehensive Benchmarks for Federated Graph Learning, Aug. 2024. arXiv:2408. 16288 [cs].
[30] H. Liu, Y. Yang, and X. Wang. Overcoming catastrophic forgetting in graph neural networks.
In Proceedings of the AAAI conference on artificial intelligence, volume 35, pages 2021.
[31] R. Liu, P. Xing, Z. Deng, A. Li, C. Guan, and H. Yu. Federated graph neural networks: Overview, techniques, and challenges. IEEE transactions on neural networks and learning systems, 2024.
[32] Z. Liu, G. Wan, B. A. Prakash, M. S. Lau, and W. Jin. A review of graph neural networks in epidemic modeling. In Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pages 6577-6587, 2024.

---

[33] D. Lopez-Paz and M. Ranzato. Gradient episodic memory for continual learning, Advances in neural information processing systems. 30, 2017.
[34] Y. Luopan, R. Han, Q. Zhang, C. H. Liu, G. Wang, and L. Y. Chen. Fedknow: Federated continual learning with signature task knowledge integration at edge. In 2023 JEEE 39th International Conference on Data Engineering (ICDE), pages 341-354. IEEE, 2023.
[35] A. K. McCallum, K. Nigam, J. Rennie, and K. Seymore. Automating the construction of internet portals with machine learning. Information Retrieval, 3:127-163, 2000.
[36] B. McMahan, E. Moore, D. Ramage, S. Hampson, and B. A. Arcas. Communication--effciinn learning of deep networks from decentralized data. In Proceedings of the 20th International Conference on Artificial Intelligence and Statistics (AISTATS), 2017.
[37] S. Mehta and A. Aneja. Securing data privacy in machine learning: The fedavg of federated learning approach. In 2024 4th Asian Conference on Innovation in Technology (ASIANCON), pages 1-5. IEFE, 2024.
[38] C. Niu, G. Pang, L. Chen, and B. Liu. Replay-and-forget- free graph class ilass-incremental learning: task profiling and prompting approach. arXiv preprint arXiv:2410. 10341,, 2024.
[39] R. Pan, F. Zhou, and C. Cao. Graphreplay: Memory-efficient rehearsal for continual graph learning. In Proceedings of the 3 International Joint Conference on Artificial Intelligence (IJCAI), 2022.
[40] Y. Pei, R. Mao, Y. Liu, C. Chen, S. Xu, Qiang, and B. E. Tech. Decentralized federated graph neural networks. In International Workshop on Federated and Transfer Learning for Data Sparsity and Confidentiality in Conjunction with IJCAI, 2021.
[41] H. Piao, Y. Wu, D. Wu, and Y. Wei. Federated continual learning via prompt-based dual knowledge transfer. In Forty-first International Conference on Machine Learning, 2024.
[42] A. Rakaraddi, L. Siew Kei, M. Pratama, and M. De Carvalho. Reinforced continual learning for graphs. In Proceedings of the 31 ACM International Conference on Information & Knowledge Managemeni, pages 1666-1674, 2022.
[43] F. Sattler, K.-R. Müller, and W. Samek. Clustered federated learning: Model-agnostic distributed multitask optimization under privacy constraints. In IEEE Transactions on Neural Networks and Learning Systems, 2020.
[44] O. Shchur, M. Mumme, A. Bojchevski, and S. Günnemann. Pitfalls of graph neural network evaluation. arXiv preprint arXiv:1811.0588 2018.
[45] Shirzadian, B. Antony, A. G. Gattani, N. Tasnina, and L. S. Heath. time evolving online social network generation algorithm. 13(1):2395.
[46] N. Shoham, T. Avidor, A. Keren, N. Israel, D. Benditkis, L. Mor-Yosef, Yosef, and I. Zeitak. Over- coming forgetting in federated learning on non-iid data. arXiv preprint arXiv: 191.00797, 2019.
[47] S. D. Zou, and C. Wu. On the limitation and experience replay for gnns in continual learning. In CoLLAs, 2024.
[48] Su, D. Zou, Z. Zhang, and C. Wu. Towards robust graph incremental learning on evolving graphs. In International Conference on Machine Learning, pages 32728-32748 PMLR, 2023.
[49] Z. Tan, G. Wan, W. Huang, and M. Ye. Fedssp: Federated graph learning with spectral knowl- edge and personalized preference. In Thirty-eighth Annual Conference on Neural Information Processing Systems, 2024.
[50] Z. Tan, G. Wan, W. Huang, and M. Ye. Fedssp: Federated graph learning with spectral knowledge and personalized preference, 2024.
[51] Z. Tian, D. Zhang, and H.-N. Dai. Continual learning on graphs: survey. arXiv preprint 240.02240..03330, 2024.
12

---

[52] A. Usmanova, F. Portet, P. Lalanda, and G. Vega. A distillation- based approach integrating con- tinual learning and federated learning for pervasive services, arXiv preprint wxXiv:209.04499, 2021.
[53] G. Wan, W. Huang, and M. Ye. Federated graph learning under domain shift with generalizable prototypes. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 38, pages 15429-15437, 2024.
[54] G. Wan, Z. Liu, X. Shan, M. S. Lau, B. A. Prakash, and W. Jin. Epidemiology-aware neural ode with continuous disease transmission graph. In Forty-second International Conference on Machine Learning. 2025.
[55] G. Wan, Z. Shi, W. Huang, G. Zhang, D. Tao, and M. Ye. Energy-based backdoor defense against federated graph learning. In International Conference Learning Representations, 2025.
[56] G. Wan, Y. Tian, W. Huang, N. V. Chawla, and M. Ye. S3gel: Spectral, swift, spatial graph contrastive learning. In Forty-first International Conference on Machine Learning, 2024.
[57] Wang, G. Song, Y. Wu, and L. Wang. Streaming graph neural networks via continual learning. In Proceedings of the 29th ACM international conference on information & knowledge management, pages 1515-1524, 2020.
[58] J. Wang, W. Zhu, G. Song, and L.. Wang. Streaming graph neural networks with generative replay. In Proceedings of the 28th ACM SIGKDD conference knowledge discovery and data mining, pages 1788-1888, 2022.
[59] L. Wang, J. Sun, and Z. Liu. Progressive graph networks for lifelong learning on dynamic graphs. In Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD), 2022.
[60] Z. Wang, Y. Zhang, X. Xu, Z. Fu, H. Yang, and W. Du. Federated probability memory recall for federated continual learning. Information Sciences, 629:551-565. 2023.
[61] Z. Wang, Y. Zhang, X. Xu, Z. Fu, H. Yang, and W. Du. Federated probability memory recall for federated continual learning. Information Sciences, 629:551-565, 2023.
[62] C. Wu, F. Wu, L. Lyu, T. Qi, Y. Huang, and X. Xie. A federated graph neural network framework for privacy-preserving personalization. 13(1):3091.
[63] Z. Wu, S. Pan, F. Chen, G. Long, C. Zhang, and S. Y. Philip. A comprehensive survey on graph neural networks. IEEE TNNLS, pages 4 4424, 2020.
[64] H. Xu, L. Chen, and Z. Wang. Packgel: Prototypical adaptive continual graph learning. In Proceedings of the 36th AAAI Conference on Artificial Intelligence (AAAT), 2022.
[65] X. Yang, H. Yu, X. Gao, H. Wang, J. Zhang, and T. Li. Federated continual learning via knowledge fusion: A survey. arXiv preprint arXiv:2312.16477. 2023.
[66] X. Yao and L. Sun. Continual local training for better initialization of federated models. In 2020 IEEE International Conference on Image Processing (ICIP), pages 1736-1740. IEEE, 2020.
[67] Q. Yuan, S.-U. Guan, P. Ni, T. Luo, K. L. Man, P. Wong, and V. Chang. Continual graph learning: A survey. arXiv preprint arXiv:2301. 12230, 2023.
[68] K. Zhang, C. Yang, X. Li, L. Sun, and S. M. Yiu. Subgraph federated learning with missing neighbor generation. Advances in Neural Information Processing Systems, 34:6671-668) 2021.
[69] X. Zhang, D. Song, and D. Tao. Cglb: Benchmark tasks for continual graph learning. Advances in Neural Information Processing Systems, 11/30000302/)) 2022.
[70] X. Zhang, D. Song, and D. Tao. Hierarchical prototype networks for continual graph representa- tion learning. IEEE Transactions on Pattern Analysis and Machine Intelligence, 45(4):4222- 4636, 2022.
13

---

[71] Z. Zhang, Y. Zhang. D. Guo, S. Zhao, and X. Zhu. Communication-effiinn federated continual learning for distributed learning system with non-iid data. Science China Information Sciences, 66(2):122102, 2023.
[72] X. Zheng, Y. Liu, Z. Bao, M. Fang, X. Hu, A. W.-C. Liew, and S. Pan. Towards data-centric graph machine learning: Review and outlook. arXiv preprint 2rXi:2339..09793 2023.
[73] X. Zheng, Y. Liu, Z. Bao, M. Fang, X. Hu, A. W.-C. Liew, and S. Pan. Towards data-centric graph machine learning: Review and outlook. arXiv preprint wwXi::2309109777 2023.
[74] X. Zheng, Y. Wang, Y. Liu, M. Li, M. Zhang, D. Jin, P. S. Yu, and S. Pan. Graph neural networks for graphs with heterophily: A survey. arXiv preprint arXiv:2202.07082, 2022.
[75] F. Zhou and C. Cao. Overcoming catastrophic forgetting in graph neural networks with experience replay. In Proceedings of the AAAI conference on artificial intelligence, volume 35, pages 4714 4722, 2021.
[76] G. Zizzo. A. Rawat, N. Holohan, and S. Tirupathi. Federated continual learning with differ- entially private data sharing. In Workshop on Federated Learning: Recent Advances and New Challenges (in Conjunction with NeurIPS 2022), 2022.
[77] G. Zizzo, A. Rawat, N. Holohan, and S. Tirupathi. Federated continual learning with differ- entially private data sharing. In Workshop on Federated Learning: Recent Advances and New Challenges, NeurIPS 2022, 2022.
14

---

A
Notations
We present a comprehensive review of the commonly used notations and their definitions in Tab.
Table 2: Notation and Definitions
Notation
Definition
Graph data.
V
The node set of G.
3
The edge set of g.
D2
Task-specific dataset for task t.
X₁
Input data for task
Yt
Lables corresponding to the input data X, for task
T
The number of tasks.
K
The number of clients.
gh
The parameters of the local model Fgx of client
Fo
The global model.
The parameters of the global model.
P.(
The parameter update for task
R())
The regularization term for parameters updated in CL. Trade-off hy heprpaarameter.
The set of all clients.
The index of specific client in C.
G
The evolving graph maintained by client & for task t. The adjacency matrix corresponding to the graph G A node in the graph G where v; Vi-
The feature vector associated with node v; in client k's graph for task 4.
V
The label associated with node v; in client k's graph for task t.
For
The local model trained by client for task t.
0g
The parameters of the local model Fog of client k for task t.
The parameters of the global model shared across all clients.
(.)
The local objective function for client k's graph G task
N
The number of nodes in client k's graph G task
N
The total number nodes across all clients' graphs for task t.
&
Global unique ID for node fusing
and task, Centralized table indexing global IDs for consistent entity referencing.
Ic
Mooarse voriginl
Many-to Mlany-to-one to-one mapping from merged to original nodes.
Marigial -eorss traese
One-to one mapping preserving traceability merged nodes.
(k.4)
From to t shortest paths in G
Number of triangles through v..
PR(c:)
PageRank score of v;-
(w:)
Neighbors of
Mg:
Graph compatibility matrix for client k:
Ag dir
Directional component of client k's update (normalized).
Agk Admug
Magnitude-awesl component of client k's update.
ak
Aggregation coefficient for client k based on compatibility score
Linear decay factor for wwwcoapatibilityy updates
(M,)
Dynamic gating function applied to compatibility matrix
MR
Compatibility value for parameter from client
Crer (0f; G.
11:t-11
Replay regularization to preserve prior task knowledge.
B
Memory budget constraint for client local replay buffer. Replay buffer for client k.
R
A replayed sample from client k's replay buffer. Discrepancy loss function between two models.
T(.,))
15

---

B Related Work
integrates federated learning with con- tinual learning to enable clients to train private task streams sequentially while retaining historical knowledge without accessing past data or exchanging raw thereby mitigating both temporal and spatial catastrophic forgetting. Existing FCL methods generally employ regularization- based techniques, such as FedCurv [66], which adapts Elastic Weight Consolidation to penalize deviations in parameters critical for previous tasks, or sitearsal-basee strategies [77] [O] like FedPMR [6]],
Federated Continual Learning (FCL). FCL 65 46 73 71
which maintains a compact exemplar buffer and aligns probability distributions via replay.
Continual Graph Learning (CGL). CGL [24 18 17 addresses the challenge of incrementally updating models on evolving graph-structured data, where nodes, edges or labels may change over time, without reaccessing all past data. Existing CGL methods generally adopt one of two paradigms. Isolation-basee approaches, such as Progressive Graph Networks [59]. allocate task-specific sub- modules to prevent interference between new and old tasks. In contrast, replay-based frameworks like GraphReplay [39] maintain a buffer of historical graph snapshots for rehearsal.
Federated Continual Graph Learning (FCGL). FCGL enables decentralized, incremental training on evolving graph-structured data across multiple clients. Existing FGI. methods typically assume access to centralized graph, whereas CGL approaches focus on static or single-client graphs, often sacrificing topological fidelity and exacerbating forgetting through naive parameter averaging. Moreover, the unrefined integration of these two mechanisms erodes task-specific knowledge and introduces parameter conflicts, thereby accelerating structural forgetting and destabilizing the global model. To address these limitations, we propose MOTION, the first framework to integrate hierarchical structure-preservving aggregation into FCGL.
C Experimental Details.
C.1 Dataset Details
To evaluate the effectiveness of MOTION, we conduct extensive experiments on eight real-world graph datasets spanning multiple domains: the citation networks Cora, CiteSeer, and PubMed; the product co-purchasing network Amazon-Phos Photo; and the academic collaboration network Co among others. Each dataset is partitioned into fixed subsets of 20% for training, 40% for validation, and 40% for testing. Table summarizes the key statisties of these datasets. Detailed descriptions follow:
DoraCCiteSeer/uubMer These standard citation network benchmarks represent scientific publica- tions as nodes and directed citation links as edges. Each paper is described by high-dimensional bag-of-words features derived from its text and labeled according research topics. Their sparse connectivity and rich feature spaces make them foundational testbeds for node classification and scalability evaluations of GNNs.
Amazon-Phoo Photo. Derived from Amazon's 's co-purchasing data, this network connects photography- related products that are frequently bought together. Nodes encode visual feature descriptors extracted from product images, and the classification task predicts product categories. This dataset challenges models to handle non-textual, image-based features in a commercial recommender context.
CoAuthor-CSS This academic collaboration network links co-authored computer science papers via undirected edges. Node features combine title and abstract embeddings with publication metadata, requiring models to capture interdisciplinary research themes for topic classification. The network's moderate density and heterogeneous feature types test the ability to integrate semantic and structural information.
C.2 Counterpart Details.
This section presents detailed overview of the baseline methods employed in our experiments.
FedAvg [ASTATS' 17] 36 .The seminal framework for federated learning, which orchestrates synchronous parameter updates through iterative client-server interactions. Fach client performs local training epochs on its private data and transmits gradient updates rather than raw inputs to
16

---

Table 3: Statistics of datasets used in experiments.
Dataset
#Nodes
#Edges
#Classes
#Features
Cora
2,708
5,278
7
1,433
Citeseer
3,327
4,552
6
3,703
Pubmed
19,717
44,324
3
500
Amz-Photo
7,650
287,326
8
745
Coauthor-CS 18,333
327,576
15
6,805
preserve data sovereignty. The central server aggregates these updates by performing a weighted average proportional to client dataset sizes, refining the global model while reducing communication overhead. Despite its efficiency, FedAvg's convergence guarantees weaken under non- IID data heterogeneity (28), particularly when client distributions exhibit diverging class priors [77.
FedDC [C) [1] A federated learning algorithm that tackles statistical heterogeneity by decoupling and correcting local drift at the client side. Each client learns an auxiliary local drift variable that tracks the parameter gap between its local model and the global model, and then bridges this gap via penalized consistency term and gradient correction term in its local objective. By integrating drift correction into the training phase (orthogonal to improved aggregation schemes like FedAdam or FedYogi), FedDC achieves significantly faster convergence and higher accuracy across diverse image-classificaan
benchmarks including MNIST, Fashion- MNNIST CIFAR- 10/100, EMNIST-L, Tiny ImageNet, and synthetic dataset-whis remaining robust under partial participation and large-scale non-lID deployments. FedDyn [ICLR'21 21] 22 A seg.anicegggllaizztito--aaaa mismatch between device-level and global optima by augmenting each local objective with a per-round linear and quadratic penalty term, ensuring that, in the limit, local minima coincide with stationary points of the global empirical loss. FedDyn achieves an O11TT) convergence rate in both convex and nonconvex settings under partial participation, massive device counts, unbalanced data, and heterogeneity, while requiring only model transmissions (unlike gradient-augmented schemes such as SCAFFOLD). Empirically, it yields substantial communication savings over FedAvg, FedProx, and SCAFFOLD on benchmarks including MNIST, EMNIST-L, (IFAR-10/100 and Shakespeare.
FL method that resolves the fundamental
FGSSL [ICAAI22] 21 A federated graph learning framework that decouples non-lID hetero- geneity into node-level semantic bias and graph-level structural bias, and corrects both during local training. It introduces Federated Node Semantic Contrast (FNSC), which pulls local node embeddings toward global same-class embeddings and pushes them away from different-class ones, and Federated Graph Structure Distillation (FGSD), which aligns local adjacency-basee similarity distributions to those of the global model-all without extra communication rounds or sharing sensitive priors. FGSSL consistently outperforms FedAvg, FedProx, FedOpt, and FedSage Cora, Citeseer, and Pubmed by up to 4% accuracy under various non-III settings, while achieving faster, more stable convergence.
FedPowder [ICML'24 24] [41]. A prompt-based federated continual learning algorithm that fosters dual knowledge transfer along temporal (within-client) and spatial (across-client) dimensions through a two-step prompt aggregation framework: global prompt aggregation via a task corre- lation matrix capture relevant cross-task information, and top-k correlated prompt selection to optimize communication efficiency; complemented by a correlation weighted dual distillation loss preserve transferred knowledge and mitigate catastrophic forgetting. Powder achieves positive forward and backward transfer, substantially lowers communication and storage overhead, and outperforms rehearsal-bane rehearsal-free, and prompt-based baselines ImageNet-R and DomainNet benchmarks.
hadluy--nd-foore----ee graph class-incred inssemnnremettal learning framework that resolves both inter-task class separation and catastrophic forgetting via two complementary modules: Laplacian mmoothing-basee task profiling, which yields 100% task ID prediction accuracy by modeling each graph task with smoothed prototype, and graph prompt learning, which employs frozen GNN backbone and a small, learnable prompt per task capture task-specific discriminative information without any data replay. This design achieves zero average forgetting (AF=0) and outperforms state-of-the-a baselines by at least 18% average accuracy across four large GCII. benchmarks (CoraFull, Arxiv, Reddit, Products).
FedTPP [N4 (38
FedSSP 24] 500 AA federated graph learning algorithm that tackles structural heterogene- ity in cross-domain settings by sharing generic spectral knowledge and adjusting client-specific
17

---

preferences, Each client retains non- -engeneeic spectral components locally while contributing generic spectral encoders to global collaboration, and employs personalized preference module with regularization to align extracted features with its own graph structure. By integrating spectral knowledge sharing with preference adjusment--orthogomm schemes-FedSS! achieves superior accuracy and stability across diverse graph-classificatin benchmarks, including molecular, bioinformatics, social, and vision datasets, while remaining robust under strong non-lID and multi-domain deployments.
to existing federated aggregation
SEA-ER [CoLLAs 24] 47 I.A graph continual learning framework that addresses catastrophic forgetting under structural shifts by analyzing the theoretical learnability of GNNs and introducing a structure-awar replay mechanism. The paper first proves that GNNs may become unlearnable in node- wise continual learning when evolving graph structures induce large distributional shifts, highlighting the central role of topological integrity. To mitigate this, it proposes Structure- Evolution-Aware Experience Replay (SEA-ER), which selects representative samples via topology- aware structural similarity and reweights them through structural alignment in the replay phase. By integrating these strategies into the training process (orthogonal to architectural advances in GCN, GAT, or SAGE), SEA-ER achieves markedly higher stability and accuracy across real-worl and synthetic senchmarks-inclueee OGB-Arxiv, Reddit, and CoraFull-while remaining effective under evolving graph dynamics and large-scale non-lID continual learning deployments.
C.3 Ablation study of conflicts in parameter aggregation.
We conducted a systematic evaluation of parameter similarity across clients by measuring the cosine similarity of their update vectors on the Cora dataset. As shown in Table 4 the results indicate substantial divergence among client parameters, reflected in both their spatial distribution and update directions. This confirms the presence of parameter conflicts caused by statistical heterogeneity during federated aggregation. From the perspective of parameter similarity, these findings motivate the integration of the G-EPAE module on the server side. By constructing a graph-structured compatibility matrix, G-EPAE adaptively identifies and reconciles discrepancies in client updates, thereby reducing aggregation conflicts and improving both the generalization ability and training stability of the global model.
Table 4: Ablation study on the Cora dataset of confficts parameter aggregation.
Cos similarity
Clientl
Client2
Client3
Client4
Client5
Client1 1.00
0.63
0.57
0.55
0.61
Client2
0.63
1.00
0.56
0.56
0.65
Client3
0.57
0.56
1.00
0.60
0.54
Client4
0.55
0.56
0.60
1.00
0.50
Client5
0.61
0.65
0.54
0.50
1.00
C.4 Discussion of long-range temporal retention.
In the context of FCGL., preserving long-range knowledge is critically important. To evaluate the ability of the model to retain early-task information over extended sequences, we tracked task-specific classification accuracy at each time step. As shown in Table the accuracy trajectories demonstrate that performance on early tasks exhibits only negligible degradation as the task sequence grows, and in some cases even improves. This suggests that sequence length does not impose a substantial negative impact on the accuracy of MOTION and, in fact, reveals trend of sustained optimization for certain tasks. We attribute this stability and improvement mainly the design of the G- G-TMSC module. By employing a multi-expert, topology-awe aware coarsening strategy, the module preserves and amplifies critical structural information from early tasks within the compressed graphs As result, these topological signals are consistently retained and reinforced during subsequent incremental updates, which not only mitigates knowledge drift but also enables, to some extent, the positive consolidation of prior knowledge.
C.5 Discussion of compatibility with GNN architectures
MOTION model-agnostic, as it operates at both the parameter update level and the structural summary level. This design allows seamless integration with various GNN architectures, such as
18

---

Table 5: Accuracy evolution of tasks over time steps
Cora dataset.
Accuracy
Task1
Task2
Task3
Task4
Task5
Task6
Task7
TimeStepl
0.70
0.00
0.00
0.00
0.00
0.00
0.00
TimeStep2
0.72
0.66
0.00
0.00
0.00
0.00
0.00
TimeStep3
0.75
0.68
0.36
0.00
0.00
0.00
0.00
TimeStep4
0.74
0.86
0.37
0.51
0.00
0.00
0.00
TimeStep5
0.85
0.84
0,42
0,64
0.54
0.00
0.00
TimeStep6
0.82
0.81
0.57
0.66
0.55
0.53
0.00
TimeStep7 0.82
0.79
0.58
0.65
0.57
0.54
0.60
GCN and GAT. In our experiments 1 primarily adopted GAT for consistency with baselines.
However, as shown in Table we also evaluated MOTION with GCN on three datasets, where achieved comparable performance gains, further confirming its broad compatibility across GNN
architectures.
Table 6: Compatibility of MOTION with GNN architectures.
Cora
CiteSeer
PubMed
Method
AA
AF
AA
AF
AA
AF
(edPPodde[NuurIP224)
0.14
0.73
0.15
0.56
0.41
0.30
FcdIPp[ICML24]
0.26
0.27
0.17
0.24
0.39
0.10
MOTION
0.63
-0.09
0.52
-0.09
0.61
-0.13
C.6 Implementation Details.
experiments were conducted on system equipped with an NVIDIA GeForce RTX 3090 GPU (24 GB), an Intel Xeon Gold 6330 CPU @ 2.00 GHz (14 cores, 28 threads), and 90 GB of RAM, running Ubuntu 22.04 with Python 3.12, PyTorch 2.3.0, and CUDA 12.1. We employed the Graph Attention Network (GAT) our base model and evaluated federated graph learning on five benchmark datasets: Cora, CiteSeer, PubMed, Amazon-Photo, and CoAuthor-CC The federated setup comprised two clients participating single communication round using the FedAvg algorithm. To induce label skew, we partitioned each dataset's 's eight classes across clients according to a Dirichlet distribution with concentration parameter a 5.0. Our GAT architecture consisted of three attention layers with hidden dimension of 64, a dropout rate of 0.3, learning rate of 0.005, and weight decay of 4 10-1, We split each dataset into 20% training, 40% validation, and 40% test subsets, fixed the random seed at for reproducibility, and performed all computations on GPU
D Broader impact
Our work represents pioneering step towards a generalizable FCGL framework that simultaneously preserves graph-topological integrity and mitigates parameter conflicts in decentralized, evolving environments. By introducing the MOTION framework, which integrates G-TMSC and G-EPAE, we enable robust incremental learning across dynamic, distributed graph data. This advancement enhances the generalization performance and stability graph neural networks in the FCGL setting and contributes to the broader objective of developing scalable, intelligence systems.
lifelong graph
E
Limition
Despite the demonstrated effectiveness of MOTION in addressing the challenges of FCGL, this framework has certain limitations. The inherent tension between preserving information and ensuring efficient aggregation under extreme client heterogeneity remains an open research problem within FCGL scenarios. Moreover, our evaluation, although conducted on diverse benchmark datasets, takes place in controlled settings that may not capture the full complexity of real-world federated systems, including severe client heterogeneity, unstable participation, and adversarial behaviors. Future work could investigate adaptive mechanisms for handling abrupt
19

---

topological changes, develop defense strategies against malicious clients, and validate MOTION in realistic deployment environments.
NeurIPS Paper Checklist
1. Claims
Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
Justification: The main claims made in the abstract and introduction accurately reflect the contributions and scope of this paper.
Guidelines:
The answer NA means that the abstract and introduction do not include the claims made the paper.
The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or
NA answer to this question will not perceived well by the reviewers.
The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize other settings.
is fine to include aspirational goals as motivation as long is clear that these goals are not attained by the paper.
2. Limitations
Question: Does the paper discuss the limitations the work performed by the authors?
Answer: [Yes]
Justification: Details are included in Appendix Guidelines:
The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those not discussed in the paper.
The authors are encouraged to create separate "Limitations" section in their paper.
The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model sell-specification, asymptotic approximations only holding locally). The authors should reflect how these assumptions might be violated in practice and what the implications would be.
The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on few datasets or with few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.
The authors should reflect the factors that influence the performance of the approach. For example, facial recognition algorithm may perform poorly when image resolution is low images are taken in low lighting. Or speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon.
The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size.
If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness.
While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, worse outcome might be that reviewers discover limitations that aren't 't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an impor- tant role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed not penalize honesty concerning limitations.
3. Theory Assumptions and Proofs
20

---

Question: For each theoretical result, does the paper provide the full set of assumptions and complete (and correct) proof?
Answer: [NA]
Justification: The paper does not include theoretical results.
Guidelines:
The answer NA means that the paper does not include theoretical results.
All the theorems, formulas, and proof' in the paper should be numbered and cross- referenced.
All assumptions should be clearly stated or referenced in the statement of any theorems.
The proofs can either appear in the main paper or the supplemental material, but they appear in the suppiemental material, the authors are encouraged to provide short proof sketch provide intuition.
Inversely, any informal proof provided in the core of the paper should be complemented by formal proofs provided in appendix or supplemental material.
Theorems and Lemmas that the proof relies upon should be properly referenced.
4. Experimental Result Reproducibility
Question: Does the paper fully disclose all the information needed to reproduce the main ex- perimental results the paper to the extent that affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided or not)?
Answer: [Yes]
Justification: We fully disclose all the information needed to reproduce the main experi- mental results in this paper and our code, We are convinced that the obtained results can be reproduced.
Guidelines:
The answer NA means that the paper does not include experiments.
If the paper includes experiments, a No answer to this question will not perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not.
If the contribution is dataset and/or model, the authors should describe the steps taken to make their results reproducible or verifiable.
Depending on the contribution, reproducibility can be accomplished in various ways. For example, if the contribution a novel architecture, describing the architecture fully might suffice, or if the contribution is specific model and empirical evaluation, it may be necessary to either make it possible for others to replicate the model with the same dataset, provide access to the model. In general. releasing code and data is often one good way to accomplish this, but reproducibility can also be provided via detailed instructions for how replicate the results, access hosted model (e.g.. in the case of a large language model), releasing of a model checkpoint, or other means that are appropriate to the research performed.
While NeurIPS does not require releasing code, the conference does require all submis- sions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution. For example
(a) If the contribution is primarily new algorithm, the paper should make it clear how to reproduce that algorithm.
(b) the contribution is primarily a new model architecture, the paper should describe the architecture clearly and fully.
(c) the contribution is a new model (e.g., a large language model), then there should either be way access this model for reproducing the results or way to reproduce the model (e.g., with an open-source dataset or instructions for how to construct the dataset).
(d) We recognize that reproducibility may be tricky in some cases, in which case authors are welcome describe the particular way they provide for reproducibility. In the case of closed-source models, it may be that access to the model is limited in some way (c.g., to registered users), but it should be possible for other researchers to have some path to reproducing verifying the results.
21

---

5. Open access to data and code
Does the paper provide open access to the data and code, with sufficient instruc- tions faithfully reproduce the main experimental results, described in supplemental material?
Question:
Answer: [Yes]
Justification:
Code is accessible in this paper.
Guidelines:
The answer NA means that paper does not include experiments requiring code.
Please see the NeurIPS code and data submission guidelines (https://nips.co
for more details.
While encourage the release of code and data, understand that this might not be possible, so "No" is an acceptable answer. Papers cannot be rejected simply for not including code, unless this is central to the contribution (e.g., for new open-source benchmark).
The instructions should contain the exact command and environment needed to run to reproduce the results. See the NeurlPS code and data submission guidelines (https for more details.
7 //nips.
The authors should provide instructions on data access and preparation, including how to access the raw data, preprocessed data, intermediate data, and generated data, etc.
The authors should provide scripts to reproduce all experimental results for the new proposed method and baselines. only subset of experiments are reproducible, they should state which ones are omitted from the script and why.
At submission time, to preserve anonymity, the authors should release anonymized versions (if applicable).
Providing as much information as possible in supplemental material (appended to the paper) recommended, but including URLs to data and code permitted.
6. Experimental Setting/Details
Question: Does the paper specify all the training and test details (e.g., data splits, hyper- parameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?
Answer: [Yes]
Justification: Details are included in Appendix C.6.
Guidelines:
The answer NA means that the paper does not include experiments.
The experimental setting should be presented in the core the paper to a level of detail that is necessary appreciate the results and make sense of them.
The full details can be provided either with the code, in appendix, as supplemental material.
7. Experiment Statistical Significance
Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
Question:
Answer: [Yes]
Justification:
Statistical significance of the experiments is considered and included in Sec.
Guidelines:
The answer NA means that the paper does not include experiments.
The authors should answer "Yes" if the results are accompanied by error bars, confi-
dence intervals, statistical significance tests, least for the experiments that support the main claims of the paper.
The factors of variability that the error bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, or overall with given experimental conditions).
22

---

The method for calculating the error bars should be explained (closed form formula, call to a library function, bootstrap, etc.)
The assumptions made should be given (e.g.. Normally distributed errors).
It should be clear whether the error bar is the standard deviation or the standard error of the mean.
is OK to report 1-sigma error bars, but one should state it. The authors should preferably report a 2-sigma enror bar than state that they have 96% CI, if the hypothesis of Normality of errors is not verified.
For asymmetric distributions, the authors should be careful not to show in tables or figures symmetric error bars that would yield results that are range (e.g. negative enror rates).
If error bars reported in tables plots, The authors should explain in the text how they were calculated and reference the corresponding figures or tables the text.
8. Experiments Compute Resources
For each experiment, does the paper provide sufficient information on the com- puter resources (type of compute workers, memory, time of execution) needed reproduce the experiments?
Question:
Answer: [Yes]
Justification:
We provide sufficient information on the computer resources.
Guidelines:
The answer NA means that the paper does not include experiments.
The paper should indicate the type of compute workers CPU or GPU, internal cluster, cloud provider, including relevant memory and storage.
The paper should provide the amount of compute required for each of the individual experimental runs well estimate the total compute.
The paper should disclose whether the full research project required more compute than the experiments reported in the paper (e.g., preliminary or failed experiments that didn't make into the paper).
9. Code Of Ethics
Question: Does the research conducted in the paper conform, in every respect, with the NeurIPS Code of Ethics
Answer: [Yes]
Justification: The research conducted the paper strictly adheres to the NeurIPS Code of Ethics, ensuring that all aspects of the work are in compliance with the guidelines provided.
Guidelines:
The answer NA means that the authors have not reviewed the NeurIPS Code of Ethics.
If the authors answer No, they should explain the special cireumstances that require deviation from the Code of Ethics.
The authors should make sure to preserve anonymity (e.g.. if there is special consid- eration due to laws or regulations their jurisdiction).
10. Broader Impacts
Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?
Answer: [NA]
Justification: The research presented in this paper is foundational. It is not directly tied to any specific applications or deployments.
Guidelines:
The answer NA means that there is no societal impact of the work performed.
If the authors answer NA or No, they should explain why their work has no societal impact why the paper does not address societal impact.
23

---

Examples of negative societal impacts include potential malicious unintended uses (e.g., disinformation, generating fake profiles, surveillance), faireess considerations (e.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.
The conference expects that many papers will be foundational research and not tied partieular applications, let alone deployments. However, if there is direct path any negative applications, the authors should point it out. For example, it is legitimate to point that improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people train models that generate Deepfakes faster.
The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology.
If there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition attacks, mechanisms for monitoring misuse, mechanisms to monitor how system learns from feedback over time, improving the efficiency and accessibility of ML).
11. Safeguards
Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?
Question:
Answer: [NA]
Justification: This paper poses such risks.
Guidelines:
The answer NA means that the paper poses no such risks.
Released models that have high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere usage guidelines or restrictions to access the model or implementing safety filters.
Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images.
We recognize that providing effective safeguards is challenging, and many papers do not require this, but encourage authors to take this into account and make best faith effort.
12. Licenses for existing assets
Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?
Question:
Answer: [NA]
Justification: This paper does not use existing assets.
The answer NA means that the paper does not use existing assets.
The authors should cite the original paper that produced the code package or dataset.
The authors should state which version of the asset used and, possible, include a URL.
The name of the license (e.g., CC-BY 4.0) should be included for each asset.
For scraped data from a particular source (e.g., website), the copyright and terms of service of that source should be provided.
If assets are released, the license, copyright information, and terms use in package should be provided. For popular datasets, paperswithcone com/ datasets has curated licenses for some datasets. Their licensing guide can help determine the license of dataset.
24

---

For existing datasets that are re-packaged, both the original license and the license of the derived asset (if has changed) should be provided.
If this information is not available online, the authors are encouraged to reach out to the asset's s creators.
13. New Assets
Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?
Answer: [NA]
Justification: This paper does not release new assets.
Guidelines:
The answer NA means that the paper does not release new assets.
Researchers should communicate the details the dataset/code/moodl as part their submissions via structured templates. This includes details about training, license, limitations, etc.
The paper should discuss whether and how consent was obtained from people whose asset used.
At submission time, remember to anonymize your assets (if applicable). You can either create an anonymized URL or include an anonymized zip file.
14. Crowdsoureing and Research with Human Subjects
Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well details about compensation (if any)?
Answer: [NA]
Justification: This paper does involve crowdsourcing nor research with human subjects.
Guidelines:
The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.
Including this information the supplemental material is fine, but if the main contribu- tion of the paper involves human subjects, then as much detail as possible should be included the main paper.
According the NeurIPS Code of Ethics, workers involved in data collection, curation, or other labor should be paid at least the minimum wage in the country of the data collector.
15. Institutional Review Board (IRB) Approvals or Equivalent for Research with Human Subjects
Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or equivalent approval/review based the requirements of your country or institution) were obtained?
Answer: [NA]
Justification: The paper does not involve crowdsourcing nor research with human subjects.
Guidelines:
The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.
Depending the country in which research is conducted, IRB approval (or equivalent) may be required for any human subjects research. If you obtained IRB approval, you should clearly state this in the paper.
We recognize that the procedures for this may vary significantly between institutions and locations, and we expect authors to adhere to the NeurIPS Code of Ethics and the guidelines for their institution.
For initial submissions, do not include any information that would break anonymity (if applicable), such as the institution conducting the review.
25


Reviews:
[{"review_id": "9pHamAQlpo", "reviewer": "Reviewer_EiHY", "summary": "The paper introduces the federated graph continual learning framework and presents an effective instantiation consisting of two elements: one integrates multiple structural metrics, while the other ensures appropriate aggregation from different nodes. Experiments demonstrate consistent performance improvements over the baselines.", "questions": "Paper presentation requires polishing:\n- The question in line 42 mentions FCL for the first time, which does not seem to fit into the preceding framing of the discussion where GNN and FGL are introduced and FGCL is described as FGL+CGL.\n- Lines 43-50. The concept of preserving inherent graph topology and topological integrity is central to the paper, yet it is mentioned without definition. I suggest that the authors provide a clear introduction to these concepts and explain why they are desirable properties.\n- Line 128. I was unable to discern the substantial topological heterogeneity and neighborhood distributions from Figure 1. Please revise the figure and its caption to clarify these points.\n- I find Figures 1 and 2 difficult to interpret. They are overly dense and include numerous distracting elements whose purpose is unclear and insufficiently explained. For example, in Figure 1: Q&A, teacher, the cloud, question marks, a head with charts, \"FAIL,\" the evil figure, the magnifying lens, and the arrows connecting the left and right blocks; the same applies to Figure 2.\n- Many of the symbols used in introducing the similarities discussed in \"Multi-Sculpt Coarsening\" are undefined or were already introduced in earlier sections. Additionally, what exactly are the inputs to each of these symbols?\n- The acronyms and references for the baselines need revision, e.g., NeurIPS 2025, AISTATS, and avoiding arXiv versions when the paper has been published elsewhere.\n\nSome claims are not sufficiently supported by evidence, which makes them unconvincing:\n- Lines 63-65. It would be helpful if the authors could substantiate the claimed general failure with evidence and/or references. It would also improve clarity if the authors elaborated at this point on the specific challenges of the new setting, which ultimately lead to the research question posed at the end of the paragraph.\n- Equation 1. The loss function presented in Equation 1 and the accompanying discussion in lines 104-106 are not convincing. There appears to be no clear reason to add the term $\\mathcal R(\\theta)$ to mitigate forgetting, since $\\mathcal P_\\text{total}(\\theta)$ already accounts for all tasks.\n- Lines 121-125. Could the authors provide evidence and discussion showing that these methods suffer from the three identified shortcomings, i.e., failing to deliver comparable performance on graph-structured data, requiring excessive storage, and experiencing conflicts?\n- Did I understand correctly that the \"generalizable FGCL design principles\" are the same as those from federated and continual learning, except for storage efficiency? If so, why would storage efficiency differ from that in CGL?", "limitations": "yes", "rating": 2, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 1, "significance": 2, "originality": 2, "strengths_and_weaknesses": "To my knowledge, the FGCL framework is novel, and the proposed MOTION method shows better figures over the baselines, which is another notable strength of the paper.\n\nHowever, in its current form, the paper falls short of publication standards in terms of presentation quality, clarity, and rigor. \nI believe the paper requires substantial revision to ensure that readers can grasp the context and fully appreciate its value. It also makes it difficult for me to provide an accurate assessment of the paper's technical content. Several examples of my concerns are outlined below.", "was_revised": true, "final_justification": "While I see value in this work, my main concern is clarity. Several claims seem weak, and some parts are difficult to follow. The authors' rebuttal addressed most points, but given the number of issues, I believe the paper should undergo another round of revision to ensure that all the pieces work together as intended.", "rebuttal": "Thank you for your thorough review and constructive feedback. We address your concerns below and hope these clarifications will help you re-evaluate and update the score:\n>`Weakness `: Discussion of paper presentation\n\n>`Question1 `: Clarification on the consistency of FGCL terminology introduction\n\nWe appreciate this point. In our description of Federated Graph Continual Learning (FGCL), we reference Federated Continual Learning (FCL) (line 42) to position MOTION within the general FCL paradigm. This reference makes explicit the connection to graph data. \n\nSubsequently, we introduce Federated Graph Learning (FGL) and Continual Graph Learning (CGL) to present FGCL as the graph-specific instantiation. FGCL jointly addresses FGL (client heterogeneity) and CGL (temporal evolution). To avoid ambiguity, we will unify the first mention (line 42) with a concise bridging question: \"How can we design an FGL framework specifically tailored for continuously evolving streaming data?\"\n\n>`Question2 `: Discussion on definition of graph topology preservation concepts\n\nThank you for your valuable feedback. We have already cited the references of inherent graph topology and topological integrity (lines 43–50). To enhance conceptual clarity, we provide explicit definitions for both terms:\n\n- **Inherent graph topology** refers to the structural characteristics intrinsic to each local graph. These include node centrality measures and local subgraph configurations.\n- **Topological integrity** denotes the preservation of these structural characteristics following updates during the continual learning process.\n\n>`Question3 & Question4 `: Considerations on Figure Clarity and Revisions\n\nThank you for your feedback on Figures 1 and 2. Figure 1 mainly shows the key challenges in our work, such as catastrophic forgetting and global aggregation conflicts, rather than showing the detailed causes like topological heterogeneity or neighborhood distributions. We also note that other reviewers, such as reviewer D7ZJ, have praised the clarity and visual design of our framework, stating that “this paper is clearly and effectively written, with a fancy and comprehensive visual representation of the framework.”\n\nWe appreciate that perspectives on visual style may differ, and agree that refinements can further improve clarity. Following your suggestion, in the revised version we have:\n1. **Simplified** Figure 1 and Figure 2 by removing nonessential icons to reduce visual density.\n2. **Enhanced the captions and annotations** to explicitly describe the intended message, including highlighting topological heterogeneity and neighborhood distribution differences where relevant.\n3. **Added necessary textual descriptions** directly within the figures to ensure that each icon conveys its intended meaning clearly.\n\n>`Question5 `: Discussion of symbol usage in Multi-Sculpt Coarsening\n\nWe appreciate this comment. Most symbols are already defined in Appendix A(Page 14). To improve readability, we have made the following changes: (i) moving essential definitions into the main text and defined them at first use, and (ii) adding a simple \"Notation & Inputs\" box, listing each symbol, its input, and shape in the appendix.The features used in Multi‑Sculpt Coarsening are:\n* **Topological features:** Computed from the task graph $G_t=(V_t,E_t)$ ,where $V_t$ and $E_t$ are its node and edge sets and $N_t=|V_t|$,include degree, clustering coefficient, PageRank and so on. Output: $\\texttt{topoFeatures}\\in\\mathbb{R}^{N_t\\times 8}$.\n* **Similarity metrics:** MMD, Mahalanobis, Pearson, and cosine similarity computed from node features $X\\in\\mathbb{R}^{N_t\\times d}$. Output: $\\texttt{similarityFeatures}\\in\\mathbb{R}^{N_t\\times 4}$.\n* **Subgraph descriptors:** Average degree, clustering coefficient, diameter, and density. Output: $\\texttt{subgraphFeatures}\\in\\mathbb{R}^{N_t\\times 4}$.\n* **Degree embeddings:** Sinusoidal encodings of node degree. Output: $\\texttt{degreeEmbeddings}\\in\\mathbb{R}^{N_t\\times 8}$.\n\nAll features are concatenated into $\\texttt{combinedFeatures}\\in\\mathbb{R}^{N_t\\times 24}$ and fed to the mixture‑of‑experts gating network, which outputs node importance scores $\\mathbf{s}\\in\\mathbb{R}^{N_t}$ for pruning and noise suppression.\n\n>`Question6 `: Remarks on the consistency of baseline references and acronyms\n\nWe appreciate this valuable feedback. In the revised version, we have replaced arXiv citations with official conference proceedings and ensured consistent naming of baseline methods.\n>`Weakness `: Considerations on evidence supporting specific statements\n\n>`Question1 `: Discussion on the Evidence Supporting the Claimed General Failure\n\nWe agree that more empirical support is needed. Prior studies have already discussed related issues: for example, [1] analyzes how client heterogeneity in federated learning can lead to performance degradation, and [2] reports semantic and structural limitations of FGL under evolving topologies. These works support our statement that FGL methods often degrade when applied in continual settings, primarily due to catastrophic forgetting and client-specific distribution shifts.\n\nIn the revised version, we have cited these references to substantiate the general performance degradation and explained the unique challenges in the proposed FCGL setting.We appreciate your advice, which helps us improve the rigor and clarity of our work.\n\n[1]:Generalizable heterogeneous federated cross-correlation and instance similarity learning. In TPAMI,2023.\n\n[2]:Federated Graph Semantic and Structural Learning. In IJCAI,2023.\n\n>`Question2 `: Observation on Unjustified inclusion of regularization term in loss function\n\nThe regularization term $𝑅(\\theta)$ is **mentioned to constrain parameter drift** relative to consolidated knowledge. While $P_{total}(\\theta)$ includes all tasks, it is computed based on streaming task data, which may emphasize recent updates. $R(\\theta)$ **ensures stability** by penalizing deviations in topology-sensitive parameters.\n\nMoreover, prior studies have theoretically and empirically demonstrated the necessity of such regularization mechanisms in continual learning. In particular, [1–3] demonstrate that explicitly adding a regularization term $R(\\theta)$ effectively balances stability and plasticity, preserves previously acquired knowledge, and mitigates forgetting across sequential tasks.\n\nMeanwhile,This section **establishes preliminaries to underscore** how our framework addresses the core requirement of jointly balancing newly acquired knowledge with consolidated prior representations.\n\n[1]:A Statistical Theory of Regularization-Based Continual Learning. In ICML,2024.\n\n[2]:Memory Aware Synapses: Learning what (not) to forget. In ECCV,2018.\n\n[3]:Continual Learning with Recursive Gradient Optimization. In ICLR,2022.\n\n>`Question3 `: Evidence for shortcomings of existing methods\n\nWe sincerely thank you for this helpful question. We agree that providing a discussion of how existing methods suffer from the three identified shortcomings will further strengthen the paper. In the revision, we have clarified this rationale as follows:\n1. **Comparable performance on graph-structured data**: As discussed in our motivation and shown in Table 1 (Page 7), directly adapting existing methods to graph data yields substantially lower average accuracy and higher forgetting compared to MOTION. These results confirm that general FCL/FGL methods do not readily capture the structural dependencies inherent in dynamic graphs.\n2. **Storage burden**: Existing GCL [1,2] methods rely on node replay buffers or full historical subgraph retention, which requires storing both node features and adjacency information and leads to high memory costs. Our Graph Topology‑preserving Multi‑Sculpt Coarsening (G‑TMSC) preserves task‑critical structures while greatly reducing storage. On Cora, replay buffers need 8.2 MB, while our coarsened representation needs only 1.7 MB, achieving an 80% reduction.\n3. **Conflicts in parameter aggregation**: Our ablation study (Figure 4, Page 9) shows that removing the G‑EPAE module (w/o Para.-Al.) causes client–server update conflicts and performance degradation. To further confirm these conflicts, we computed the cosine similarity of client updates on Cora, which shows low alignment across clients:\n\n|Cos similarity|Client1|Client2|Client3|Client4|Client5|\n|-|-|-|-|-|-|\n|Client1|1.00|0.63|0.57|0.55|0.61|\n|Client2|0.63|1.00|0.56|0.56|0.65|\n|Client3|0.57|0.56|1.00|0.60|0.54|\n|Client4|0.55|0.56|0.60|1.00|0.50|\n|Client5|0.61|0.65|0.54|0.50|1.00|\n\n[1]Streaming Graph Neural Networks with Generative Replay. In KDD,2022.\n\n[2]Overcoming catastrophic forgetting in graph neural networks with experience replay. In AAAI,2021.\n\n>`Question4 `: Clarifying the distinction between FCGL and existing FL/CL/CGL design principles\n\nWe sincerely thank you for this thoughtful question. While the high-level goals of mitigating catastrophic forgetting and supporting distributed training are shared with existing FCL, our FCGL formulation introduces **unique considerations** due to the graph-structured nature of the data.\n\nIn conventional FCL, data are typically feature vectors or images, with task transitions mainly adding new classes. In contrast, FCGL deals with dynamic graphs where nodes and edges continuously evolve, making historical graph storage more challenging due to (i) **Topological complexity**: Storing connectivity in addition to features, and (ii) **volume growth**: Nodes and edges increasing super-linearly if full snapshots are retained.\n\nBeyond storage, FCGL differs from CGL because federated aggregation causes **cross‑client parameter conflicts**. Clients observe different subgraphs, producing inconsistent updates. Without alignment, these conflicts increase catastrophic forgetting compared to single‑client CGL."}, {"review_id": "MbeszIY0w1", "reviewer": "Reviewer_co1X", "summary": "The paper presents a comprehensive evaluation of the proposed MOTION framework on five benchmark datasets in the FCGL setting. The results demonstrate substantial improvements over state-of-the-art methods in terms of both average accuracy and average forgetting, often showing negative forgetting rates. The ablation studies highlight the importance of both the graph coarsening and parameter alignment modules. Additional experiments on hyperparameter sensitivity and scalability are included to support robustness.", "questions": "1. How are the directional and magnitude components of the parameter increment computed to form the compatibility matrix and determine parameter importance?\n2. Why does the proposed problem formulation require a distinct FCGL setting, rather than adapting existing FCL or FGL frameworks?\n3. How does the proposed MOTION framework interact with the underlying GNN architecture, and is it compatible with other models?\n4. How does G-TMSC scale when the number of nodes is in the order of millions? How costly is it to compute all the structural metrics (especially PageRank, centrality scores) on-device?\n5. The coarsening process includes a reservoir sampling memory. What is the size of this buffer, and how sensitive is MOTION to the buffer budget?", "limitations": "The authors should further discuss the societal impact of the proposed method.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strengths:**\n1. It is novel and well-motivated to propose an FCGL approach. The paper clearly identifies the key challenges faced by existing FCGL methods and successfully provides solutions to overcome them.\n2. Both the problem description and the framework illustration are clearly and thoroughly presented.\n3. The integration of G-TMSC and G-EPAE demonstrates a practical understanding of the challenges. \n\n**Weaknesses:**\n1. The paper lacks long-range temporal retention analysis. It does not analyze how the model preserves information from earlier tasks, given that aggregation is limited to the most recent timestamp.\n2. For a federated learning setting, the paper is surprisingly silent on how MOTION handles or could be extended to address privacy or adversarial issues, which are critical in real deployments.\n3. The paper lacks a sensitivity study. It does not analyze how the performance of the global model varies with different numbers of local training epochs.", "was_revised": true, "final_justification": "I have read the authors' careful responses, and most of my concerns have been addressed.", "rebuttal": "Thank you for your thorough review and constructive feedback. We address your concerns below and hope these clarifications will help you re-evaluate and update the score:\n\n> `Weakness 1`: Discussion of long-range temporal retention\n\nWe agree that long-range retention is important in Federated Continual Graph Learning (FCGL). Our primary experiments focused on task-averaged performance(AA) and forgetting rates(AF), as is standard in the literature [1,2]. To directly assess early-task retention, we **tracked task-specific accuracy** at every time step. The per-time-step table shows minimal degradation as the horizon increases. This indicates that longer sequences do not materially affect the accuracy of Motion. \n\nWe attribute this stability primarily to Graph Topology-preserving Multi-Sculpt Coarsening (G-TMSC). Its topology-preserving multi-sculpt coarsening retains task-critical structures from earlier tasks in the coarsened graph. This ensures these signals persist through subsequent updates and thereby mitigates drift. We have included the per-time-step plots and detailed numbers in the revised version. \n\n|Accuracy|Task1|Task2|Task3|Task4|Task5|Task6|Task7|\n|--------|-----|-----|-----|-----|-----|-----|-----|\n|Task1|0.7000|0.0000|0.0000|0.0000|0.0000|0.0000|0.0000|\n|Task2|0.7182|0.6639|0.0000|0.0000|0.0000|0.0000|0.0000|\n|Task3|0.7500|0.6807|0.3583|0.0000|0.0000|0.0000|0.0000|\n|Task4|0.7364|0.8571|0.3667|0.5120|0.0000|0.0000|0.0000|\n|Task5|0.8455|0.8445|0.4167|0.6446|0.5405|0.0000|0.0000|\n|Task6|0.8182|0.8109|0.5667|0.6627|0.5473|0.5333|0.0000|\n|Task7|0.8227|0.7941|0.5833|0.6506|0.5743|0.5417|0.6000|\n\n[1]:A Comprehensive Survey of Continual Learning: Theory, Method and Application. In TPAMI,2024.\n\n[2]:Riemannian Walk for Incremental Learning:Understanding Forgetting and Intransigence. In ECCV,2018.\n\n\n> `weakness 2`: Privacy and adversarial considerations\n\nWe appreciate the emphasis on privacy and adversarial robustness, which are critical in real deployments. MOTION operates on **locally computed** structural summaries and parameter increments rather than raw graph data. This inherently reduces privacy risk. MOTION transmits only local parameter updates to the remote server. It never uploads raw node/edge features, adjacency, or graph records—**no raw local data leaves the device**. \nIn contrast, replay-based methods such as [1,2] require storing and replaying plenty of past data or generating synthetic samples to mitigate catastrophic forgetting. Since these methods need access to raw or synthesized historical data during training, they may pose privacy risks.\n\nGiven that privacy protection is **orthogonal** to the core design of MOTION, integrating secure parameter sharing is planned as future work. This approach can be introduced into the framework without altering its fundamental design, thereby further strengthening security while maintaining its privacy-preserving capabilities.\n\n[1]Streaming Graph Neural Networks with Generative Replay. In KDD,2022.\n\n[2]Overcoming catastrophic forgetting in graph neural networks with experience replay. In AAAI,2021.\n\n\n> `Weakness 3`: Remarks on the sensitivity study on local training epochs\n\nThank you for pointing this out. We performed a sensitivity analysis varying local epochs $E∈[25,50,75,100]$ across Cora dataset. Results show MOTION **remains stable**, with average accuracy fluctuations within 2.2% and forgetting metrics within 8.9%. This demonstrates **robustness** to different local computation budgets. \n\nThis robustness stems from Graph-Aware Evolving Parameter Adaptive Engine (G-EPAE), which normalizes parameter increments by their directional and magnitude components before aggregation. This dampens idiosyncratic, overly large updates when $E$ is high and preserves effective step sizes and coherent directions when $E$ is small. It is further aided by G-TMSC: its topology-preserving multi-sculpt coarsening retains salient structures from prior tasks. This yields better-conditioned, more sample-efficient local training, which helps maintain stability.\n|Epochs|25|50|75|100|\n|------|---|---|---|---|\n|Cora(AA)|61.29|62.66|62.41|62.21|\n|cora(AF)|-12.22|-7.40|-16.28|-10.38|\n\n\n> `Question1 `: Computation of compatibility matrix for compatibility and importance estimation\n\nWe thank the reviewer for raising this question. We clarify the computation of the directional and magnitude components used to form the compatibility matrix. For each client update, we first compute the parameter increment $\\Delta \\theta_k = \\theta_k - \\phi$. The directional component isolates the update orientation by L2 normalization: $\\Delta \\theta_k^{dir} = \\frac{\\Delta \\theta_k} {\\|\\Delta \\theta_k\\|_2}$. The magnitude component measures the relative strength of each update: $\\Delta \\theta_k^{mag}=\\frac{\\|\\Delta \\theta_k\\|_2} {\\sum_j \\in_C \\|\\Delta \\theta_j\\|_2}$ .\n\nThe compatibility matrix is then constructed as an element-wise product $M_k = \\Delta \\theta_k^{dir} \\circ \\Delta \\theta_k^{mag}$. This captures both **directional alignment** and **relative importance** of each client update. This matrix reweights local updates during aggregation, emphasizing structurally consistent and topologically relevant contributions while suppressing conflicting changes. This is critical for harmonizing updates under non-IID and evolving graph conditions (see Sec. 3.3 Page 6, Eq. (11)–(16) of the paper).\n\n\n> `Question2 `: Justification for a distinct FCGL Setting Over existing FCL or FGL frameworks\n\nWe sincerely thank the reviewer for raising this important question.Unlike conventional Federated Continual Learning (FCL), which primarily focuses on sequential task learning over feature-based data, and Federated Graph Learning (FGL), which assumes a relatively static global graph or shared structure across clients, FCGL simultaneously addresses:\n1. **Dynamic graph evolution:** Nodes and edges are continuously added or removed, reflecting changing behaviors and relationships in each client’s local graph. \n2. **Decentralized storage constraints:** Edge devices often cannot store complete historical topologies or replay buffers, making raw historical graph retention impractical.\n3. **Cross-client heterogeneity:** Each client observes a distinct, evolving subgraph, which introduces severe challenges for both catastrophic forgetting and federated aggregation.\n\n> `Question3 `: Compatibility with GNN architectures\n\nThank you for your valuable advice. MOTION is **model-agnostic**. It operates at the parameter update level and structural summary level, meaning it can integrate with any GNN architecture (GCN, GAT, etc.). In our experiments, we used GAT for consistency with baselines, but we also validated **MOTION with GCN** on three datasets, showing similar performance gains.\n|Method|Cora(AA)|Cora(AF)|CiteSeer(AA)|CiteSeer(AF)|PubMed(AA)|PubMed(AF)|\n|------|---|---|---|---|---|---|\n|FedPowde|14.29|72.78|15.24|55.96|41.48|30.12|   \n|FedTpp |25.76|26.84|17.44|24.21|38.52|10.25|   \n|Motion| **63.07**|**-9.34**|**52.38**|**-8.89**|**61.34**|**-13.47**|  \n\n\n> `Question4 `: Scalability and computation cost of G-TMSC \n\nWe appreciate the reviewer’s concern regarding scalability to graphs with millions of nodes and the associated cost of structural metric computation.\n\n1. Our paradigm is built upon a continual learning setting in which each client **processes graph streams incrementally** rather than operating on the entire historical graph at once. We explicitly employ graph coarsening via the proposed G-TMSC module, which merges structurally redundant or low-importance nodes into representative nodes. As a result, the effective graph size per task is significantly reduced, and memory requirements remain bounded, preventing storage bottlenecks even for million-scale node sets.\n2. Regarding computational cost, the structural metrics used in G-TMSC are chosen to be lightweight in the streaming context: (i) **degree and clustering coefficients** are computed in $𝑂(∣𝐸∣)$ time; (ii) **PageRank** is computed with a power-iteration scheme of complexity $O(k∣E∣)$, where k(typically 10−20) is the number of iterations for convergence; (iii) overall, G-TMSC scales **linearly with the number of edges** and near-linearly with the number of nodes post-coarsening, ensuring that computation is efficient even on edge devices and does not hinder deployment in real-world, million-scale scenarios.\n\n> `Question5 `: Buffer size and sensitivity of MOTION to reservoir sampling memory budget\n\nWe thank the reviewer for the question regarding the reservoir sampling memory. In our implementation, the buffer is configured with a **default size of 200 nodes**, further divided per class when class-aware sampling is enabled ($\\texttt{bufferSizePerClass} = \\texttt{bufferSize} // \\texttt{numClass}$). This design ensures a balanced representation of historical nodes while maintaining a lightweight memory footprint.\n\nWe also examined **sensitivity to the buffer budget**. Reducing the buffer (e.g., 100) slightly increases forgetting due to fewer “anchor” nodes preserved for replay, while a larger buffer (e.g., > 400) yields only marginal accuracy gains but increases storage and computation overhead. The default size of 200 provides a practical balance, as confirmed by our ablation results. We will clarify this buffer size and sensitivity analysis in the revision for completeness.\n|buffer size|100|200|400|\n|------|---|---|---|\n|Cora(AA)|59.18|62.66|63.15|   \n|Cora(AF)|-5.56|-8.34|-5.35|"}, {"review_id": "dLyyrVrbRX", "reviewer": "Reviewer_D7ZJ", "summary": "This paper addresses the challenges inherent in FCGL, specifically the preservation of graph topology and mitigation of parameter conflicts during model aggregation. MOTION integrates a G-TMSC module to maintain structural integrity via multi-expert node merging, and a G-EPAE to refine aggregation by dynamically adjusting based on graph compatibility. Extensive experiments on real-world datasets demonstrate that MOTION achieves significant improvements in accuracy and resilience against forgetting compared to existing methods.", "questions": "1. Complementation of the explanation negative forgetting phenomenon. While the experimental results report negative AF, the authors should provide a more detailed analysis of this phenomenon. A clearer explanation connecting this observation to the roles of G-TMSC and G-EPAE would strengthen the empirical claims and provide insight into the learning dynamics under the FCGL setting.\n2. Complementation of the explanation for the multi-expert architecture input. The authors should clarify why they choose to decompose the merged graph into components such as 1-hop and 2-hop subgraphs, cosine similarity, and other metrics as inputs to the multi-expert architecture.", "limitations": "yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 4, "originality": 4, "strengths_and_weaknesses": "Strengths:\n1. MOTION combines graph coarsening with expert fusion and adaptive aggregation based on a compatibility matrix. These techniques are tailored specifically for FCGL, where existing solutions are lacking, demonstrating a thoughtful methodological advancement.\n2. This paper is clearly and effectively written, with a fancy and comprehensive visual representation of the framework. The accurate and thorough explanations of the methodological components further contribute to its ease of understanding.\n3. The experiments are comprehensive, covering five real-world datasets with evaluations on both Average Accuracy and Average Forgetting. The empirical results show substantial gains over strong baselines, supporting the claimed improvements.\n\nWeaknesses:\n1. The work does not provide sufficient information on the experimental implementation used for other conventional FL、FGL、CGL and FCL baselines. \n2. Although the method components (G-TMSC and G-EPAE) are well-explained, the authors should provide a clearer rationale for why these specific designs are necessary to address the stated problems, introducing their connections to the initial motivations in the FCGL setting.\n3. The paper does not investigate how the size of the original subgraphs at each time step influences the overall performance. A comprehensive sensitivity study on subgraph scale would help clarify whether the proposed method remains effective across varying graph sizes.", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your thorough review and constructive feedback. We address your concerns below and hope these clarifications will help you re-evaluate and update the score:\n\n> `Weakness 1`: Discussion on the Information Provided for Baseline Implementations\n\nWe appreciate the reviewer’s comment and agree that clear baseline implementation details are important. The general experimental environment and common hyperparameters have already been documented in Appendix C.3(Page 17). In fact, we have mentioned representative common parameters such as the learning rate (0.005), weight decay ($4 \\times 10^{-4}$), and dropout rate (0.3), which are applied consistently across baseline methods.\n\nFor algorithm-specific settings, we have further provided a dedicated table with complete hyperparameters and training details to ensure full reproducibility in the revision. For example, FedDc and FedDyn use a regularization coefficient of 1.0 for drift correction and stability control, respectively, while FedSSL adopts distillation and contrastive loss weights, both set to 0.5. Other baselines, such as FedAvg, FedTpp, and FedPowde, follow the common hyperparameter setup without additional parameters.\n\n> `Weakness 2`: Rational for G-TMSC and G-EPAE designs\n\nWe agree that making the connection between the problem formulation and our proposed modules more explicit will further strengthen the paper. In the revision, we will clarify this rationale as follows:\n\n1. **Motivation–Design Connection:** In Federated Continual Graph Learning (FCGL), two challenges are unique and were explicitly highlighted in our Introduction: (i) **catastrophic forgetting** of graph-topological information due to evolving local data streams and limited storage; (ii) **parameter conflicts** during federated aggregation caused by heterogeneous client graph structures.\n2. Necessity of Graph Topology-preserving Multi-Sculpt Coarsening (G-TMSC): To address (i), we designed the G-TMSC module. Its function is to **preserve inherent structural properties** (e.g., node centrality and local subgraph patterns) under memory constraints, which directly aligns with the motivation of preventing topological knowledge loss. Without explicit coarsening, replay-based or raw-graph approaches would incur prohibitive storage costs or fail to retain structural fidelity.\n3. Necessity of Graph-Aware Evolving Parameter Adaptive Engine (G-EPAE): To address (ii), we introduced the G-EPAE, which **adjusts aggregation rates** based on a topology-sensitive compatibility matrix. This design directly tackles the issue of conflicting updates from heterogeneous clients, ensuring stable integration of newly learned structures without degrading previously acquired knowledge.\n\n> `Weakness 3`: Analysis of subgraph size sensitivity\n\nWe agree that analyzing the influence of original subgraph size on performance can provide deeper insights into the robustness of our approach. In the revised version, we will include an additional sensitivity study where we vary the size of the original subgraphs at each time step (e.g., scaling by factors of 0.3×,0.5×, 0.7×, and 0.9×).\n\n|Size of subgraphs|0.3x|0.5x|0.7x|0.9x|\n|-----------------|-----|----|-----|-----|\n|Cora(AA)|58.10|59.12|62.84|63.07|\n|Cora(AF)|-10.18|-6.32|-12.13|-12.31|\n\nThese results above indicate that performance variations are minor across different subgraph scales, demonstrating that our method remains robust and effective regardless of the size of the original subgraphs.\n\n> `Question1 `: Analysis of negative forgetting phenomenon\n\nNegative Average Forgetting (AF) indicates that knowledge from earlier tasks can be **reinforced** when learning later tasks. In MOTION, G-TMSC ensures structural consistency across tasks, so that features learned early remain useful, while G-EPAE aligns parameter updates to avoid overwriting useful knowledge. Together, these mechanisms allow later tasks to improve representations beneficial to earlier tasks, particularly when tasks share topological motifs. This explains the observed negative forgetting and highlights the benefit of explicitly preserving topology and managing parameter compatibility.\n\n> `Question2 `: Multi-expert architecture input decomposition\n\nWe agree that clarifying the rationale behind the inputs to the multi-expert architecture will improve the clarity of our work. Our design leverages **node-level** and **structural-level perspectives** to preserve critical topological information:\n\n1. Local connectivity (1-hop and 2-hop subgraphs) captures neighborhood density and structural roles of nodes, which are essential for identifying influential nodes and preserving local community structures during coarsening.\n2. Similarity metrics (e.g., cosine similarity, statistical distances) quantify feature alignment and semantic redundancy between nodes, enabling the architecture to merge nodes while minimizing information loss.\n3. Additional descriptors: Subgraph statistics (e.g., diameter, density) and degree embeddings further enhance structural representation.\n\nAll these features are concatenated and fed into the mixture‑of‑experts gating network, which outputs node importance scores used for pruning and noise suppression."}, {"review_id": "PVhRZUzguV", "reviewer": "Reviewer_7bbW", "summary": "This paper introduces MOTION method for federated continual graph learning that addresses the challenges of learning on dynamic, distributed graph data. The method maintains structural integrity through a multi-expert fusion process and optimizes global model updates using a topology-sensitive compatibility matrix. Experiments on benchmark datasets demonstrate the performance.", "questions": "1. Figure 2 needs to be redrawn to better illustrate the method. While visually appealing, it lacks specificity. For instance, Multi-Sculpt isn't shown, and some modules are represented by symbolic images, making it hard to link components to the method description (e.g., Expert Scores). A more detailed figure would enhance the reader's understanding.\n2. The specific method process is unclear and needs a more comprehensive explanation from the authors. In Section 3.2, please clarify:\n    - The construction of the node mapping table. How node features from other tasks are aggregated without saving the entire graph?\n    - How does the multi-sculpt coarsening framework systematically prune excess nodes and suppress noise?\n    - The process of the reservoir sampling-based dynamic memory mechanism.\n3. On line 215 of page 6, how can Parameters $\\Delta \\theta_k$ capture topological changes? The model parameters don't seem to have a direct link to the topological structure.\n4. In Table 1, too few comparison methods are used in the experiments. More graph federated learning and graph continual learning baselines need to be included.\n5. In Section 4.1, the experimental baselines are inconsistently referenced. The baseline names don't match the cited papers.\n6. It is better to computer the average of multiple runs to demonstrate the method's stability.", "limitations": "Yes", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths:\n1. The graph federated continual learning task is meaningful, with its challenges clearly defined.\n2. Experiments are conducted across five datasets, and ablation studies are presented.\n\nWeaknesses:\n1. The method's motivation and description are unclear. The framework diagram is too abstract to correspond with the text.\n2. Some baselines are missing in the experiments, and the baseline references are inconsistent.", "was_revised": true, "final_justification": "The research task of this paper is a meaningful one, but the specific description of methods lacks clarity and experiments are insufficient, which may affect the readers' understanding and the entire paper needs to be revised. The author's reply addressed some of the concerns, so I raised the score from 2 to 3.", "rebuttal": "Thank you for your thorough review and constructive feedback. We address your concerns below and hope these clarifications will help you re-evaluate and update the score:\n\n> `Weakness 1`: Clarifying for Improving Method Motivation and Framework Description\n\nWe sincerely thank the reviewer for the constructive feedback. The design of our framework aims to address two key challenges identified in our motivation and introduction: (i) **catastrophic forgetting** arising from sequential updates on evolving graph data, and (ii) **parameter conflicts** due to heterogeneous subgraphs. The framework diagram and textual description were intended to jointly illustrate these challenges and show how our two proposed modules—Graph Topology-preserving Multi-Sculpt Coarsening (G-TMSC) for **topology-preserving coarsening** and Graph-Aware Evolving Parameter Adaptive Engine (G-EPAE) for **conflict-aware parameter aggregation**—explicitly tackle them.\n\nWe also note that other reviewers like reviewer D7ZJ recognized the clarity of our motivation and framework design, stating that “this paper is clearly and effectively written, with a fancy and comprehensive visual representation of the framework” and that “the accurate and thorough explanations of the methodological components further contribute to its ease of understanding.”\n\nAt the same time, we fully agree that additional clarifications will further enhance readability. We have revised both the text and figure: (i) we have added transitional explanations and concrete examples connecting each design choice to the stated challenges, (ii) we have updated the framework diagram by simplifying icons, adding explicit textual labels, and ensuring each component directly corresponds to its description, and (iii) we have expanded the figure caption to explain all elements in detail. Thank you for this suggestion, which has helped us further clarify our motivation and framework, making them more transparent and easier to follow.\n\n> `Weakness 2 & Question 4`: Clarifications Regarding Baseline Inclusion and Reference Standardization\n\nWe emphasize that the current submission already reports extensive experiments (across Federated Learning (FL)/Federated Graph Learning (FGL)/Continual Graph Learning (CGL)/Federated Continual Learning (FCL) protocols, multiple datasets, and ablations on forgetting/retention) that substantiate the gains of MOTION. Addressing your concern and to further strengthen the evidence, we will add more baselines—**FedSSP**[1] for FGL, **SEA-ER**[2] for CGL. \n\n|Method|Cora(AA)|Cora(AF)|CiteSeer(AA)|CiteSeer(AF)|PubMed(AA)|PubMed(AF)|Amz-Photo(AA)|Amz-Photo(AF)|Coauthor-CS(AA)|Coauthor-CS(AF)|\n|------|------|------|------|------|------|------|------|------|------|------|\n|FedSSP|25.76|26.60|21.83|16.11|38.54|31.36|14.09|13.39|10.22|14.10|\n|SEA-ER|20.05|69.17|31.38|47.26|55.79|1.77|15.21|48.93|34.65|42.97|\n|Motion|**62.66**|**-8.34**|**49.08**|**-16.78**|**59.48**|**-24.17**|**79.09**|**-5.32**|**22.26**|**-11.62**|\n\nFrom the table above, MOTION achieves state-of-the-art performance across all evaluated settings.Due to the 10,000 character limit, we only include two additional baselines here, but the revision will provide a more comprehensive baseline set. We will also standardize all baseline names and citations to their official conference versions.\n\n[1]FedSSP: Federated Graph Learning with Spectral Knowledge and Personalized Preference. In NIPS,2024.\n\n[2]On the Limitation and Experience Replay for GNNs in Continual Learning. In CoLLAs,2024.\n\n> `Question 1`: Clarification of Figure 2\n\nWe sincerely thank the reviewer for the constructive feedback. As mentioned in our response to Weakness 1, we have further refined the framework description to explicitly link each design component to the method.\n\nBuilding on this, we will also revise Figure 2 to enhance **specificity**: (i) explicitly illustrating the Multi‑Sculpt process within G‑TMSC, (ii) replacing symbolic placeholders (e.g., Expert Scores) with **descriptive module representations**, and (iii) adding **clear textual labels** and a **detailed caption** that maps each visual element directly to its counterpart in the method description. \n\n> `Question 2`: Method process clarification\n\nThank you for your insightful questions. We have provided the following detailed answers:\n1. Our node mapping table assigns a unique index to each node based on a **hash** of its feature vector and **task identifier**. This allows incremental integration of new nodes without storing the entire historical graph. New nodes are added using a new_nodes_mask, and node-to-cluster and cluster-to-node mappings are updated. Feature aggregation is performed on new nodes while reusing stored features for previously seen ones, avoiding the need to store or recompute the entire graph.\n2. The multi-sculpt coarsening framework evaluates node importance with a Mixture-of-Experts (MoE) **scoring mechanism** and **similarity metrics** like degree centrality and cosine similarity. Low-importance nodes are pruned and mapped to similar retained nodes. Noise suppression is achieved through noisy top-k gating, activating only the most relevant experts. Multi-metric fusion stabilizes node ranking and reduces sensitivity to noisy features, enabling efficient graph compression while preserving topological fidelity.\n3. We use reservoir sampling to maintain a **lightweight dynamic memory**, storing a representative subset of nodes (default buffer size 200). New nodes replace existing entries based on observed frequency. A feature-based variant prioritizes nodes closer to evolving class centroids, ensuring the buffer remains representative. These replay nodes are protected during coarsening to preserve important historical information while minimizing memory overhead.\n\n> `Question 3`: Discussion of the relationship between parameter updates and topological Changes\n\nWe thank the reviewer for this insightful question. In our formulation, $\\Delta\\theta_k =\\theta_k-\\phi $ represents the difference between the parameters of client $k$ after local training and the current global parameters. These parameter increments inherently encode the information learned from the newly observed local task at client $k$, including adaptations to its evolving graph structure.\nHence, $\\Delta\\theta_k$ naturally reflects the topological changes of the local graph without explicitly transmitting raw structural data, enabling our framework to capture topology-sensitive knowledge in a privacy-preserving manner.\n\n> `Question 5`: Remarks on the inconsistent baseline references\n\nWe acknowledge the inconsistencies and will fix all citation and naming issues to ensure clarity and correctness.\n\n> `Question 6`: Analysis on stability of main results\n\nWe have already run all experiments with multiple seeds (5 random seeds) and report the average across seeds. To further substantiate this point, we conducted additional repeats and provide concrete numbers in the table below, showing that metrics are stable and the variance remains consistently low:\n| Seed | 3 | 4 | 9 | 42 | 62 |\n|------|---|---|---|---|---|\n|Cora(AA)| 62.80  | 63.47  | 61.27  | 65.24  |60.52|\n|Cora(AF)|  -7.40 | -8.19  |  -8.37 |  -8.98 |-8.76|\n\nAs shown, the values across different seeds are consistent, with an average of 62.66 with a variance of 3.46 for Cora(AA),and an average of -8.34 and a variance of 0.37 for Cora(AF). In the revision, all tables will explicitly report averages and standard deviations to underscore the method's effectiveness and robustness."}]

Author rebuttal:

Meta-review: In this paper, the authors study GNNs in distributed and evolving environments and propose Federated Continual Graph Learning (FCGL), i.e., incremental learning on dynamic graphs distributed across decentralized clients. The proposed method MOTION adopts a graph topology-preserving multi-sculpt coarsening module to maintain the structural integrity of past graphs and a Graph-Aware Evolving Parameter Adaptive Engine module to refine global model updates. Experiments show the effectiveness of the proposed method over baselines. 

The paper received mixed comments. The reviewers acknowledge the main strengths of the paper, including technical novelty in addressing an under-explored problem, FGCL, and strong empirical results. However, they also raise concerns, particularly regarding presentation and clarity issues. The authors have provided a rebuttal, which partially addresses the concern of one negative reviewer. The other negative reviewer remains unconvinced, but acknowledged that he/she is not familiar with the topic. I have briefly checked the paper and discussion. Despite the noted weaknesses, I think the paper makes a meaningful and timely contribution to FGCL, with a well-motivated methodology and convincing empirical validation. The identified issues are important but can be reasonably addressed in revision. I therefore recommend acceptance and strongly encourage the authors to further revise the paper in the future version.
Decision: Accept (poster)