GMV: A Unified and Efficient Graph Multi-View Learning Framework
Authors: Qipeng zhu
Jie Chen
Jian Pu
Junping Zhang
Venue: NeurIPS 2025 poster ()
Keywords: Graph Neural Network
Graph Classification
Primary area: deep_learning

Abstract: Graph Neural Networks (GNNs) are pivotal in graph classification but often struggle with generalization and overfitting. We introduce a unified and efficient Graph Multi-View (GMV) learning framework that integrates multi-view learning into GNNs to enhance robustness and efficiency. Leveraging the lottery ticket hypothesis, GMV activates diverse sub-networks within a single GNN through a novel training pipeline, which includes mixed-view generation, and multi-view decomposition and learning. This approach simultaneously broadens "views" from the data, model, and optimization perspectives during training to enhance the generalization capabilities of GNNs. During inference, GMV only incorporates additional prediction heads into standard GNNs, thereby achieving multi-view learning at minimal cost. Our experiments demonstrate that GMV surpasses other augmentation and ensemble techniques for GNNs and Graph Transformers across various graph classification scenarios.

GMV: A Unified and Efficient Graph Multi- View Learning Framework
Qipeng ; Chen': Jian Pu Junping Zhang
Shanghai Key Laboratory of Intelligent Information Processing,
College of Computer Science and Artificial Intelligence, Fudan University 2 College of Computer and Data Science, Fuzhou University
Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University qpzhu23@m. fudan. edu. en, jiechen202$fzu, edw. en, {jpzhang, jiaapu/@ffdaal edu. cn
Abstract
Graph Neural Networks (GNNs) are pivotal in graph classification but often strug- gle with generalization and overfitting. We introduce a unified and efficient Graph Multi-Vies (GMV) learning framework that integrates multi-view learning into GNNs to enhance robustness and efficiency. Leveraging the lottery ticket hy- pothesis, GMV activates diverse sub-networks within single GNN through a novel training pipeline, which includes mixed-view generation, and multi-view decomposition and learning. This approach simultaneously broadens "views" from the data, model, and optimization perspectives during training to enhance the generalization capabilities of GNNs. During inference, GMV only incorporates additional prediction heads into standard GNNs, thereby achieving multi-view learning minimal cost. Our experiments demonstrate that GMV surpasses other augmentation and ensemble techniques for GNNs and Graph Transformers across various graph classification scenarios. The open source code can be found in https://gthub..oo/smuriiiii
Introduction
Graph Neural Networks (GNNs) have emerged as powerful tool for graph classification tasks, attracting considerable attention. Despite their success, GNNs struggle with generalization and overfitting due to the complex nature of graph structures and the limited availability of labeled graph data [I 2. As shown in Fig simply increasing the parameters
GNNs does not consistently enhance their performance [3]. A promising solution lies in multi-view learning. which enables models extract diverse repre- sentations by aggregating complementary per- spectives of data [4 5 By forcing models to reconcile differences across views, multi-view learning offers a fundamental insight of diversity for enhancing model generalization.
GNN ST G-MIMO
GNN x2
GNN SabMis
SubGraah
Figure 1: Accuracy vs. memory/speed. Specifi- cally, "GNN x*" represent different sizes of GNNs.
Qipeng Zhu and Jie Chen are co- first authors. Junping Zhang and Jian Pu corresponding authors.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Existing graph learning strategies implicitly leverage multi-view principles but remain suboptimal. Graph data augmentation (e.g.. DropEdge [6. S-Mixup 77] diversifies input views via edge removal or graph interpolation, acting as "data-view" expansions. However, these methods often degrade structural integrity (e.g., random edge dropping disrupts critical topological hierarchies [], limiting their effectiveness structured graphs. Ensemble learning [9 T0] [1] achieves "model-view" diversity by training multiple GNNs, but at the cost of significant computational overhead as illustrated in Fig The need for separate forward passes across networks renders these methods infeasible for large graphs. These strategies treat data and model views in isolation, failing to exploit the synergistic power of multi-view learning.
In this paper, we introduce a unified and efficient Graph Multi View (GMV) learning framework. GMV is model-agnostic and expands views from three complementary perspectives data, model, and optimization activate diverse sub-networks within a single GNN. Inspired by the lottery ticket hypothesis [2). where neural networks contain latent sub-networks with comparable performance to the full model, we aim to overcome the challenge that standard supervised training fails to activate such diversity 13 4] Specifically, we design novel training pipeline integrating mixed-view generation and multi-view decomposition and learning.
During training, GMV employs a three-fold coherent strategy to unify multi-view learning. From data perspective, we propose structure enhanced subgraph mixing, which samples two subgraphs that preserve both the topological structure and semantic nodes to generate mixed graph views. This mixed view contains the multi-view knowledge and addresses the structural loss prior augmentations. From a model perspective, we introduce lightweight dual-output prediction head to explicitly activate two sub-networks within any single GNN and Graph Transformer (GT). This design enables parallel encoding of mixed views and wiew decomposition in one forward pass, eliminating the multi-model overhead of ensemble methods while preserving representation diversity. From a optimization perspective, we design multi-view and mixed-view loss functions. These two losses collectively supervise view-specific predictions and activate sub-networks to learn diverse multi-view representations. During inference, GMV processes standard graph input and simply averages dual- head outputs with single-mode efficiency. By unifying data, model, and optimization perspectives of multi-view learning, GMV provides generalizable solution for GNNs and GTs. As illustrated in Fig GMV achieves the best trade-off between overhead and accuracy.
Our contribution can be summarized as follows: 1) We introduce GMV, a unified and efficient multi-view learning framework that enhances the robustness and generalization of both GNNs and GTs in graph classification tasks. 2) We propose new structure-enhanced subgraph mixing techniques, accompanied by multi-view and mixed-view loss, to encourage models to learn from diverse graph views. 3) Our comprehensive experiments evaluate the efficacy, robustness, and generalization of GMV. GMV significantly improves GNNs/GTs and achieves state-of-the-a results compared to various graph augmentation and graph ensembling methods.
2 Related Work
Graph Neural Network. Graph Neural Networks (GNNs) leverage the message passing mecha- nism [4 [5] to aggregate and update node representations for graph data processing [66] 17 18].
The Graph Convolutional Network (GCN) [9] uniformly aggregates neighbor messages to update node embeddings. GrEphSAGE (20) introduces subgraph sampling with diverse aggregation methods for adaptive representations. The Graph Isomorphism Network (GIN) (1 further refines this by cap- turing graph isomorphism, enhancing model sensitivity to graph topology. Moreover, combining the GNN with transformer architecture, such as Graphomer [22] and GraphGPS (23), has also emerged in graph learning fields.
Multi- view Learning, In computer vision, multi-view data, typically derived from various perspec- tives with shared high-level semantics, has become a crucial data type [24.. Asif et al. [4] apply multi-view learning theory to multi-class classification, suggesting that each image has an inherent "multi-view" structure, where these "multi-view" structures correspond to multiple data features that can help deep neural networks in accurate classification. They demonstrate how multi-view learning can improve both the generalization and robustness of deep neural networks. While several multi-view learning strategies 25 26 27
28 29 have been proposed for graph tasks, their appli- cation to supervised graph classification remains challenging due to differences in task objectives

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and data characteristics. For example, Yuan et al. [27 generate node feature views for both labeled and unlabeled nodes node classification, whereas Liu al. (88] generate views based on pairs of positive and unlabeled graphs in graph classification. Both focus on semi-supervised learning. Compared to image classification, generating nixeddviews that preserve both structural and semantic information in graph classification is more difficult. In this paper, we propose generating mixed-views to activate dual sub-networks within GNNs, enhancing multi-view learning capabilities from the data, model, and optimization perspectives.
Graph Augmentation. We conceptualize graph augmentation as a specialized form of multi-view learning, aimed at expanding graph datasets through modifications. One approach involves randomly modifying the original graph while assuming the label remains unchanged, such as DropNode [30], DropEdge (6), and Subgraph [3.. However, the simplicity of these operations often limits the diversity of the resulting graph views and may introduce noise. Other approaches integrate mixup techniques 32 into graph classification. For example, S-Mixup 7 aligns pairs of graphs using soft alignment matrix derived from trained Graph Matching Network (GMN), followed by linear interpolation of the aligned graphs. Neverthcless, the complexity and resource demands of training an effective GMN often lead to suboptimal performance due to inadequate mapping. Techniques [34] connect subgraphs sampled from different graphs to facilitate model-agnostic graph augmentation. However, these methods do not fully exploit the sub-views of graphs and often neglect structural information. In contrast, GMV effectively integrates structure- eenhanedee sub-views to generate mixed views, while utilizing a multi-view decomposition and learning pipeline to extract diverse view representations.
like SubMix 33 and GraphTranspin
Ensemble Learning. Ensemble learning 9 4 35 aims to improve the robustness and generalization of single model by combining the outputs of multiple models. This approach, however, comes with high computational and memory demands. The Lottery Ticket Hypothesis [12 posits that dense neural networks contain sparse subnetworks ("winning tickets")) capable of achieving comparable performance when trained isolation, which suggests the possibility of ensemble learning with these subnetworks. In the realm of image classification, MIMO [3] introduces multi-input multi- output techniques to ensemble sub-networks within a single convolutional neural network. Despite these advancements, applying ensemble learning effectively to Graph Neural Networks (GNNs) remains a challenge, primarily due to the arbitrary sizes of graphs. G-MIMO [37] addresses this by implementing graph multi-input and multi-output schemes, adding multiple parallel graph encoders and decoders. However, this approach complicates the forward passing process in GNNs and struggles with limited graph views. In contrast, our proposed method, GMV, minimizes transformations for GNNs and achieves efficient ensembling through a single forward pass, efficiently enhancing the multi-view learning capability.
3 Method
To enhance the robustness and generalization of GNNs through multi-view graph learning, we simultaneously increase the diversity of input graph views and the multi-view learning capabilities of GNNs. As illustrated in F we first outline the process of mixed-view generation. Then, we introduce details of mixed-view decomposition and multi-view learning, which activate dual sub-networks within a single GNN for efficient ensemble.
3.1 Preliminaries
An undirected graph 9 =< V, >, where = S i n) represents the set of nodes, and & = (Eil/; E VA É V o is connected to 0z} is the set of edges. The matrix X E IRa contains the node features, while A E 1] x is the adjacency matrix where Aij = nodes v; and 8y are connected. The degree matrix D E _ga has entries D,; = E,A, on the diagonal, with Dij = for i * j. Each node v; E V has a neighborhood set, denoted (v;;;) = (ryl |o; is connected to Uj A my E V). For graph classification, collection of n undirected graphs represented as = ((9e. y.) f where y, E (0. 1,..., ,.. 1} denotes the label for each graph G. and C' is the number of classes.
3

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Triining buckward
PPR
Sompling
Testing inforence
Egg
Viewarc
POR
rundemly sample
Sress
Gard Suy
GNNGG
G/(9)
Bug
Viow
Eston
9
Score
Guex
VieWatx
Structuneennlmred
Sumpling
9wc
/ 2
(a) Mixed-view Generation
(b) Decomposition Learning
Figure 2: (a) For data perspective, GMV connects two structure enhanced subgraphs to generate the mixed-view. (b) For model perspective, GMV employs dual sub-networks in GNN/GT to gain diverse view representations, denoted as multi-view decomposition. For optimization perspective, we design the multi-view learning process with multi-view (Eview) and mixed-view loss (Emix) optimize dual sub-networks. When testing, GMV simply averages two predictions of dual sub-networks in GNN/GT as the final output.
3.2 Mixed-view Generation
From data perspective, we explore how to integrate diverse views from different graphs into single graph, allowing the GNN to process them concurrently and activating sub-networks to learn multi-view representations. Unlike previous graph augmentations [6 31], method explicitly considers the critical structural information (38] to generate a mixed graph view. This is achieved through structure-enhanced subgraph sampling, followed by structure-enhanced subgraph mixing.
3.2.1
Structure Enhanced Subgraph Sampling
Unlike random corruption of graphs 6 [00, sampling subgraphs preserves more semantic informa- tion [39 We employ subgraph sampling methods to construct richer views. A key challenge is exploring various subgraphs that encapsulate the most crucial semantic and structural information. Compared to randomly sampling [40], subgraph sampling methods based on Personalized PageRank (PPR) [41] and Determinantal Point Processes (DPP) 42 can enhance the performance of GNNs without altering their architectures. However, the PPR-based method does not explicitly preserve the structure of the original graph, while the DPP-based method may overlook some key nodes due to its limited search scope. Considering that topology information effectively preserves label information during subgraph sampling 44, we propose a novel STructure Enhanced PPR subgraph sampling method (ST-PPR), which considers both key nodes and structural information.
The specific process outlined in Algorithm [ We first pick a random root node from the graph G. We consider both structural and semantic information of G by merging different node candidate (DFS) algorithm and Sreath-First-Searre easily extract the original topology structure of G. And the PPR algorithm considers semantic information by iteratively calculating the importance score of every node in g [33). Therefore, we respectively use DFS, BFS and PPR methods to gain sampling node set (Brrs, Vors. VPPR) from G. We set w as the maximum searching steps for DFS and BFS algorithms. To preserve those important nodes, calculate the affinity personalized pagerank score matrix SppR 41 follows:
sets 44 Depth-First-Searce
(BFS) algorithm (45) can
20
SpPR Σ 8(1
88(1 33" (D DD-1/2 (ID-111
(I)
where and A respectively the degree matrix and the adjancy matrix of G and I the identity matrix. We set teleport probability 8 as 0.15 and affinity scores of nodes with respect to node

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are contained in Sppk/:. u|. Then we sort nodes in 1/ following the scores SpeRI:, u] and select top Sppr nodes get the node set Ver- And BES and DPS both contain 82 nodes respectively sampled from Vprs and VErS- We merge three node sets (VPpR DFS VERS) and reorder nodes by SppR ( v)
to obtain V.
Algorithm Structure Enhanced PPR Subgraph Sampling
Input: Graph 9 =< V,,, A, >, augmentation ratio of (0, 1), structure augmentation ratio of q. number of walks w
Output: Ordered node set V
1: v + pick a random root node from G.
2: sppr + sample size is max (O, p) 9 q, 0} SppR
3: 82 + sample size is L(p-
2]
4: Sppr compute score by PPR(G,r)
5: VPpr f So SPPR [., u)), VPR + [: sPpR
6: VDFS DFS(G, v, w), DES
Sample VDFS, $2)
7: VEFS + BFS(G, w), V BFS + Sample VBFS, $2)
8: V & merge (ViER, DES: VAESs and sort them by SPPR
Combining PPR, BFS, and DFS, the sampled subgraphs covers global hubs, local communities, and long-range paths. This ensures comprehensive feature extraction including global topology hierarchical transitions and local communities, which boosts the performance of GNNs. The proof stated in Appendix 6.1
3.2.2 Structure Enhanced Subgraph Mixing
To enable GNNs to effectively process diverse views simultaneously for multi-view learning, we integrate these views of diverse sub-grat sub-graphs into single mixed-graph. Inspired by SubMix [33]. we propose a STructure-enhanced Subgraph Mixing method (ST-SubMix), which connects two subgraphs according SubMix connects two structure-enhancel subgraph views, thereby preserving more structure and label information from original graphs. The specific process is detailed in Algorithm 2
node mapping algorithm based SppR- Compared to SubMix, ST-
Given a source graph (a primary training sample within a given batch), Gue, we randomly sample target graph (another graph from the same training batch), Gug from G/[G.r) We connect two subgraphs sampled from them to generate Gmix- According to Algorithm we gain V and V respectively sampled from Vare and Vug. To ensure the equality of sizes between V and Vig. we let 8 = min (ve, Vug), }- To efficiently mapping two node sets, we make the one-to-one mapping from V to Vig. As shown in Fig 2
we connect GhT and Gug/ Gug//'1pp Gig. which ensures the size distribution of graphs keeping the same the original distribution [33]. Specifically,
replace the subgraph G' in the graph GAn with the subgraph Gig. To represent the label of the mixed-view, we calculate the confidence of labels of two graphs. As descrihed in Equation (2), the confidence measured by the count of edge sets within it:
Wsr 1 1Eng Wug 1/
The procedure in AggrrithmTouulinsss subgraph interpolation method for graph augmentation. It first establishes canonical node correspondence between source (G.re) and target (Gug) graph by ordering their respective nodes via Personalized PageRank (PPR) scores, following the SubMix methodology. This alignment guides the replacement of a target subgraph with its source counterpart to generate mixed-vies graph. For downstream representation decomposition, two binary assignment matrices, Esrc and Etrg, are constructed. Each row is a one-hot vector indicating if a node in the mixed graph originates from the source or target. The property I E.re + Eug ensures a disjoint partition of the node set, which is used to separate the view-specific representations from the mixed-wa -iew output.
5

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Algorithm 2 Structure Enhanced Subgraph Mixing
Input: Graph 9m =< Vaac Exte, As,, X 2, Graph Gug =< Vag: Eng. Aug. X Xug
Output: Mixed graph Gmix =< Vmix, Emix, Amix. Xmix 2, assignment matrices Exr,, Eug. confidence
of labels of two graphs Ware Wing
V. Ving 6- -sample subgraphs respectively from Gsc. Gug ST-PPR based Subgraph Sampling
2: min([Varcl. 1/gl
3: V + Vscl: s), Vig < Viyl:
4: @ + Make the one-to-one mapping from Ve to Ving
5: Eng - f(uu v((u,)) E Eng -(u Ving AUE Ving) 6: &g +- ((d(u)) (())))(u,)) E E A (u E VA A E )(
7: Vinx, Emix: Xmix <- Vag. Egre U ing Xirg
8: X (mix(o(Va)))) &- Srro [V
9: Amix f- densify
edge set Emix
10: Ware; Wag + 1 - |E / ////mm /
11: Ege, Eug + one hot vectors to record nodes in Vmix originated from V and V
3.3 Multi-view Decomposition and Learning
From a model perspective, ensembles of diverse neural networks can be seen as learning varied representations of views, thereby improving generalization [4] However, combining several networks with multiple forward passes leads to high computational costs.
We introduce an innovative pipeline for multi-view decomposition and learning, which activates two sub-networks within a single GNN with minimal computational overhead. During training, we utilize a dual-output predictor with mixed and multi-view loss functions ensure the learning of multi-view from an optimization perspective.
3.3.1 Mixed-view Encoding
We utilize standard GNNs to encode the mixed-view graph Gmix. which typically leverage repeated message passing process. The process of the 1-th message passing MPNN((-) GNNs formulated as follows:
MPNN,
(1-1)) mix
Amix)
mix
where (0) denotes the I-th layer output of our GMV. We consider the node features Xmix of Gmix as ( mix during training. The output of the mixed-viee view encoder in GNN as (L. mix
Moreover, we also consider GraphGPS (23 as the shared graph transformer backbone. For each layer of GraphGPS, it consists of three components, including (-)N, GlobalAttn/() and M-),(-). Therefore, the process can be decribed as follows:
H mix
3.3.2 Multi-view Decomposition
Diverse views offer greater evidence for GNN to classify graphs. Given mixed-view representation (L)
mix we introduce a Multi- View Decomposition (MVD) to obtain three view representations, denoted as (View; E {sre, trg, mi }. The MVD can be formulated as follows:
View, E. I.)
(5)
where (Eę | E (src, trg, mix}) are assignment matrices, which are calculated in Sec 3.2.2 Then, utilize common pooling layer [2T 46 47. denoted as Pool(-), ), to respectively readout graph representations of diverse views, i.e., [p: i E {src, trg, mix)]:
p; = Pool (ieww).
(6)

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Method
PROTEINS
NC1109
REDDITB
REDDIT-MS
COLLAB
#graphs
1000
1113
4110
4127
2000
1500
4999
5000
#classes
havg modes
19.8
39.1
29.9
29.7
429.6
13.0
508.5
74.5
#avg edges
96.5
72.8
32.3
32.1
497.8
65.9
594.9
2457.2
Vanilla
72.30 72.30:24.34
72.15::3.75
72.38
70.27=2.66 68
87.60
49.001 3.96
50.83=3.992
$1.16:1.77 1.72
DropEdge
72.10:t4.21
73.41+44225
73. 73.94=2.73
67.19-2.42 22
89,25=3.03
48.87+3.077
50.29=2.21
81.56=00.88
DropNode
73. 23.30++2.76
72.69++4425
73.07-22.96
69.76-139
88.45+22.4
39.933
53.73-2.98
81.50++2.3
Suhgruph
72.70.1.5.16
73.05.13.70
72. 2..30
69.13
29.301..61
49.271.383
50.09 3.45
1..42.1.21
M-Mixup
73.70:44.11
72.15+44.26
65. 16-22.448
62.92-2.15
87,60+3.67
49,80+3.90
48.91=2.08
75.58++1.22
GCN
G-Mixup
73.20-1:5.60
71.18-33.72
72.75
72.23-2.50
86.85
49.33-1-.667
51.77=
81.17
Suhmix
73.80:13.55
73.50.15.38
82.91-8225
37.90
49.0013.75
S-Mixup
72.
72.50:+2.20
72.42:24.19
67.27=22.35
69.57-2.56 56
88.50=11244
49.93:33.51
$1.69=2.21
81.4811 1.28
Ensemble
73.60=t4.63
72. 72.60:+3.445
73.58=22225
20.29-2.26
90,45=1.75
49.60-t4.26
53.35=2.59
82.52++10
G-MIMO
72.70:22.53
73.41244.37
76.16:2.47
72.16=3.16
1..15
50.93:1345
54.05=4.05
82.36 1.53
GMV
75.50+3.677
74.67=5.84
76.96=2.33
76.86=2.15
21,40=2226
51,53+2.58
54,15=3.15
83,92=1.75
Vanilla
71.7011.100
64.70.16.42
78.47.1241
78.97
90.1011.77
48.67.
53.89-..115
80.48 1.33
DropEdge
71.70144.03
68.29914.01
76.45=2.76
75.33=2.02
89.90=2.17
50.00144.38
54,19=2.23
79.78=1.65
DropNode
74.00+t4.63
72.51+2.53
18.98=1.86
78.77=1.92
90,55=1.92
51 31.00+3.000
55,23-2.34
80. 16 1.71
Suhgruph
73.20-4-3225
72.244+5.76
77.57+2.71
77.32-1.71
88,50--2.77
49.07+3.84
53.37-2.61
80.66 1.75
M-Mixup
73.10:t4.21
71.97+3.75
78. 28.52=22.05
81.03=0.88
82.25=3.87
80::3.90
51,49=2.01
10.18
GIN
G-Mixup
72.40+45.64
64.69++3.60
78.20= 1.58
79.75-2.70
90,20+2284
99-933-2282
54.33-1.99
80. 00.18+1162
Suhmix
72.50:14.94
69.8111.577
82,90 2.45
81,04 1.57
90,20
49.80114.22
14.59-1.29
1.76
M-Mixup
72.80:1.3.82
67.57.13.50
69.03:1161
69.57
87,001:.225
48.5313.38
$2.75-2.53
79.5011.22
Ensemble
74.00=t3.10
33.50:33.04
80.34 56
80.15=1.8 83
92.70=1887
49 80#:2.91
55.19=2.58
81.58=1.55
G-MIMO
73.70.12.65
1.83
91.50
50.40.14.78
81.2411.50
GMV
74.20:1.337
74.40:13.95
22,38=2.15
82.53_1.95
92.50=1.00
52.27
55.35=2.41
83.02=1447
Table 1: Comparison between GMV and other baselines are conducted on TUDataset benchmark.
3.3.3 Multi-view Learning
During training, we employ three-layer multilayer perceptron (MLP) as a predictor simultaneously classify diverse views. Unlike traditional ensemble methods, we simply double the output dimension of the predictor, transforming it into dual-output predictor that generates two outputs. It can guide the shared backbone to facilitate the cost-effective realization of two sub-networks:
$!.9? Predictor(p:),
where i e {src, trg, mix]. Moreover, to optimize GNN with these diverse views, we propose the mixed-view loss mix and the multi-view loss Eview:
emix Wer CE($ mix Vsre) + Wing CE mix Ving).
(8)
Eveew CE(Vlee )ssc) + CE ug Yug),
(9)
Wsre and Wing are considered as confidence labels two graphs, calculated in Equation 2 The mixed-view loss eii helps GNN inferring partial labels of Gue and Gug. playing role of regular- ization, while the multi-view loss Eview directly boosts the capacity of diverse view representations of GNN. These two losses collectively improve the diversity of sub-networks integrated into GNN, enhancing the generalization and robustness:
fix + alvieww + R(f),
(10)
where l is the final loss, is the hyper parameter and R(0) denotes the regularization item, e.g., l2 norm. The detail of mieti-view learning process is in the Algorithm 3 of Appendix 6.2
3.4 Inference
During inference, GMV processes unseen input Grest via standard forward pass. The primary distinction of GMV from standard GNNs lies its dual prediction heads. Unlike the training phase, subgraph processing and multi-view decomposition are not required during inference. The final prediction is obtained by averaging the outputs of the dual prediction heads. This approach effectively acts efficient ensemble within single model, leveraging the benefits of multi-view learning:
1 Σ fo (5(m) gres) m=1
fo (fuss Wss Guex)
(11)
7

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Experiments
Baselines.
GCN 19 GIN are uti- lized GNN backhones, and GraphGPS [23] selected as
Method
HIV
ВВBP
BACE
PPA
#graphs
41127
2039
1513
158100
the GT backbone. We evaluate our effectiveness of GMV com- pared with graph augmentation methods, such as DropEdge [6.
#classes
tavg nodes
25.5
24.1
34.1
243.4
#avg edges
Vanilla
75.38++0.21
65.74=0017
71.74=0.233
68.33 +-0.33
Submix
75.63-+0.11 17
65.90+-0.54
78.00+00322
68.97 +-0.39
DropNode 33) Subgraph [31]
GCN
G-MIMO
75.97:+0.18
65,87=0
78.23=0.35
70.02 +0.32
M-Mixup [8] G-Mixup [49
GMV
76.16:20.15
66.18::0.10
78.51=0.32
70.21 00.21
and SubMix [33]
Vanilla
76.01=0.11
06.34-0.32
78.42=0.42
=0.18
Submix
77.00:10.46
67.67:0.299
78.93=0.43
70.43 10.23
For ensemble learning 2 we consider an classic ensemble and G-MIMO 37 For fair compar- ison, we only consider ensemble of two networks/sub-networks.
GIN
G-MIMO
77.43.10.23
68.38.10.48
78.8910.13
70.08 10.18
GMV
78.23-+0.43
68.56-0.31
7..43-0.28
71.56 +-0177
Vanilla
77.53-10.80
67.84+1166
80.54+
80.15+-0.12
GraphGPS
78.47400.4
68.38+1.221
81.21+0,255
80.60+0.35
G-MIMO
78.65=+1.04
68.78=0.88 86
82.07=2.599 70.32:0094
80,88=0.21
GMV
80.23++1.02
83.99=0.17
81.21
Experiment Details. For each method, we conduct 10-fold cross-validation experiments on each dataset from TUDataset Benchmark, calculating the mean accuracy and standard deviation to derive results. Following S-Mixup 77. the datasets are split into training. validation and test sets. Specifically, 80% for training. 10% for validation, and 10% for testing. For the datasets from OGB Graph Banchmark [50], we adopt the public vrain/vllidation/test splits, and report the results of the test set. We conduct each experiment three times and utilize area under curve (AUC) measurement on these OGB graph datasets. All experiments are conducted on NVIDIA 3090TI GPUs.
Table Comparison between GMV and other baselines are con- ducted on four OGB benchmark datasets.
Datasets. We consider different sizes and numbers of graphs to evaluate the performance of our proposed method. Table [ and Table 2 outlines the specifies of eight real-world datasets from the TUDatasets benchmark [1] and three datasets from open graph benchmark (OGB) [52].
4.1 Overall Comparison
Table [ and presents the results of GNNs with GMV alongside other baselines across eight benchmark datasets from TUDataset and four benchmark datasets from OGB. By simultaneously incorporating multi-view learning from the perspectives of model, data, and optimization, GMV significantly improves the average accuracy of both GCN and GIN on the TUDataset benchmark datasets. Unlike other graph augmentation and ensemble methods, which typically expand the "view" from a single perspective, GMV offers a unified and efficient approach.
To evaluate the effectiveness of GMV on large-scale graph classification tasks, we use the widely adopted GraphGPS (33 as the backbone for experiments on OGB datasets and TUDataset. As shown in Table 6a and Table [ GMV achieves the best performance across all tested datasets. This approach has established state-of-the-an results, further highlighting GMV's superiority over traditional methods. In Appendix 6.3 Table 6 we also conduct experiments state-of-arts GNNs.
4.2 Generalization and Robustness
Limited Labels for GMV. Following NoisyGL [53] conduct the comparison study limited and noisy labeled graph data to demonstrate robustness and generalization of GMV. We adopt 75%, 50%, 25% and 10% training label ratios to verify the generalization of GMV. As shown in Fig F a)) GMV consistently outperforms other methods with different label ratios, thereby achieving great generalization.
Noisy Labels for GMV. simulate label noise, we randomly corrupt 10%, 20% and 40% training labels IMDBB and PROTEINS datasets, while keeping validation and testing datasets unchanged.

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2014
105
175
175
315
105
105
Raii
M-Ntisp
(a) Limited Label Study
Noisy Label Study
Figure 3: Comparison study between GMV and other methods for different ratio of label/varying levels of label corruption on IMDBB and PROTEINS for GCN.
Vanilla
Random
PPR
BFS
DPP
DPP w. BFS
ST-PPR
IMDBB
72.30.12.4
72.7015.16
73.0014.33 73.05+3.70
72.60.2.37
72.60.3.69
73.20.14.26 72.63++2.61
74.1013.01 1.62
PROTEINS 72.15+3.75
72.60+2.37
12973+1190
1..84+1.77
Table 3: Comparisons among different subgraph sampling methods for GCN.
As shown in Figure GMV achieves better results under different noisy condition, which evaluate the robustness of it.
4.3 Ablation Study
Comparison of View Generation Methods. We first compare the effectiveness of our proposed ST-PPR with other subgraph sampling methods. Vanilla indicates the GCN without graph augmenta- tions. As shown in Table 3 our subgraph sampling method achieves the best performance among them because it considers both structure and semantic information. Moreover, we investigate the effectiveness of ST-PPR, SubMix and ST-SubMix. As depicted in Table [)), ST-SubMix achieves higher accuracy than SubMix by considering the property the structure. In Appendix 66.4 Table 7b) we also compare different graph augmentation methods for G-MIMO to generate richer training samples. These methods yield lower accuracy than GMV, thereby verifying the effectiveness of GMV,
Ablation of MVG and MVD. We examine the efficacy of mixed-view generation (MVG) and multi-view decomposition (MVD) for GMV (GCN) the IMDBB and PROTEINS datasets. The results, reported in Table (b). show that both MVG and MVD play crucial role in enhancing performance. Combining these two achieves the best performance, which implies that expanding views from both data and model perspectives simultancously can help the model learn better multi- view representations. More details can be found in the When only "MVG" is applied, GMV enhances GNN performance from a data perspective, playing same role of ST-SubMix. In contrast, with only "MVD" GMV boosts GNNs from model perspective. With consistent graph pair inputs, GMV modifies the GNN structure in manner the same as G-MIMO 37 Unlike simply increasing the size of the prediction head (54 this approach leverages distinct graphs to activate different sub-networks within the GNN, achieving simple ensemble. These two methods respectively improve of GCN, as shown in Table 4b
Loss. Additionally, we conduct an ablation study to verify the impact of mixed-view loss and multi-view loss in the GMV framework on the IMDBB dataset. As shown in Table4icc) these two losses collectively enhance the accuracy of the GNN. When we only adopt each of these losses, GMV achieves lower accuracy than when both are considered. Therefore, both losses are necessary to encourage sub-new bub-networks to learn from mixed and multi-views, thereby enhancing the multi-view learning ability from an optimization perspective.
Ablation of Mixed-view/MMltti-veee
4.4 Efficiency Study
During inference, GMV requires only a single forward pass of standard GNNs with an additional prediction head. Consequently, GMV's time complexity is nearly identical to that of standard GNNs, as illustrated in [ig where GMV demonstrates the optimal balance between accuracy and computational overhead. As for training, the mixed-view generation process can be preprocessed only once to obtain sampled nodes for each graph, therefore significantly accelerating the training

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Methods
IMDBR
PROTEINS
PROTEINS
Au.
IMDBR
PROTTENN
72.15+3.75
72.50+-4.34
72.15+3.75
72.15+33.5
SubMix
23.8013..57
73.5015.38
74. 14.10.33.66
74,8015988
74.55+2.52
74/00=2.88
ST-PFR
74.00:33.01
72.87:24.00
72. 22.70
73.41
74 55:5313111
73.87:1.95
Sabbixiix
7..00::306
74,0015.98
75.50 35.50:3307
74.67:584
75.50.13077
74.07-5.44
(a) Comparison of VG
(b) Ablation of Components
(c) Ablation of Losses
Table 4: Results of ablation studies. (a) Comparison of different view generation methods (VG)
including our proposed ST-PPR and ST-SubMix. (b) Ablation of two components of proposed GMV. (c) Ablation of our proposed mixed-view loss (fiiz) and multi-view loss (Eviem).
Disggne
DxL
Accuracy
0.70
20
Vanilla
70.27
Trashing
Submix
0
72.91
0:10
Ensemblee
10.02
1.56
70.29
DRAN
G-MIMO
1.63
GMV
13.40
5.41
76.86
0.2
10r 15t.
200 250 300
102 150 200 250
50 100 150 207 250 300
Table 5: Comparison of predic- tion on NC1109 between dual sub- networks of GMV and baselines within GCN.
Figure 4: Training Time v.s. Training/Validation/Teetii Loss on IMDBB.
process. Specifically, given Gare and Gug. the time complexity of mixed-view generation process O(Varl + |ugl)). We monitor the evolution of training and validation loss over time in Fig 4 While the vanilla GCN converges fastest, it suffers from significant overfitting. In contrast, graph augmentation techniques like M-Mixup and Submix, along with the ensemble method G-MIMO, help mitigate overfitting to some extent. our GMV framework inherently functions more powerful regularizer compared to these standard methods. This is evidenced by GMV achieving lower validation loss and, consequently, better generalization to the test set.
4.5 Quantitative Study of Diversity.
We evaluate the diversity of predictions made by GCN within GMV and other baseline methods on the NCI109 dataset. We employ disagreement
and average Kullback-eibler divergence [13] (DKL) as diversity metrics. Suppose fi and fe are two net-)sneworkks Disagree is computed as Σ (g) * f2(9)), where (()) equals 1 only if (9) # fz(G). DKL. is calculated
GEU
(Eg, (log ú2 log + Eg, log(uı log (2). As shown in Table 5, GMV achieves higher Disagree. DKL. and accuracy, indicating an enhanced capacity to represent diverse views for better generalization.
as of (KL ((2)) + (L
Conclusion
We have introduced GMV, unified and efficient framework that significantly enhances the robust- ness and generalization capabilities GNNs/GTs in graph classification. During training, GMV encourages GNNs/GTs to explore diverse views by integrating data, model, and optimization perspec- tives through a mixed view generation and multi-view decomposition and learning pipeline. During inference, GMV appends an additional prediction head to standard GNNs/GT's enabling superior performance a single forward pass with ensemble-like behavior. Our extensive experiments across various datasets demonstrate that GMV consistently outperforms existing augmentation and ensemble techniques, establishing it as a highly effective and promising method to improve the performance and generalization of GNNs/GTs.
Acknowledgments and Disclosure of Funding
This work is supported by National Natural Science Foundation of China (NSFC 62176059, 62576103). The computations this research were performed using the CFFF platform of Fu- dan University.
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6 Appendix
6.1 Proof of ST-PPR Algorithm
Theorem: Let subgraph sampling strategy S generates subgraph. Define structural preserva- tion score p(gs) as the graph kernel similarity between 93 and the original graph p(g.)
(e()), where of-) is graph kernel mapping function. For any graph G, there exist constants 62, 63 such that: p(Ginte)) 2 max (p(GvoR), ((Gnrs), ((DDEs)) Einteg: where eineg represents the gain from integration. This ensures comprehensive feature extraction including global topology. hierarchical transitions and local communities, which boosts the performance of GNNs.
[((())))))))
Proof: PPR selects high- nodes via its stationary distribution π. For any node u, its PageRank Aes
value satisfies: (u)) Evey (()) d(v) + (1 a))(u), where d(u) is the degree of u, and (())
is the initial distribution. High-r(u) nodes form the backbone of G, ensuring p(pPpR) 2 For any node u, its local clustering coefficient Cu) in BFS subgraph satisfies: CBFS(") (u) 2 Ca(u) 61, where d1 bounds sampling error. Thus, p(Brs)) 2 DFS retains long-range dependencies. Let D be the diameter of G. The diameter of the DFS subgraph Dors satisfies: DDrS D 82, where 82 bounds path truncation error. Hence, p(GDrs) 2 63. The joint structural representation is: ((integ) = ((PPR) @ ((GRFS) (GDES)) where @ denotes node concatenation. By linearity of kernel functions: p(Gimeg) 2 max (p(GopR), ),pp p (GrFs), p(Gres)) When structural information from three strategies non-overlapping. finteg
6.2 Algorithm of Multi-view Decomposition and Learning
Algorithm 3 Multi-view Decomposition and Learning
Input: Graph dataset G {(G,, ye) )e the graph model fCMv, loss weight a Output: Trained graph model fGMV
1: while not convergence do
2:
for src = n do
3:
Guy: Ying randomly sample graph from (
4:
Gmix: Egrc, Eug. Ware: Wing +- employ ST-SubMix between graph Sue and Gug
ST--ubMix
5:
Usees Vug. Wiitio Haix + fGMV Eve, Eug)
6:
emix +- Were CBC(in Morc) + Wing CFCCCi Uurg)
7:
Eview + -CE(ii Vsac) ) + CCC Mag)
8:
[ L+llis + allvve +R(#)
9:
Update parameters of the model fawv end for
10:
11: end while
In Algorithm 3 we generate mixed-view and feed it into the GNNs. We then perform multi-view decomposition and predict the labels for each of the decomposed diverse views. To activate the dual nub-networks in the GNNs, minimize both the mixing loss and the multi-view loss, thereby enhancing the multi-view representation the GNNs.
6.3 Comparison Study
To validate the efficacy of our proposed GMV method, we conduct a series of comparison studies. As shown in Table 6al within the GraphGPS framework, GMV outperforms baseline methods, including Vanilla and G-MIMO, on both the IMDBB and PROTEINS datasets. Furthermore, to examine its generality, we apply GMV to several mainstream GNN backbones. The results in Table 6b indicate that GMV can serve GatedGCN, GINE, and NSA (55) across multiple molecular graph datasets, thereby demonstrating its broad applicability and effectiveness.
plug-and-play module, consistently improving the performance of
20

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HIV
BBBP
BАCE
Method
IMDBB
PROTEINS
GatedGCN
76.39
67.05
78.75
/w. GMV
77.04
69.43
79.86
Vanilla
74.50 +4.53
74.76 + 3.24
Submix
75.34 13.68
75.21 11.4
GINE
76.45
67.56
77.91
G-MIMO
75.68
+4.34
75.08
#3.32
/w. GMV
77.76
70.30
78.82
GMV
76.70
1:322
75.78 14.13
NSA (55)
84.0
72.0
(a) Comparison on GraphGPS framework.
/w. GMV
85.50
74.1
(b) Comparison on different backbones.
Table 6: Comparison studies evaluating the effectiveness and generality of proposed GMV
method. (a) Performance comparison against other methods on the GraphGPS framework. (b)
Generality study by integrating GMV with different GNN backbones.
6.4 Ablation Study
Ablation of Mixup. From a data perspective, we compare various mixup strategies for mixed-view generation. As shown in Table 7a GMV consistently achieves higher accuracy than other mixup methods, demonstrating its effectiveness. The full GMV enhances the ability of multi-view represen- tation from data, model and optimization perspectives, including mixed-view generation, multi-view decomposition and multi-view learning. M-Mixup linearly interpolates graph representations to create mixed-views, making it difficult to apply multi-view decomposition and learning. S-Mixup uses trained graph matching transformer to map the source graph to the target graph, which distorts the information of the source graph and hinders multi-view decomposition and learning. "GMV w. M-Mixup" and "GMV w. S-Mixup" only employ mixing loss to optimize dual sub-networks within GNNs. In contrast, SubMix and ST-SubMix generate mixed-viewe by connecting subgraphs, preserving subgraph view information, and enabling them consider three perspectives concurrently, "GMV w. SubMix" and "GMV w. ST-SubMix" simultaneously consider mixed-viee -iew generation, multi-view decomposition and learning to enhance the performance of GNNs. Consequently, they outperform GMV with other mixup methods. SubMix focuses on semantic information, while ST-SubMix considers both structural and semantic information to create structure enhanced subgraph views, thus achieving state-of-the-ee performance and generalization for GNNs.
Further Comparation with MIMO. In this section, we perform additional experiments on G- MIMO with various augmentations and observe that graph augmentations combined with ensemble learning enhance GNN performance. As shown in Table 76b integrating G-MIMO with drop based augmentations improves GCN accuracy on IMDBB. Different augmentations create diverse views
Method
GCN
GIN
Method
Accuracy
Vanilla
72.30- 31.70++3.10
Vanilla GCN
72.30-12.84
M-Mixup
73.70=4.112 43.10
G-MIMO
72.70+22.53
S-Mixup
72.50-2.220 33.80
G-MIMO W. DropNode
43.30
SubMix
73.50 72.50
G-MIMO W. DropEdge
72.50+22.4
ST-SubMix
74.00=3.66 74.50+3.32
G-MIMO w. Subgraph (R)
73.40=44.15
GMV /w. M-Mixup
72.30-22.33 14.19
G-MIMO w. Subgraph (PPR)
74.10
GMV /w. S-Mixup
73.10=4.12 14.00:4.115
G-MIMO w. Subgraph (ST-PPR)
74.40-44.33
GMV /w. SubMix
75.00=4.28
10.3.223
GMV
75.60-13.67
GMV /w. ST-SubMix
75.50-3.67 74.20
(b) Ablation on augmentation types.
(a) Ablation on mixup methods.
Table Ablation studies on the IMDR-BINARY dataset. All results are based on the GCN backbone. (a) Comparison of different mixup strategies. Our full model, "GMV /w. ST-SubMix", achieves the best performance. (b) Comparison of GMV against various augmentation techniques used in G-MIMO.
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that boost performance of G-MIMO. The utilization of mixed-view generation provides richer view information, activating sub-networks in GNNs for enhanced representations. Additionally, GMV com- bines mixed-view generation and multi-view decomposition, enabling effective multi-view learning. Performance vs. number of sub-networks. To assess framework scalability and efficiency, we com- pare GMV against G-MIMO by varying the num- ber of sub-networks. The results in Table & are striking. GMV not only consistently outperforms G-MIMO, but its efficiency is such that using only two sub-networks (75.50%) already surpasses a 10- sub-network G-MIMO (75.30%). This significant performance gain stems from GMV's integrated de- sign, which fosters more diverse and complementary predictions among the generated views, leading to stronger generalization. All results are based rigorous and fair comparison protocol.
Sub-nets
G-MIMO
GMV
2
72.70
75.50
4
74.40
75.90
6
74.52
76.10
8
74.73
76.12
10
75.30
76.43
Table Performance vs. number of sub- networks on IMDB-B. GMV shows superior efficiency.
6.5 Hyperparameter Analysis
We conducted sensitivity analysis key hyperparameters: the feature augmentation ratio (p), the structure augmentation ratio (q), and the loss weight (a). As shown in Table 9 the results on the BACE dataset demonstrate the robustness of our model. Performance remains stable across wide range values for each hyperparameter, obviating the need for exhaustive or fragile tuning to achieve strong results. Notably, the optimal values fall within conventional ranges guided by prior work, reinforcing the model's s stability and ease of adoption. To ensure full reproducibility, our complete source code and detailed settings will be made publicly available.
Augmentation Ratio (p)
Structure Ratio (q)
Loss Weight (a)
Value
Accuracy
Value
Accuracy
Value
Accuracy
0.2
78.82
0.2
78.93
0.5
78.57
0.4
79.43
0.4
78.98
1.0
78.98
0.5
79.32
0.5
79.18
2.0
79.43
0.6
79.02
0.6
79.43
0.8
78.72
0.8
78.34
Table 9: Hyperparameter sensitivity analysis the BACE dataset with GIN backbone. The model exhibits robustness, with stable performance across a wide range of values. The best-performing setting for each hyperparameter is highlighted in bold.
6.6 Efficiency Study
We provide a transparent analysis of our method's computational cost, examining both the one-time preprocessing overhead and the online training efficiency.
One-Time Preprocessing Cost. Our method requires a one-time, offline preprocessing step to generate and cache views. As shown in Table TO this cost is negligible. On the PROTEINS dataset, it amounts to less than five minutes, which is merely 0.4% of the total training time. This efficiency scales the larger COLLAB dataset, where the 2-hour preprocessing cost is only 1.1% of the 180-hour training duration. This fixed cost is comparable to other advanced augmentation methods and is incurred only once, making it highly practical investment.
Dataset
Graph Count Preprocessing (Hours)
Total Training (Hours)
PROTEINS COLLAB
1.113
00.8
20
5,000
~
180
Table 1O: Offline preprocessing analysis. The one-time cost is minimal compared the total training time (10-fold CV) on an NVIDIA 3090Ti GPU.
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Online Training Overhead vs. Performance Gain. The online training phase is lightweight. Since all views are pre-computed and cached, the only overhead stems from view lookups and the forward passes for the sub-networks. Table quantifies the trade-off between this training overhead and the resulting accuracy improvement over GCN baseline. The results clearly show that for manageable training overhead of +1 100-1255, our method delivers substantial and consistent accuracy gain of approximately +9% across all datasets. This demonstrates a highly favorable and predictable return on computational investment, confirming the practical value of our approach.
Dataset
Num. Graphs
Avg. Edges
Training Overhead
Accuracy Gain
NCII
4,110
32.3
+113%
+9.4%
PROTEINS 1,113
72.8
+1 +120%
+8.8%
COLLAB
5,000
2,457.2
+125%
+9.0%
Table II: Training time overhead vs. accuracy gain over a GCN baseline. manageable increase in training time yields significant and consistent performance improvement.
6.7 Multi-view Study
(a) 176.83
(b) 200.28
(c) 180.41
(d) 208.05
Figure 5: T-SNE among prediction outputs of vanilla GIN and GMV. (a) vanilla GIN; (b) and (c) two sub-networks within GMV; (d) GMV. The blue pentagrams denote three class center, and the digit is distance among three class centers.
Visualization of Multi-view Representation. We employ both qualitative and quantitative methods to assess the diversity of predictions, thereby investigating the multi-view learning capacity of GMV. In Presentss the t-SNE for the vanilla GIN, two sub-networks of GIN within GMV and GMV itself, as applied to the COLLAB dataset. Different colored circles denote three classes in COLLAB, while pentagrams mark the class centers of three classes. We observe significant difference between the two predictions, affirming the diversity sub-networks. Moreover, the digit represents the sum of normalized distances among three centers. GMV achieves the largest distance among classes, which also validates the benefits of multi-view learning.
Ist
1st
2nd
2nd
3rd
Source Graph
Targel Graph
Mixed-View
Source Graph
Targel Graph
Mixed-Vis View
(a) IMDBB.
(b) IMDBM.
Figure 6: Visualization of mixed IMDBB and IMDBM.
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Visualization of Mixed-view. We utilize networkx to visualize some mixed-views in Fig 6 Each row denotes the source graph, target graph and generated mixed-view. ST-SubMix consider both structure and semantic information, so it generates the subgraph views preserving the original topology structure and semantic key nodes. ST-SubMix generates diverse mixed-views for GMV to enhance multi-view representation of capacity of GNNs.
6.8 Discussion
The framework naturally extends to other crucial tasks, such as node classification and link prediction. This is achieved by leveraging the powerful paradigm of task reformulation, where local tasks are converted into graph-level problems, a strategy validated by recent work. This requires minimal architectural changes: For Node Classification: The task can be reframed as classifying node's s contextual subgraph. GMV is then applied directly this subgraph to predict the central node's label, thereby benefiting from a robust, multi-view representation of its neighborhood. For Link Prediction: Similarly, this becomes a binary classification problem on the subgraph enclosing pair of nodes. GMV's ability to capture diverse and subtle topological patterns makes it ideally suited for predicting the existence of link between them. Furthermore, the core principles of GMV are adaptable to more complex domains, such as dynamic graphs (by applying the framework to temporal snapshots) and heterogeneous graphs (by acting as a modular wrapper around specialized GNN backbones).
24


Reviews:
[{"review_id": "19UVTuDCNn", "reviewer": "Reviewer_og8D", "summary": "The authors make several contributions to GNN-based graph classification, which are summarized under the term graph multi-view learning. First, a subgraph sampling method based on personalized page rank, DFS and BFS is proposed. A subgraph sampled from a graph in the dataset is then integrated into another graph randomly sampled from the dataset (target graph) to form a mixed graph. The mixed graph is then processed by a GNN using multiple loss functions on the parts of the mixed graph. The experiments show small but consistent improvements over the baselines and other multi-view approaches.", "questions": "**Q1)** How is 10-fold cross-validation combined with an 80/10/10 split into training, test, and validation sets for the TUDataset graphs? \n\n**Q2)** Figure 4 suggests that the competitors suffer from overfitting. Which standard countermeasures have been tried to fix this problem?\n\n**Q3)** Can you provide examples of mixed graphs for molecular datasets (see W1)?", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "## Strengths\n**S1)** The multi-view approach is an interesting generalization of augmentation methods.\n\n**S2)** The experiments show small but consistent improvements.\n\n**S3)** Extensive ablation studies show the contribution of individual modules.\n\n## Weaknesses\n**W1)** I am missing a convincing example or intuition why the approach can be expected to improve the predictive performance. The structure enhanced subgraph mixing integrates a subgraph into a target graph. It is unclear why the resulting graph is meaningful. The approach is applied to molecular graphs. It would be great to show examples of the resulting mixed molecular graphs. I would not expect them to be chemically valid molecular graphs. Why is this unproblematic?\n\n**W2)** The introduction mentions several links between the proposed approach and existing concepts, highlighting the lottery ticket hypothesis (LTH). The relation is abstract and not entirely clear to me. The LTH is about pruning parameters before training, which is not the case in the proposed method. Overall, the motivation of the approach is weak due to W1 and W2.\n\n**W3)** The paper is not sufficiently self-contained, e.g., Sec 3.2.2 makes references to the appendix and is not comprehensible without reading the appendix. The generation of the assignment is a crucial detail that should be discussed in the main paper.\n\n**W4)** The experimental evaluation lacks some details that should be clarified (see questions)\n\n## Minor remarks\n* l128 The definition of the edge set is problematic. Typically, the edge set $\\mathcal{E}$ simply is a subset of $\\mathcal{V}\\times\\mathcal{V}$ and two vertices $u$ and $v$ are *connected* if  $(u,v) \\in \\mathcal{E}$. The same holds for the neighborhood set.", "was_revised": true, "final_justification": "The authors clarified the motivation for graph mixing, which helped me to better understand the underlying idea, lifting in particular the concern mentioned in W1. I have raised my score accordingly.", "rebuttal": "We would like to express our sincere gratitude for your detailed review and invaluable feedback on our paper.\nWe are pleased that you recognized our multi-view approach as an interesting generalization (S1), that our experiments show small but consistent improvements (S2), and that our extensive ablation studies demonstrate the contribution of individual modules (S3).\nWe address your concerns and questions in detail below.\n\n### **W1, W2, Q3: On the Motivation for an Integrated Data, Model, and Optimization Framework**\n\n**1. Data-Level Motivation: Generating Diverse Structural Views (W1 & Q3)**\n\nThank you for this insightful question. We would like to clarify the motivation behind our graph mixing approach by drawing parallels to seminal data augmentation techniques in computer vision, and then elaborate on its adaptation to molecular graphs.\n\nIn computer vision, techniques like **Mixup and its powerful variant, CutMix (Yun et al., ICCV 2019 [2]),** do not aim to generate photorealistic images. **CutMix, for instance, creates explicitly non-realistic images by cutting a patch from one image and pasting it onto another.** The power of these methods lies in creating synthetic training instances that challenge the model. This design prevents the model from merely memorizing dominant patterns in the training set; instead, it encourages the model to learn more generalizable features, including rare but meaningful ones. As demonstrated in studies like (Zou et al., NeurIPS 2023 [1]), this mechanism effectively mitigates overfitting and enhances generalization—precisely because the synthetic samples are not required to be \"realistic\" in the traditional sense, but rather to expand the model’s exposure to diverse feature combinations.\n\nIn our case, we adopt a similar philosophy. Our goal is not to generate chemically valid or structurally \"realistic\" molecular graphs. Instead, the value of our structure-enhanced subgraph mixing lies in how it facilitates multi-view learning for GNNs. Specifically, through careful design—such as PPR-based subgraph sampling—we ensure that the sampled subgraphs retain semantically meaningful substructures (e.g., functional groups in molecules) that serve as structurally **complementary views** of the original graph. By mixing these subgraphs in a controlled manner, we force the model to reconcile and learn from these diverse views, rather than over-relying on a single dominant perspective of the molecular structure.\n\nThis is why the lack of strict chemical validity is unproblematic: the mixed graphs are not intended to represent \"real molecules,\" but to act as a regularization tool that expands the model’s exposure to diverse structural patterns. Just as Mixup and CutMix in computer vision succeed by leveraging synthetic compositions to improve feature learning, our approach harnesses mixed subgraphs to strengthen the GNN’s ability to learn from multiple structural views—ultimately enhancing its robustness and predictive performance on molecular graph classification tasks.\n\nIn summary, the mixed graph is meaningful not as a valid chemical structure, but as a **carefully designed training artifact**. It is a means to an end: leveraging the feature-learning power of Mixup to explicitly enforce the learning of complementary multi-view representations. We provide concrete examples of these mixed-view graphs in **Appendix (Figure 6)** to offer further intuition.\n\n**2. Model-Level Motivation: Efficiently Learning from Multiple Views & Clarifying the LTH Connection (W2)**\n\nThis data-level strategy introduces a key challenge: how can a single, parameter-efficient GNN learn from these varied views concurrently without a prohibitive increase in complexity? Our solution is a novel **Multi-View Decomposition (MVD)** architecture.\n\nHere, we wish to clarify the connection to the **Lottery Ticket Hypothesis (LTH)** in response to Reviewer W2's concern. Our use of LTH is inspired not by its classic application of \"pruning,\" but by its core insight: **a large, over-parameterized network has the capacity to contain many powerful sub-networks.** Our MVD architecture does not \"find\" these sub-networks by pruning. Instead, it is designed to **proactively \"activate\" and \"train\" them** within a single set of parameters. By employing dual prediction heads connected to a shared GNN backbone, we effectively encourage the model to activate distinct \"sub-networks.\" Each sub-network is implicitly guided to specialize in one of the structural views (e.g., one focusing on local neighborhood patterns from BFS/DFS, the other on global influence from PPR). This design enables the model to develop parallel and complementary interpretations of the graph, representing a highly efficient implementation of multi-view learning without incurring additional parameter costs.\n\n**3. Optimization-Level Motivation: Unifying the Learning Process (W1 & W2)**\n\nFinally, the data and model components are unified by a tailored multi-view loss function. This loss is not a simple aggregation of individual losses. Its specific design is to **explicitly enforce complementarity between the representations learned by the different sub-networks**. The loss function guides the optimization process to ensure that the knowledge from each view is effectively integrated, culminating in a final representation that is more robust and comprehensive than what could be achieved from any single view in isolation. This aligns with established principles that learning from diverse sources can mitigate overfitting and improve generalization [1].\n\n**A Holistic and Indivisible Framework**\n\nThese three pillars—data-level view generation, model-level decomposition, and optimization-level unification—form a tightly integrated and indivisible whole. The core novelty of our work resides in this holistic framework. Our extensive ablation studies, presented in **Table 4(b) and 4(c)**, provide direct empirical evidence for this synergy. The results unequivocally demonstrate that removing any of these components leads to a significant degradation in performance. This proves that all parts are non-trivial and essential, and that their combination provides a powerful, new approach to improving GNN generalization and robustness.\n\n---\n\n[1] Zou, et al. The Benefits of Mixup for Feature Learning. (NIPS 2023).\n[2] Yun, et al. Cutmix: Regularization strategy to train strong classifiers with localizable features. (ICCV 2019).\n\n### **W3: Improving Self-Containedness**\n\nWe agree with the reviewer that the paper should be as self-contained as possible. Thank you for this constructive suggestion. To enhance readability and ensure the core logic is accessible without referencing the appendix, we will move the detailed explanation of our **mixed-view generation process and the construction of assignment matrices** (currently in Algorithm 2) directly into **Section 3.2.2** of the main paper.\n\n### **W4, Q1 & Q2: Experimental Details and Overfitting**\n\nWe appreciate the reviewer's questions regarding our experimental setup and results.\n\n*   **Q1 (Data Splitting Protocol):** We apologize for the omission of the specific data splitting details. We utilized a standard **nested cross-validation** methodology. For each of the 10 folds, the data was partitioned into **80% for training, 10% for validation, and 10% for testing**. We will explicitly clarify this standard procedure in the experimental setup section of the revised manuscript.\n\n*   **Q2 (Clarification on Overfitting in Figure 4):** Regarding the overfitting analysis in Figure 4, we wish to clarify its purpose. All baseline models were indeed trained with standard regularization techniques (i.e., L2 regularization and Dropout) to ensure a fair comparison. The key takeaway from this figure is that our **GMV framework inherently functions as a more powerful regularizer** compared to these standard methods. This is evidenced by GMV achieving a lower validation loss and, consequently, better generalization to the test set. We will add this explicit clarification to the caption of Figure 4 and the corresponding discussion in the main text to make our point clear.\n\n### **Minor Remarks**\n\nWe are grateful for the reviewer's meticulous reading and for pointing out the notational inconsistency. We will correct the definition of the edge set to the standard formal notation, **$\\mathcal{E} \\subseteq V \\times V$**, in the revised version.\n\n---\n\nThank you once again for your insightful feedback, which has been invaluable in helping us improve our work. We are confident that the revised paper will be significantly stronger, clearer, and more self-contained."}, {"review_id": "6ybzH1NiHY", "reviewer": "Reviewer_ypuU", "summary": "This manuscript introduces GMV (Graph Multi-View), a unified framework that enhances Graph Neural Networks (GNNs) and Graph Transformers (GTs) by integrating multi-view learning from data, model, and optimization perspectives. GMV generates mixed graph views via structure-enhanced subgraph mixing (ST-SubMix), activates dual sub-networks within a single model via multi-view decomposition (MVD), and optimizes them via mixed-view and multi-view losses. During inference, GMV averages predictions from two heads, achieving ensemble-like performance with minimal overhead. GMV outperforms existing graph augmentation and ensemble methods across 12 benchmark datasets (TUDataset and OGB).", "questions": "My concerns refer to weaknesses.", "limitations": "Limited discussion of limitations. It is recommended to add some discussion about the model's applicability (see W6).", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "**Strengths**\n\n- **S1.** The manuscript is comprehensive, and the author clearly describes the method for addressing the generalization and overfitting issues in graph classifications.\n\n- **S2.** The proposed GMV unifies data augmentation (ST-SubMix), model decomposition (MVD), and optimization (dual-loss) into a single pipeline. This holistic approach addresses the limitations of prior methods that only expand views from isolated perspectives (e.g., DropEdge for data, G-MIMO for model). GMV can work with any GNN/GT backbone, offering a plug-and-play solution for graph classification tasks.\n\n- **S3.** Experiments are conducted on multiple public datasets. Across 12 benchmark datasets (TUDataset and OGB), GMV outperforms baselines (e.g., DropEdge, SubMix, G-MIMO). Ablation studies confirm that ST-PPR sampling, MVD, and dual-loss are all critical.\n\n- **S4.** The manuscript is well written, and the proposed method is relatively straightforward, simple, and easy to understand.\n\n\n**Weaknesses**\n\n- **W1.** Incremental Advances. While the combination is unexplored, the individual components (e.g., subgraph mixing, dual-loss) build upon prior work (SubMix, MIMO), thereby reducing the perceived breakthrough.\n\n- **W2.** Limited Theoretical Novelty. No new learning theory or generalization analysis is introduced. The paper relies on empirical validation rather than fundamental advances. While the lottery ticket hypothesis motivates GMV and is empirically strong, the manuscript does not provide theoretical guarantees on generalization error or convergence rates for the proposed framework. The lack of generalization bounds or convergence analysis weakens the theoretical foundation.\n\n- **W3.** High Preprocessing Complexity. While efficient in model inference, the training phase requires preprocessing each graph via ST-PPR, which involves PPR, DFS, and BFS. The preprocessing adds $O(|V|)$ complexity per graph, potentially slowing training for very large datasets.\n\n- **W4.** Unknown Hyperparameter Sensitivity. GMV introduces new hyperparameters (e.g., augmentation ratio $p$, structure augmentation ratio $q$, number of walks $w$, and loss weight $\\alpha$) that require careful tuning. The manuscript lacks a sensitivity analysis.\n\n- **W5.** Low Reproducibility. The proposed method introduces many hyperparameters (see W2) that require careful tuning. However, the authors only provide algorithmic descriptions of key modules (ST-PPR, subgraph mixing, assignment matrices) without providing the relevant code implementation, which greatly reduces the reproducibility of the manuscript.\n\n- **W6.** Single Task Focus. GMV is evaluated only for graph classification. Its efficacy for node classification, link prediction, or graph generation is unexplored, despite potential multi-view benefits in these tasks. In addition, the framework assumes static graphs. Its applicability to dynamic graphs or heterogeneous graphs is untested, limiting real-world utility.", "was_revised": true, "final_justification": "The authors have addressed my concerns. I have raised my score (4 -> 5).", "rebuttal": "We would like to express our sincere gratitude for your thorough review and valuable feedback. We are very encouraged by your recognition of our work's comprehensiveness (S1), its unified and plug-and-play framework (S2), the extensive experiments (S3), and the clarity of the writing (S4). Your positive assessment is greatly appreciated.\n\n### **W1 & W2: On Novelty and Theoretical Contribution**\n\nWe thank the reviewer for contextualizing our work alongside important foundational efforts like SubMix and MIMO. This comparison allows us to clarify our distinct contributions. Our primary innovation lies not in any single component, but in their **synergistic unification into the first cohesive multi-view learning framework for graph classification, spanning data, model, and optimization.**\n\nOur core contribution is a **new perspective**: we propose a general framework that provides a unified direction for improving the generalization of GNNs. From this viewpoint, prior methods can be seen as powerful but specialized solutions addressing specific aspects of this broader challenge. The novelty of our work is this holistic and integrated approach, which our extensive experiments confirm is more effective than its individual components. For instance, our ST-SubMix is a non-trivial extension of SubMix, specifically engineered to incorporate vital structural information via ST-PPR—a component our ablation study confirms is critical for performance.\n\nRegarding the request for a deeper theoretical contribution, our focus was to establish this unified framework and demonstrate its practical power and robustness across a wide range of scenarios. While providing formal generalization bounds for such a complex, multi-component system is a significant research challenge in its own right and beyond the scope of this initial work, we wish to highlight that **we do provide theoretical justification for our proposed ST-PPR component in the appendix.**\n\nWe believe our extensive empirical validation across 12 diverse datasets serves as strong evidence for the framework's effectiveness. In summary, our contribution is a new and valuable perspective that is shown to be empirically powerful and opens up new avenues for future work in robust graph representation learning.\n\n### **W3: On High Preprocessing Complexity**\n\nThank you for raising this important point regarding computational cost. We wish to clarify that the ST-PPR computation is a **one-time, offline preprocessing step**, and its cost is modest relative to the overall computational budget for training.\n\nTo provide a transparent analysis of this overhead, we compare the one-time preprocessing cost against the total training time. The following table presents this comparison for both a small and a large dataset, with all units converted to hours.\n\n| **Dataset** | **Graph Count** | **One-time Preprocessing (Hours)** | **Total Training (GPU Hours)** |\n| :---------- | :-------------- | :--------------------------------- | :----------------------------- |\n| PROTEINS    | 1,113           | ~0.08                              | 20                             |\n| COLLAB      | 5,000           | ~2                                 | 180                            |\n\n*Table: Computational cost analysis on PROTEINS and COLLAB. Preprocessing time is compared against the total training time (10-fold cross-validation) in hours on an NVIDIA 3090Ti GPU.*\n\nAs the data shows, the trade-off is highly favorable:\n\n*   On the **PROTEINS** dataset (1,113 graphs), the entire one-time preprocessing takes approximately 0.08 hours (less than 5 minutes). This constitutes only **0.4%** of the 20 GPU hours required for the full 10-fold cross-validation.\n*   This efficiency holds even on larger datasets. On **COLLAB** (5,000 graphs), preprocessing takes about 2 hours, which is merely **~1.1%** of the 180 GPU hours needed for total training.\n\nIn both scenarios, the preprocessing cost represents a small, fixed fraction of the total training time. It is also crucial to note that this cost is on par with other advanced augmentation methods like SubMix, which require a similar one-time offline computation.\n\nOnce this initial cost is paid, the generated samples are **cached and reused across all subsequent training epochs**. This design ensures there is **zero per-epoch overhead** from our view generation, allowing our model to achieve significant performance gains while maintaining efficient training and inference.\n\nWe will add this detailed quantitative comparison to our revised manuscript to make the efficiency trade-off clear to the reader.\n\n### **W4 & W5: On Hyperparameter Sensitivity and Reproducibility**\n\nWe agree completely that reproducibility and robustness are paramount. We apologize for omitting a detailed hyperparameter analysis due to page constraints and thank the reviewer for highlighting this. To thoroughly address this, we will add a **comprehensive hyperparameter sensitivity analysis to the appendix** of the revised paper. This new section will complement our existing ablation studies and demonstrate the stability of our method across a range of key hyperparameters.\n\nAs a preview, we present an analysis of the feature augmentation ratio ($p$), the structure augmentation ratio ($q$), and the loss weight ($\\alpha$) on the BACE dataset using the GIN backbone.\n\n---\n\n**Hyperparameter Sensitivity Analysis on BACE (GIN)**\n\n*The best-performing setting for each hyperparameter is highlighted in bold.*\n\n| **Mixup Ratio ($p$)** | **Accuracy (%)** |\n| :-------------------- | :--------------- |\n| 0.2                   | 78.82            |\n| **0.4**               | **79.43**        |\n| 0.5                   | 79.32            |\n| 0.6                   | 79.02            |\n| 0.8                   | 78.72            |\n\n| **Structure Ratio ($q$)** | **Accuracy (%)** |\n| :------------------------ | :--------------- |\n| 0.2                       | 78.93            |\n| 0.4                       | 78.98            |\n| 0.5                       | 79.18            |\n| **0.6**                   | **79.43**        |\n| 0.8                       | 78.34            |\n\n| **Loss Weight ($\\alpha$)** | **Accuracy (%)** |\n| :------------------------- | :--------------- |\n| 0.5                        | 78.57            |\n| 1.0                        | 78.98            |\n| **2.0**                    | **79.43**        |\n\n---\n\nCrucially, these results demonstrate that our method is **not overly sensitive to its hyperparameters**. Performance remains stable and strong within a reasonable range around central values (e.g., $p \\in [0.4, 0.6]$). This indicates that achieving good results does not require exhaustive or fragile tuning.\n\nFurthermore, our hyperparameter search space was intentionally guided by prior work; we followed the standard practices established by methods like SubMix and found that optimal values were located within these conventional ranges. This reinforces that our framework is robust and its results are readily reproducible.\n\nTo guarantee full reproducibility, we are committed to open science and will **release our full, anonymized source code and detailed hyperparameter settings** as supplementary material with the final submission.\n\n### **W6: On Single Task Focus and Scope**\n\nThank you for this insightful comment regarding the scope of our evaluation. While our current work focuses on graph classification—a fundamental and challenging benchmark for testing generalization—we designed the **GMV framework to be highly versatile**.\n\nThe framework naturally extends to other crucial tasks, such as node classification and link prediction. This is achieved by leveraging the powerful paradigm of **task reformulation**, where local tasks are converted into graph-level problems, a strategy validated by recent work [1]. This requires minimal architectural changes:\n\n*   **For Node Classification:** The task can be reframed as classifying a node's **contextual subgraph**. GMV is then applied directly to this subgraph to predict the central node's label, thereby benefiting from a robust, multi-view representation of its neighborhood.\n\n*   **For Link Prediction:** Similarly, this becomes a binary classification problem on the subgraph enclosing a pair of nodes. GMV's ability to capture diverse and subtle topological patterns makes it ideally suited for predicting the existence of a link between them.\n\nFurthermore, the core principles of GMV are adaptable to more complex domains, such as dynamic graphs (by applying the framework to temporal snapshots) and heterogeneous graphs (by acting as a modular wrapper around specialized GNN backbones).\n\nWe will add a dedicated discussion on these natural extensions to our revision to underscore the **broad applicability** and future potential of the GMV framework. We appreciate the opportunity to clarify this.\n\n---\n\n[1] Sun et al. \"All in One: Multi-Task Prompting for Graph Neural Networks\" (KDD 2023)."}, {"review_id": "Eqrh5g6hi6", "reviewer": "Reviewer_9EsQ", "summary": "This paper proposes a multi-view learning framework for graph classification task. In details, different from exisitng multi-view methods which  empoly only one way for sub-graph extraction, the proposed method combined multiple approaches for sub-graph sampling. Furthermore, sub-graphs are mixed with structure enhancement for different graph view generation. Finally, a dual-stream predictor is employed for final prediction.", "questions": "1. The authors should highlight their contributions. Especially the design of the mixed-view generation part. \n2. The authors need to carefully review the wording of the paper, including the definitions of many formulas.\n3. What concerns me most is the experimental results. The authors need to give more detailed explanations about why the results are reported differently from the original paper.", "limitations": "yes", "rating": 4, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Pros:\n1. Compared to existing methods, the authors significantly reduce the model’s parameters and complexity while maintaining performance, which is highly beneficial for deployment in real-world scenarios.\n2. The authors conduct extensive experiments to prove the effectiveness of the proposed method.\n\nCons:\n1. The overall novelty of this paper does not appear to be very strong. The key contribution of this paper is based on the multi-view graph generation process. However, the authors appear to have simply combined three existing sampling methods—PPR, DFS, and BFS. From the implementation details, it is evident that these methods are sequentially applied to the main graph to generate subgraphs, which are then directly merged. I believe this approach alone is insufficient to support a novel contribution.\n2. Some concepts or formulas are not clearly explained. For example, in line 167, what is \"source graph\", and what is the purpose of \"target graph\"? in line 164, the definition of $S_{PPR}$ is missing. Although it is explained in Appendix 6, it is important to have every formulas defined in the main body of the paper.\n3. It seems not necessary for light weight design, given the existing models are already very small (only 30~300KB).\n4. The experimental results of G-MIMO [1] reported in Table 1 are different from (lower than) the results reported in the original paper. The authors should give a further explanation.\n\n[1] Zhu, Qipeng, et al. \"G-MIMO: Empowering GNNs with Diverse Sub-Networks for Graph Classification.\" 2024 IEEE International Conference on Multimedia and Expo (ICME). IEEE, 2024.", "was_revised": true, "final_justification": "During the rebuttal, the authors provided a clear explanation of the model’s novelty, and also addressed my primary concern regarding the importance of the lightweight design. This has improved the overall coherence of the paper, which led me to revise my score.", "rebuttal": "Thank you for your detailed review and constructive feedback. We are encouraged that you recognized the practical benefits of our method in significantly reducing model parameters while maintaining performance (Pro 1) and the thoroughness of our experimental validation (Pro 2).\n\n### **C1 & Q1: On Novelty and Contribution**\n\nOur primary innovation is a holistic framework, GMV, which enhances GNN generalization by introducing synergistic improvements across three key axes: **(1) a novel data-level augmentation strategy, (2) an efficient multi-view model architecture, and (3) a tailored optimization objective.** As our comprehensive ablation studies demonstrate, innovations in each of these three areas contribute significantly to the final performance gain.\n\nThe synergy between these components is not merely conceptual but quantifiable. For instance, on the IMDB-BINARY dataset (Table 4b), the baseline accuracy of **72.30%** improves to **74.10%** (+1.8%) with only our data-centric Mixed-View Generation (MVG) and to **72.70%** (+0.4%) with only our model-centric Multi-View Decomposition (MVD). However, when both are enabled, accuracy reaches **75.50%**. This total gain of **+3.2%** significantly exceeds the sum of the individual parts (+2.2%), providing clear quantitative evidence of synergy and demonstrating that our contribution is a comprehensive system, not just an isolated data technique.\n\nWith this broader context, the **mixed-view graph generation** strategy, which the reviewer's question focuses on, should be understood as the crucial **data-level pillar** of our framework. While we build upon established sampling methods like PPR, DFS, and BFS, our contribution lies not in the methods themselves, but in **how we strategically combine and adapt them as a tool to serve our multi-view learning objective.** Our goal was to design a practical and effective method to generate these complementary views.\n\nThis design is neither arbitrary nor trivial, and its contribution is supported by both theoretical reasoning and empirical evidence:\n1.  **Theoretical Necessity:** We provide analysis showing that combining these specific methods is necessary to capture a rich spectrum of structural information. DFS/BFS excel at capturing local neighborhood structures, while PPR captures a node's global influence. Using them in concert ensures the generated views are genuinely complementary, which is a prerequisite for our multi-view framework to succeed.\n2.  **Empirical Validation:** Crucially, we validate this design choice empirically. Our ablation studies **(please refer to Table 4)** directly compare our mixed-view generation strategy against using single sampling methods or other alternatives. The results consistently show that our proposed approach yields superior performance, confirming that our specific method for generating views is a significant and effective part of our overall framework's success.\n\nIn summary, the novelty should be viewed holistically. It is the **synergy between the high-level conceptual framework (GMV) and its effective, theoretically-grounded, and empirically-validated data-level implementation** that constitutes our core contribution. The mixed-view generation is an integral part of this system, designed specifically to enable the multi-view learning that drives the performance gains.\n\n### **C2 & Q2: On the Clarity of Concepts and Formulas**\n\nThank you for this valuable feedback. \n\nTo directly address the terminology in our ST-SubMix method (line 165):\n\n*   The **source graph ($\\mathcal{G}_{src}$)** refers to a primary training sample within a given batch.\n*   The **target graph ($\\mathcal{G}_{trg}$)** is another graph randomly selected from the same training batch.\n\nThe core idea is to mix a subgraph from the \"source\" with a subgraph from this \"target\" to generate a new, challenging training sample that pushes the model to learn more robust and generalizable features.\n\nTo ensure these concepts and formulas are clear in the revised manuscript, we will make the following concrete changes:\n\n1.  **Define Key Terms:** We will revise Section 3.2.2 to explicitly define \"source graph\" and \"target graph\" at their first appearance, removing any potential for confusion.\n2.  **Improve Formula Accessibility:** We will move the formal definition of ST-PPR from Appendix 6.1 directly into the main body (Section 3.2.1). This will ensure all core components of our method are defined in place, making the paper more self-contained and easier to follow.\n\nWe are confident these revisions will significantly improve the clarity of our paper and thank the reviewer for helping us strengthen the manuscript.\n\n### **C3: On the Necessity of a Lightweight Design**\n\nThis is an excellent point that allows us to clarify the core motivation behind our computationally efficient design. Our primary goal is to **minimize inference latency**, which is often the critical bottleneck for deploying Graph Neural Networks (GNNs) in real-world, time-sensitive applications.\n\nThe key insight is that for GNNs, the dominant computational cost lies in the **message-passing mechanism**, not merely the parameter count. A model of ~300KB might seem small in other deep learning domains, but its inference speed on graph data is dictated by the expensive, iterative process of aggregating neighborhood information.\n\nThis is precisely where our design provides a crucial advantage over alternatives like ensembling.\n\n*   **Traditional Ensembling:** An ensemble requires running the expensive message-passing process multiple times—once for each model. As vividly illustrated in our results (Figure 1(b)), this approach is prohibitively slow for practical use. For instance, on the COLLAB dataset, the Ensemble method shows a test latency of over **400ms** while achieving an accuracy of 82.36%.\n\n*   **Our GMV Framework:** In stark contrast, GMV is architected to perform message passing **only once**. It uses a single, unified GNN body to learn the core graph representation. The diverse \"views\" are then processed by lightweight prediction heads *after* the costly message-passing stage is complete. The result is a dramatic improvement: GMV not only surpasses the ensemble's performance (achieving 83.02% accuracy on COLLAB) but does so with a **more than 4x speedup**, reducing inference latency from over 400ms to a level comparable with a standard single GNN.\n\nThis architectural principle—gaining the benefits of a more complex system at the cost of a simpler one—mirrors emerging trends in large-scale AI. For example, the recently proposed **\"Parallel Scaling Law for Language Models\" (Qwen 2025) suggests that intelligent parallel architectures can unlock the capabilities of much larger models without the prohibitive computational overhead**. In this light, GMV can be seen as a graph-centric application of this powerful idea: achieving superior generalization through smart design, rather than brute-force computation. This makes GMV a practical and scalable solution for the latency-sensitive applications where GNNs are increasingly being deployed.\n\n### **Q3: On the G-MIMO Baseline Performance**\n\nThis is a crucial question, and we thank the reviewer for their careful scrutiny, as it allows us to clarify the rigor of our experimental setup. The difference in G-MIMO's performance stems from our commitment to a strict and fair **\"apples-to-apples\" comparison**.\n\nThe primary reason for the difference is that we **standardized the number of sub-networks (or \"views\") to two** for all competing methods, including G-MIMO and our GMV. This ensures that any observed performance gain comes from the superiority of the framework's design, not simply from using more model components. The original G-MIMO paper reported results achieved with a larger number of sub-networks.\n\n---\n\n**Empirical Evidence on IMDB-BINARY**\n\nTo be fully transparent, we provide a detailed comparison of performance as the number of sub-networks varies for both G-MIMO and our GMV on the IMDB-B dataset.\n\n**Performance vs. Number of Sub-networks on IMDB-BINARY**\n*GMV consistently outperforms G-MIMO at every level.*\n\n| **Number of Sub-networks** | **G-MIMO Accuracy (%)** | **GMV Accuracy (%)** |\n| :------------------------- | :---------------------- | :------------------- |\n| 2                          | 72.70                   | **75.50**            |\n| 4                          | 74.40                   | **75.90**            |\n| 6                          | 74.52                   | **76.10**            |\n| 8                          | 74.73                   | **76.12**            |\n| 10                         | 75.30                   | **76.43**            |\n\n---\n\nThis data reveals two key insights:\n\n1.  **Consistent Superiority:** Our GMV method consistently and significantly outperforms G-MIMO across all tested numbers of sub-networks.\n2.  **Framework Efficiency:** This highlights the remarkable efficiency and effectiveness of our framework: **GMV with only two sub-networks (75.50%) already outperforms G-MIMO even when it uses ten sub-networks (75.30%).**\n\nFurthermore, our re-implemented G-MIMO result of 72.70% for two sub-networks is consistent with the performance trend from the original work, validating our implementation's correctness.\n\nFinally, as stated in our \"Experiment Details\" (lines 232-236), this standardization was part of a **broader unified protocol** where all baselines were re-run with the same backbone, data splits, and tuning strategy. Our analysis in Table 5 of the main text explains *why* GMV is more effective: its integrated design fosters more diverse and complementary predictions (higher $D_{Disagree}$ and $D_{KL}$), which directly leads to better generalization under these controlled, fair conditions.\n\nIn summary, the reported results are a direct consequence of a rigorous and fair experimental design, which in turn reveals the significant advantages of our GMV framework."}, {"review_id": "Ux4UM9ffIc", "reviewer": "Reviewer_GVQ8", "summary": "This paper presents ​​Graph Multi-View (GMV)​​, an innovative framework that enhances the generalization and robustness of Graph Neural Networks (GNNs) and Graph Transformers (GTs) for graph classification tasks. By integrating ​​multi-view learning​​ from data, model, and optimization perspectives, GMV activates diverse sub-networks within a single GNN/GT through a novel training pipeline involving ​​structure-enhanced subgraph mixing​​ and ​​multi-view decomposition​​. During inference, GMV efficiently leverages dual prediction heads to achieve ensemble-like performance with minimal computational overhead. Extensive experiments on benchmark datasets demonstrate that GMV outperforms existing augmentation and ensemble methods, achieving state-of-the-art results while maintaining scalability for large-scale graphs. The framework's ability to preserve structural integrity and learn diverse representations is further validated through theoretical analysis and robustness tests under noisy and limited-label scenarios.", "questions": "There are some typographical errors that the authors need to correct.\n\nCan the generalization ability of the GMV model be applied to unsupervised tasks?\n\nAmong the comparison algorithms, there are relatively few models from the past three years.\n\nThe paper proposes a unified framework (GMV) combining data, model, and optimization perspectives for multi-view learning. How does the interaction between these three perspectives quantitatively contribute to performance gains compared to isolated implementations? \n\nST-SubMix claims to preserve structural information better than prior methods (Section 3.2.1). However, Figure 6 shows mixed-view generation alters original graphs. What metrics quantify structural preservation, and how does distortion impact performance on tasks sensitive to topology ?\n\nThe experiments focus on graph classification. Could GMV's multi-view approach improve other tasks like node classification or link prediction? Are there theoretical or empirical results supporting broader applicability?\n\nGMV adds minimal overhead during inference (Section 3.4), but training requires dual sub-network activation. How does training time scale with graph size, and does the benefit of multi-view learning diminish for very large graphs due to computational constraints?", "limitations": "The performance of the GMV model depends on the characteristics of the dataset.", "rating": 4, "confidence": 1, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Introducing multi-view learning into GNNs to enhance generalization performance is a strong and valuable innovation. The theoretical foundation is also solid.\n\nThe experimental results are relatively rich and comprehensive, and in particular, the various ablation studies effectively demonstrate the validity of the proposed model.", "was_revised": false, "final_justification": "", "rebuttal": "We are particularly grateful for the following acknowledgments:\n\n*   **Innovation and Theoretical Soundness:** We are pleased the reviewer found our core contribution—the integration of multi-view learning into GNNs—to be a **\"strong and valuable innovation\"** and our theoretical foundation **\"solid.\"**\n\n*   **Experimental Validation:** We also appreciate the reviewer's recognition of our experimental evaluation as **\"rich and comprehensive\"** and our ablation studies as **\"effective\"** in demonstrating the model's validity and robustness.\n\n### **Q1: Adaptability to Unsupervised Learning**\n\nThe transition is straightforward, requiring one key modification: replacing the supervised losses with a **multi-level contrastive objective** (e.g., InfoNCE). The model would be trained to maximize mutual information between corresponding \"positive pairs\" generated from an input graph ($G_{\\text{mix}}$) and its augmentation ($G'_{\\text{mix}}$), treating other graphs as negatives.\n\nThe positive pairs would be:\n\n*   **Composite View:** The full mixed graph and its augmentation ($G_{\\text{mix}}, G'_{\\text{mix}}$).\n*   **Decomposed Views:** The corresponding source subgraphs ($G_{\\text{src}}, G'_{\\text{src}}$)\n    \n    and target subgraphs ($G_{\\text{tag}}, G'_{\\text{tag}}$).\n\nThis multi-level contrastive strategy would compel the model to learn representations that are robust to augmentation and semantically consistent across both composite and decomposed views. We agree this is a very promising direction for future work.\n\n### **Q2: Comparison with Additional State-of-the-Art (SOTA) Methods**\n\nWe thank the reviewer for this valuable suggestion to benchmark against more recent SOTA models. While our initial experiments focused on foundational methods for a clear comparison, we agree that a broader evaluation is crucial.\n\nTo that end, we have conducted new experiments during the rebuttal period, integrating our GMV framework as a plug-and-play enhancement module with the powerful NSA [1] model. The results, summarized below, show that GMV provides a consistent and significant performance uplift on top of this already strong baseline, demonstrating its effectiveness as a general-purpose enhancement.\n\n| **Method**           | **BBBP**  | **BACE**  |\n| -------------------- | --------- | --------- |\n| NSA (baseline)       | 84.0%     | 72.0%     |\n| **NSA + GMV (Ours)** | **85.5%** | **74.1%** |\n\nAs the table illustrates, applying our GMV framework boosts the performance of the NSA backbone from 84.0% to **85.5%** on BBBP and from 72.0% to **74.1%** on BACE. These results highlight that GMV is not only a standalone framework but also a compatible module that can enhance other strong, state-of-the-art architectures. \n\n---\n\n[1] Buterez et al. \"An end-to-end attention-based approach for learning on graphs.\" *Nature Communications* (2025).\n\n### **Q3: Quantitative Analysis of Framework Synergy**\n\nWe thank the reviewer for this question, which highlights the core principle of our work: the **synergistic interplay** between our framework's data, model, and optimization perspectives. Our ablation studies in Table 4 provide direct quantitative evidence for this.\n\n**1. Synergy between Data (MVG) and Model (MVD):**\nOn IMDB-BINARY (Table 4b of the main text), the baseline accuracy of 72.30% improves to 74.10% with only our data-centric **Mixed-View Generation (MVG)** and to 72.70% with only our model-centric **Multi-View Decomposition (MVD)**. However, when **both are enabled**, accuracy reaches **75.50%**. This gain significantly exceeds the sum of the individual parts, providing clear quantitative evidence of synergy.\n\n**2. Synergy in Optimization:**\nThis principle is reinforced by our optimization strategy (Table 4c). While using either the mixed-view loss ($\\ell_{\\text{mix}}$) or the decomposed-view loss ($\\ell_{\\text{view}}$) alone yields an accuracy of 74.55%, only their **joint application** unlocks the peak performance of **75.50%**. This confirms both objectives are indispensable and mutually reinforcing.\n\nIn summary, these results provide decisive quantitative evidence that the three pillars of our framework are fundamentally synergistic, not merely additive. \n\n### **Q4: The Role of Structural Information in Augmentation**\n\nOur goal is not to preserve an identical topology—which offers no learning benefit—but to introduce **controlled structural distortions**. This strategy retains semantically crucial patterns while creating challenging views that enhance model robustness, a claim we support both theoretically and empirically.\n\n**1. Quantifying Structural Preservation**\n\nOur method is designed to generate augmentations that are more structurally faithful than alternatives.\n\n* **Theoretical & Empirical Proof:** Our **ST-PPR sampling** is provably better at preserving key structural patterns than simpler methods (see Appendix for formal proof). Empirically, a topological analysis on the COLLAB dataset confirms this. As shown below, our augmentations (ST-SubMix) produce statistics significantly closer to the original graph than standard SubMix.\n\n  *Topological statistics on COLLAB. Our method's results are closer to the original.*\n\n| **Topological Statistic**      | **Original Graph** | **ST-SubMix (Ours)** | **Standard SubMix** |\n| ------------------------------ | ------------------ | -------------------- | ------------------- |\n| Average Clustering Coefficient | 0.6055             | **0.6322**           | 0.6877              |\n| Average Node Size              | 74                 | **80**               | 88                  |\n\nThis data quantitatively demonstrates that our method introduces more controlled and realistic structural changes.\n\n**2. How Controlled Distortion Drives Performance**\n\nThis controlled distortion is precisely what compels the model to learn more generalizable representations. The effectiveness of this strategy is confirmed by two key results:\n\n*   **Success on Topology-Sensitive Tasks:** Our SOTA performance on the highly topology-sensitive COLLAB dataset (Table 1) provides strong empirical proof that these structural variations are beneficial, enhancing the model's understanding of essential features rather than degrading it.\n\n*   **Mechanism: High-Diversity Views:** The reason for this success is revealed in Table 5. Our framework produces sub-networks with significantly higher prediction diversity ($D_{\\text{Disagree}}$, $D_{\\text{KL}}$) than all baselines. These structurally distinct yet accurate views are highly complementary. By forcing the model to reconcile them, our framework achieves superior generalization and a final accuracy that surpasses all other methods.\n\n### **Q5: Generalizability to Other Graph-Based Tasks**\n\nWe thank the reviewer for this excellent question. The reviewer is correct that the principles of our GMV framework are highly general and extend directly to other fundamental tasks, such as **node classification** and **link prediction**, by reformulating them as graph-level problems [1].\n\nThis extension requires minimal architectural changes and allows the full power of our framework to be applied:\n\n*   **For Node Classification:** The task is transformed into classifying a node's contextual subgraph. Our ST-PPR sampling is ideally suited for extracting these meaningful neighborhoods, and GMV's multi-view approach would create robust representations of the node's environment for a more accurate prediction.\n\n*   **For Link Prediction:** This is framed as a binary classification problem on an enclosing subgraph containing both nodes. Our framework's ability to generate diverse structural views is particularly advantageous for learning the complex topological patterns that signal a connection.\n\nBy adopting this graph-level perspective, GMV becomes a naturally applicable and powerful tool for these tasks.\n\n---\n\n[1] Sun et al. \"All in One: Multi-Task Prompting for Graph Neural Networks.\" *KDD* (2023).\n\n### **Q6: Computational Efficiency and Scalability**\n\nWe thank the reviewer for this important practical concern. Our GMV framework is designed for efficiency and scalability via a **one-time, offline pre-processing stage**.\n\n**1. Efficiency by Design:**\nBefore training, we perform a single pass to generate and cache all views. The computational complexity of this step is **O(V)**, which is on par with existing methods like SubMix and ensures our more sophisticated view generation does not create a bottleneck. The online training phase is therefore lightweight, with the only overhead coming from fast view lookups and additional forward passes for the sub-networks.\n\n**2. Empirical Scalability and Performance Trade-off:**\nOur empirical analysis confirms this favorable trade-off. We measured the training overhead and accuracy gain against a GCN baseline:\n\n| **Dataset** | **Num. Graphs** | **Avg. Edges** | **Training Time Overhead** | **Accuracy Gain** |\n| :---------- | :-------------: | :------------: | :------------------------: | :---------------: |\n| NCI1        |      4,110      |      32.3      |           +113%            |     **+9.4%**     |\n| PROTEINS    |      1,113      |      72.8      |           +120%            |     **+8.8%**     |\n| COLLAB      |      5,000      |    2,457.2     |           +125%            |     **+9.0%**     |\n\nThe data shows two clear results:\n\n1.  **Substantial & Consistent Gain:** GMV delivers a significant and consistent accuracy improvement of **~+9%** that scales across all datasets.\n2.  **Manageable Overhead:** This SOTA performance is achieved for a predictable and justified training overhead of ~+110-125%.\n\nIn summary, our efficient O(V) pre-processing design enables a significant performance gain for a modest increase in training cost, confirming a highly favorable trade-off between computation and generalization power."}]

Author rebuttal:

Meta-review: This paper introduces an augmentation scheme based on subgraph preprocessing that drives modest but consistent improvement across experiments. While reviewers generally hesitate due to limited novelty and lack of theoretical contribution, the experiments are convincing. Therefore, I would recommend acceptance.
Decision: Accept (poster)