Open Your Eyes: Vision Enhances Message Passing Neural Networks in Link Prediction
Authors: Yanbin Wei
Xuehao Wang
Zhan Zhuang
Yang Chen
Shuhao Chen
Yulong Zhang
James Kwok
Yu Zhang
Venue: ICML 2025 poster (2025)
Keywords: Multimodal Learning
Link Prediction
Graph Neural Networks
Primary area: deep_learning->graph_neural_networks
TL;DR: We first integrate vision structural awareness into MPNNs for link prediction, exploring new research questions and offering best practices.

Abstract: Message-passing graph neural networks (MPNNs) and structural features (SFs) are cornerstones for the link prediction task. However, as a common and intuitive mode of understanding, the potential of visual perception has been overlooked in the MPNN community. For the first time, we equip MPNNs with vision structural awareness by proposing an effective framework called Graph Vision Network (GVN), along with a more efficient variant (E-GVN). Extensive empirical results demonstrate that with the proposed frameworks, GVN consistently benefits from the vision enhancement across seven link prediction datasets, including challenging large-scale graphs. Such improvements are compatible with existing state-of-the-art (SOTA) methods and GVNs achieve new SOTA results, thereby underscoring a promising novel direction for link prediction.

Open Your Eyes: Vision Enhances Message Passing Neural Networks in Link Prediction
Yanbin Wei 1
Xuehao Wang'
Zhan Zhuang 13 Yang Chen
Shuhao Chen Yulong Zhang James Kwok
Yu Zhang'
Abstract
sentations and aggregates them into link representations to predict the existence of links. Besides, various structural features (SFs), which are characteristics derived from the graph topology to capture relationships and properties of nodes and edges, are integrated into MPNNs enhance their link prediction capabilities (Zhang & Chen, 2018; You et al., 2021; Zhu et al., 2021; Yun et al., 2021; Chamberlain et al., 2023; Wang al., 2024). This integration led to sig- nificant advancements, making the SF-enhanced MPNNs dominate the link prediction task.
Message-passie passeeg--snnngggg graph neural networks (MPNNs) and structural features (SFs) corner- stones for the link prediction task. However, common and intuitive mode of understanding, the potential of visual perception has been overlooked in the MPNN community. For the first time, we equip MPNNs with vision structural awareness by proposing an effective framework called Graph Vision Network (GVN), along with efficient variant (E-GVN). Extensive empirical results demonstrate that with the proposed framework, GVN consistently benefits from the vision enhancement across seven link prediction datasets, including challenging large-scale graphs. Such improvements are compatible with existing state-of-the-art (SOTA) methods and GVNs achieve new SOTA results, thereby underscoring promising novel direction for link prediction. The official code is available at https:/github.com/WWBYaaaa (wt.Y//nbbn999/GG/// 1999/EGVN.
Considering human perception of graph data, one of the most crucial means intuitively interpreting of graph in- formation through visual perception. While the structural awareness in MPNNs is derived from message-passing paths, and SFs are typically based on specific heuristic priors, both approaches have overlooked the potential of utilizing visual modalities to comprehend graph structures. As a fundamental capability of human perception, vision has matured into thriving field supported by robust re- search tools, such as readily available visual encoders such as VGG16 (Simonyan & Zisserman, 2015), ResNet50 (He et al., 2016), and ViT (Dosovitskiy et al., 2021). These tools offer powerful capabilities for visual information aware- ness and extraction. Various research domains, including natural language processing, have successfully integrated visual modalities, leading to significant advancements in areas such as visual question-answering (Antol al., 2015) and multimodal large language models (Zhang et al., 2024).
1. Introduction
Link prediction, which predicts the presence of a connection between two nodes, is a core task in graph machine learning. is crucial in numerous applications such as recommenda- tion systems (He al., 2020), drug interaction prediction (Yamanishi al., 2008), and knowledge-basce based reasoning (Bordes et al., 2013; Wei et al., 2023).
Given these developments, it is both timely and logical to consider incorporating vision into MPNNs. To be specific, we focus on integrating visual graph awareness into the MPNN architecture and exploring the roles that vision can play in enhancing link prediction. To this end. we propose three important but unexplored research questions:
Nlessage-asssing graph neural network (MPNN) (Kipf & Welling, 2017; Hamilton et al., 2017) is a prominent and powerful tool for link prediction. It generates node repre-
'Southern University of Science and Technology, Shenzhen, China 'Hong Kong University of Science and Technology, Hong Kong, China 'City University of Hong Kong, Hong Kong, China "Zhejiang University, Hangzhou, China. Correspondence to: Yu Zhang <yu.zhang.uu @ coaie@gmailocoo com'..
For the link prediction task, what is the effective approach to be aware of graph structures from vision?
RQ1:
Does incorporating vision awareness into graph structures enhance link prediction? If so, what are the underlying reasons?
RQ2:
Proceedings of the ndnd International Conference Machine Learning. Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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Open Your Eyes: Vision Enhances Message Passing Neural Networks in Link Prediction
RQ3: If vision-based structural awareness proves ben- eficial, how can it be effectively fused into the MPNN architecture?
(Zhang & Chen, 2018) and Distance Encoding (DE) (Li et al., 2020).
SF-enhanced MPNNs. The expressive power of naive MPNN architectures is limited (Zhang et al., 2021), con- strained by the 1 1-dimensional Weisfeiler-Lehmann (1-WL) test (Morris et al., 2019), and they fail to finely perceive substructures like triangles (Chen et al., 2020). To over- come these limitations, more recent studies adopt various structural features to enhance MPNNs. For example, SEAL (Zhang & Chen, 2018) incorporates SPD as structural fea- tures into MPNNs by concatenating the SPD from each node to the target nodes u and v with the node features. Neo-GNN (Yun et al., 2021) and BUDDY (Chamberlain et al., 2023) use heuristic functions to model high-order common neighbor information. NCNC (Wang al., 2024) directly concatenates the weighted sum of node representa- tions of common neighbors of u and u with the Hadamard product of MPNN representations of u and v.
To address the above research questions, we propose a novel framework called Graph Vision Network (GVN), as well as a more efficient variant E-GVN. The proposed models seam- lessly incorporate visual awareness of graph structures into MPNNs for link prediction, while maintaining orthogonal compatibility with existing methods. Extensive experiments across seven major link prediction benchmarks, including challenging large-scale graphs, demonstrate the benefits of integrating vision into MPNN-based link prediction by adopting the proposed GVN framework.
To our knowledge, GVN is the first method that incorpo- rates vision awareness into MPNNs. It demonstrates consis- tent SOTA effectiveness across various graph link prediction tasks, highlighting a promising but unexplored direction.
Main Contributions. (i) We propose novel frameworks GVN and E-GVN, that are the first in incorporating the vision modality into MPNN for link prediction. They are fully compatible with current models, ensuring seamless integrations. (ii) We reveal properties during graph visual- ization tailored to link prediction tasks and provide good practices. (iii) We analyze the underlying benefits of vision awareness in link prediction and provide empirical demon- strations. (iv) We delve into the scalability on large-scale graphs and propose efficient optimization in E-GVN. (v) We demonstrate the efficacies of GVN and E-GVN across seven common link prediction datasets, where vision awareness brings orthogonal enhancements to the SOTA methods.
Graph Learning with Vision. Recent research has ex- plored the potential of vision in graph Icarning. Das et al. (2023) find that the vision- laniun-a models have competi- tive node classification abilities. Wei al. (2024) shows that visual perception benefits language- based graph reasoning tasks. However, no existing work realizes the potential of vision in enhancing MPNN for link prediction, which is the focus of this paper.
3. Preliminaries
Notations. A graph G = (V, F)) comprises of a set V of nodes and a set E of links. We denote the adjacency matrix of by A E R=** where A(a..) > O and only if the edge (u.v) v) exists (i.c., (u, E E). We define (u) ;= {o e VlAu. > 0} as the set of neighbors of node v, and (v) as the set of k-hop neighbors of node v. other words, a node u (t) if and only u and v are reachable within k hops. The node feature matrix XG E RTXP contains the node features in G, where the v-th row x, corresponds to the feature of node v. We use 5t denote the k-hop subgraph enclosing the link (u, v). where vk un is the union of k-hop neighbors of u and v, and Ek is the union of links that can be reached by a kshop walk originating at u or v. Moreover, St is the k-hop subgraph starting from node v.
2. Related Works
Link Predictor. Link predictors can be divided into three classes: 1) Node embedding methods (Perozzi et al., 2014; Tang et al., 2015; Grover & Leskovec, 2016) represent each node as an embedding vector and utilize the embeddings of target nodes to predict links. 2) Link prediction heuristics (Liben-Nowell & Kleinberg, 2003; Barabási & Albert, 1999; Adamic & Adar, 2003; Zhou al., 2009) create SFs through manual design. 3) MPNN-bused link predictors produce node representations via the passsage-passigg mechanism (Kipf& & Welling, 2017).
(V F to
Structural Features. Structural Features (SFss are char- acteristics derived from the graph topology to capture the relationships and properties of nodes and edges. Common SFs are divided into two types: 1) Common Neighbor-basee SFs, including the Common Neighbor Count (CN) (Barabási & Albert, 1999), Resource Allocation (RA) (Zhou et al., 2009) and Adamic-Adat (AA) (Adamic & Adar, 2003). 2) Path-based SFs, such as the Shortest Path Distance (SPD) (Dijkstra, 1959), Double Radius Node Labeling (DRNL)
MPNNs for Link Prediction. The MPNN is a monly used model for link prediction. In MPNN, message passing is employed to iteratively update node representa- tions based on information exchanged between neighboring nodes. Mathematically, this mechanism can be written as
h = -'(tt- (AG(( (A. E N(o)))),
YG = MPNN(XG. G) yv = hh
2

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Open Your Eyes: Vision Enhances Message Passing Neural Networks in Link Prediction
GVN Framework
Efficient GVN (E-GVN)
Image Illustraions
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Figure 1. An illustration of the GVN framework (left) and its efficient variant E-GVN (middle), with the example illustrations of subgraph visualization images (right). GVN and E-GVN seamlessly incorporate visual awareness of graph structures into MPNNs, which boosts the link prediction capabilities while maintaining the orthogonal compatibility with existing methods.
where h. is the representation of node v after / layers, UC, M and AGG are the update, message-passingg and aggre- gation functions of layer i, respectively. YG E R=*=F the matrix of final node representations by MPNN for G. whose the uth row y. is the final representation of Given Ya, link probabilities can be computed as p(u, v) = No), where R is a learablee readout function.
To be specific, utilizing existing automated graph visual- ization tools (Details in Appendix F) such as Graphviz (Gansner & North, 2000), Matplotlib (Tosi, 2009), and Igraph (Gabor Csardi, 2006), a given query link (u, v) and its surrounding k-hop subgraph S are mapped one-to-one into an image 1 by graph visualizer GV. Formally, this is expressed as I GV(S uv
uv. u, v).
In this process, three key aspects are noteworthy:
4. Methodology
1) Keeping Style Consistency. It is crucial that all visual- ized subgraphs maintain consistency in the graph visualizer GV, such as uniformly using Graphviz with fixed configura- tions (e.g., graph layout algorithm, node colors, and shapes). This prevents inconsistent image styles from introducing additional learning difficulties and unstable training.
In this section, we present the proposed GVN framework. An illustration of GVN is in Figure 1. In Sections 4.1 to 4.3, we will delve into the detailed designs inside, along with ad- dressing the research questions raised in the introduction. In Section 4.4, we propose a computationally efficient variant of GVN for large-scale graphs.
2) Highlighting the Queried Link. The unique role of the queried link is essential for link prediction. By default, the end nodes of the queried link are colored emphasize their roles, and the link itself is masked for prediction.
4.1. Scope-Decoupled Subgraph Visualization
Link-Cente Link-Centered Subgraph Visualization. Beginning with RQI (i.e., For the link prediction task, what is the effective approach to be aware of graph structures from vision?), we transform graph structures into visual representations by rendering them as images during pre-processing. As aarge-scale graphs often have thousands of nodes and edges, we utilize k-hop subgraph sampling, common practice in graph learning (Hamilton et al., 2017). This method concentrates on visual awareness via the most relevant local k-hop subgraph Sh around the central link (u, v). while excluding distant structures that may introduce noise. In line with the locality principle' and effective practices of many MPNNs with & (Kipf & Welling, 2017: Hamilton et al., 2017; Xu et al., 2019; Velickovic et al., 2018: Chen et al., 2022), we limit k. which defines the visualized scope, to maximum of 3.
3) Ablating Node Labels. All the node labels are omitted, enabling the model to focus on the graph structure, which benefits generalizability.
k
2
3
k
'Lcaality Principle: Correlated information is contained within the near neighbors (Bronstein et al., 2017; Wu et al., 2020).
Figure 2. Illustrations of visual graph images with different A's. Decoupled Vision Scope. While the perception scope ex-
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Open Your Eyes: Vision Enhances Message Passing Neural Networks in Link Prediction
pands during message passing in MPNN, we fix the visual perception scope k during visualization. This ensures that the scope in vision can be decoupled from which in message passing and offers two key advantages. First, both theoreti- cal analysis and empirical evidence (Zeng et al., 2021) show that a decoupled scope independent from message-passing can improve expressivity of MPNN by addressing the over- smoothing issue (Li et al., 2018: Kenta Oono, 2020; Shen et al., 2024), and enhances the computational scalability of the models by alleviating the neighbor explosion problem (Chiang et al., 2019; Zeng et al., 2019). Second, as shown in Figure 2. an excessively large visual perception scope can lead to overcrowding of nodes/edges on a fixed-size canvas, resulting in cluttered appearance that complicates graph interpretation. By using a small k. we maintain image clarity independent of message passing.
(e)
(b)
(c)
Figure 3. (a) An illustration of the challenge in distinguishing links with isomorphic nodes. (b) and (c) are the 1-hop subgraphs sur- rounding the links (v), 02) and (vi, 0s). respectively.
scope, our method allows the model set the independent scope of MPNNs via its depth. This enables the model to benefit both from the refined structure awareness pro- vided by VSFs and the capability to access more structure information in a wider scope through deep MPNNs.
Fine-ge sine-grained Substructure Awareness. The ability to cap- ture substructures (motifs) is another perspective of MPNN expressive power and plays a crucial role in areas like bi- ology, molecular, and social networks (Chen et al., 2020; Kanatsoulis & Ribeiro, 2024; Yan et al., 2024). However, this can be challenging for MPNNs (Chen et al., 2020; Arvind et al., 2020). We demonstrate in the following that VSFs are helpful for MPNNs in capturing substructures. Specifically, we follow the experimental setup in (Chen et al., 2020). This involves generating two types of graph datasets, Erdös-Rényi graphs and random regular graphs, and compute the counts of two substructures including tri- angles and 3-stars as ground -ruth labels. We use MPNN followed by a 3-layer MLP decoder as the architecture and the VSFs are concatenated after the MPNN- repre- sentations. The evaluation metric is the normalized mean squared error (i.e., ratio of the mean squared error over the variance of ground-truth labels). Table 1 shows the best and median (third-best) performance over five runs with different random seeds. As can be seen, incorporating VSFs significantly improves the substructure capturing abilities of MPNNs. More details of this experiment are provided in Appendix E.
4.2. Adaptive Extraction of Visual Structural Features
The obtained visual graph image the passes through a vision encoder VEg. with trainable parameter v/, to extract visual structural features (VSFs) Vue VE (T
R$ for the local subgraph around the queried link (u, v). By default, we use the vision encoder of ResNet50", and extract VSFs from its last convolutional layer.
To answer RQ2 (i.e., Does incorporating vision awareness into graph structures genuinely enhance link prediction? If so, what are the underlying reasons?), we analyze the superiority of VSFs for link prediction from three aspects:
Link Discriminative Power. MPNNs struggle to differen- tiate links involving isomorphic nodes (Zhang et al., 2021; Chamberlain et al., 2023). As depicted in Figure 3(a), nodes 1/ and vy have isomorphic subgraphs, resulting in iden- tical node representations Yu2 = Yus after permutation- equivariant message passing, akin to the 1-dimensional Weisfeiler-Lehman test. Consequently, the link probabilities p(11, 022 = R(y.,,
and p(11, v3)) = R(y,, vvs) are identical. This fails to account for the differences between U/2 and V/ w.r.t. U1 and is detrimental for link prediction. For example, U2 is 5 hops away from U1, while v3 is just 2 hops away. Moreover, Vi and 1y share a common neighbor, but not i1 and 12. On the other hand, Figures 3(b) and 3(c) show the I-hop subgraphs surrounding these two links, and they are clearly very different. Therefore, 1-hop VSFs extracted from them help distinguish these links.
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Table 1. The performance of MPNNs with VSFs for counting tri- angles and 3-star on Erdōs-Rényi and Random regular graphs.
Remark 4.2. VSFs can provide fine fine-grained substructure capturing ability for MPNNs via VSFs.
Remark 4.1. With the same perceptive scope, VSFs can discriminate links involving isomorphic nodes, whereas MPNNs or the I-dimensional Weisfeiler-Lehmar test cannot.
Information-rich and Adaptive SF Extraction. While the design of existing structural features rely on heuris- tics, VSFs encode the whole subgraph, making them more information-rich. Figure 4 shows the reproduction ratios
Note that when VSFs provide discriminative power in its
httpps: http://wwwlllla cadd w/ddw//aaa.pyyoorrcccc.cccc 50-067 00ba61.pp .th..
"The reproduction ratio is defined as the percentage (%) of SFs successfully predicted.

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Open Your Eyes: Vision Enhances Message Passing Neural Networks in Link Prediction
Comparisan Reproduction Ratios
just their emphasis on different types of structural informa- tion, thus providing scenario adaptability.
Reproduccion Rasto (%)
80-
80.23%
78.47%
75.85%
73.34%
72.12%
60-
VSFs are not permutation-eqqivarian yet they remain ef- fective with MPNNs, as will be shown in Section 5.1. This is potentially attributed to two reasons: 1) Learnable VSFs capture specific information like structural patterns or motifs (see Remark 4.2). 2) Visualization introduces permutation- based augmentations (e.g., varying layouts), making the decoder less sensitive to node order.
40
20
CN
8A
AA
SPQ
DRNI
D2
Figure 4. Reproduction ratios of various structural features based on VSFs on the ogbl-ddi dataset.
of various SFs based on VSFs on ogbl-ddi. by feeding the VSFs extracted from the pretrained ResNet50 into a train- able 3-layer MLP. As can be seen, VSFs effectively capture most of the information from wide array of structural fea- tures, underscoring their comprehensive nature as a versatile structural feature pool.
4.3. Compatible Features Integration
After extracting valuable visual structure features Vuu. the next step is to integrate them with MPNNs, addressing RQ3 (i.c.. If vision-bbssee basond structural awareness proves beneficial, how can it be effectively fused into the MPNN architecture?).
Remark 4.3. VSFs involve the information of a wide range of structural features.
To ensure general applicability of the GVN framework, the feature integration process should be compatible with exist- ing methods, to benefit from both previous advances and the newly introduced visual structural awareness. Based on this compatibility principle, we offer three widely applicable feature integration strategies, all of which are independent of the message-passing passing process in MPNNs.
The reproduction ratios of various SFs reflect the relative distribution of information within the VSFs. Table 2 com- pares the reproduction ratios of SFs between VSFs obtained from a pre-trained ResNet50 and those after finetuning. The latter is derived from ResNet50 encoder fine-tuned for link prediction with a 2-layer MIP on the ogbl-ddi and PubMed datasets. Note that ogbi-ddi is a very dense graph, while PubMed is much sparser. As shown in Table 2, after finetuning on ogbl-ddi, the reproduction ratio of path-based SFs (SPD, DRNL, and DE) consistently decreases. This aligns with the under-perte inder-performance observed in path-based link prediction models like SEAL (Zhang & Chen, 2018) and NBFNet (Zhu et al., 2021) on the ogbl-ddi dataset. This is because in the ogbl-ddi dataset, most node pairs are reach- able within two hops, making path-based structural features like SPD less informative. On the other hand, in the sparser PubMed dataset where path information is more valuable, the reproduction ratios of common neighbor-based simi- larity functions (CN, RA, AA) consistently increase after finetuning, This trend is demonstrated by models such as NcoGNN, Buddy, and NCCN (Yun et al., 2021; Chamber- lain et al., 2023; Wang et al., 2024), which consistently benefit from common neighbor similarity functions across various datasets. These observations highlight the ability of VSFs to adapt the internal information types to meet the specific demands of different scenarios through finetuning.
I) intention-basede Integration. We first project Vee E SR. to Vue RF for dimension alignment. Then the MPNN- produced node representations yu E F and yo R F are updated with Vae via cross-attention (denoted CA), result- ing in vision-aware node representations y, = CA Vav) and y. CA(y V.w). Finally the link existence proba- bility can be computed as p(u, v) = R(y.. Vv). where is the readout function.
2) Concatenated Integration. We concatenate Vue with y. and y. produce vision-aware node representations y. and Yu. as: y, = Vullvuos V. = lullvu.- Then we use the readout function to produce the link existence probability p(u, u) = So).
3) Weighted Integration. We use an MLP to construct a rision-based decoder model (denoted VDecoder). which takes Var input directly predict the link existence probability based solely visual structural awareness, i.e., Poision v) = VDecoder(v...). Simultancously, the readout function predicts the link existence probabil- ity based on the node representations produced by the MPNN, i.e., PMPNN v) = R(y.,, The final link existence probability p(u, v) is a weighted integration of both predictions with a learnable weight d, i.e., P(a,v)
Common Neighbor Si's
Path-based Si's
CN
RA
AA
SPD
DRNL
DB
ogbi-ddi (wlo)
80.23%
78.47%
78.89%
75.85%
73.34%
72.12%
ogbi ddi (w/)
82.39%
79.66%
80.24%
31.11%
29.20%
35.49%
8 Prisson (u, v) + (1 5) PMPNN (u, v).
PubMed (wlo) 76.39%
78.87%
72.56%
76.60%
72.36%
71.19%
PubMed (w/)
83.96%
82.80%
78.86%
78.77%
73.34%
71.59%
These integration strategies can be freely chosen as needed, Empirically, we observe that attention-based integration is more effective and therefore used by default.
Table Reproduction ratios SFs in VSFs with and without finetuning the ogbl-ddi and PubMed datasets.
Remark 4.4. Through finetuning, VSFs can adaptively ad-
Thus far, we have presented the GVN framework to address
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Open Your Eyes: Vision Enhances Message Passing Neural Networks in Link Prediction
Algorithm 1 The GVN Framework (Attention-baseed).
learnable parameter Φi which processes the static VSF ve to adaptive Ve, where V. = Adaptor, for each node v.
Require: Graph G = (V, E) with node attributes Xc,
queried links Q =
Pre-MPNN Integration on Attributes. Unlike GVN, which integrates VSFs after the MPNN, E-GVN incorpo- rates v. into the node attribute x, to produce vision-aware node attribute x,, which are then fed into the MPNN as inputs. Due to the integration occurs before message pass- ing, this allows the vision-awart structural information to participate in the message propagation and aggregation to get further enhanced.
Ensure: Link existence probabilities (p(u, (u) E )
1: YG MPNN(G, Xx)
2: each (u,z) E Q do
3: Step 1: Scope-decoupled Subgraph Visualization
4:
S uur + Extract k-hop subgraph around (u, v)
5: I + GV(S"..)
6: Step 2: Adaptive Extraction of VSFs
7:
Vur + VEE.g (The)
8:
Step 3: Compatible Features Integration (default)
To achieve this, the three integration strategies in GVN are adapted as follows: 1) Attention-basee Integration:
9:
Yv f- Yolu], Yoluj
10:
Vur f- Linear( Vav)
x, = CA(x., Vo); 2) Concatenated Integration: X,
11:
Yv t CA(ya, Vur), Ca(y,, Vue) p(u, u) +- Nv)
x, x,,lVoi 3) Weighted Integration: x, = òLinear कn (x,) + (1 - -1))iieeaaa (Vo), where ò is learnable weight and Linears, , Linear are linear layers. Finally, the MPNN- produced node representations are processed by a readout function to predict the link existence probability.
12:
13:
Output v)
14:
end for
the three research questions corresponding to the three main steps in GVN to integrate vision information into MPNNs. We summarize the GVN framework with default attention- based integration in Algorithm GVN Algorithms with other integration are in Appendix A.1.
Time Complexity. Let n and / be the numbers of nodes and links, respectively, F and F' be the dimensions of node features and MPNN- representations, respectively, (MPPNN) and O(VE) be the complexities of the MPNN and vision encoder, respectively, and S be the dimension of the VSF. With the default attention based integration, the time complexities of GVN and E-GVN are O(MPNN) + (V + O(((S'' + F²)) and O(MPNN) + (VE) + + SF respectively. We can see that E-GVN reduces the computational complexity, as n is much less than I. More details are provided in Appendix B.
4.4. E-GVN: An Efficient Variant
Considering the scalability of GVN on large- graphs, we propose a more efficient variant called Efficient GVN (E- GVN), whose architecture is presented in Figure 1 and the algorithm is in Appendix A.2. The specialized modifications are introduced as follows.
Node-centered Subgraph Visualization. GVN requires subgraph visualization for the surrounding area of each link, which can be time-consuming. Therefore, in E-GVN, the visualization area is changed from a link-centered k-hop neighborhood Sh to node-centered hoh subgraph st, with the central node colored to highlight its role. This vi- sualization process is formalized as 1 = GV(S$, v). Due to the fact that the number of nodes is much smaller than the number of links in most natural graphs, this approach sig- nificantly reduces the visualization cost from (l) to On), where and n denote the total number of links and nodes.
5. Experiments
In this section, we conduct a series of experiments to demon- strate the effectiveness of the proposed GVN and E-GVN.
5.1. Evaluation on Rerl-World Datasets
Datasets. We conduct experiments on seven widely used link prediction benchmarking, including the Planetoid cita- tion networks: Cora (MeCallum et al., 2000), Citeseer (Sen et al., 2008), and Pubmed (Namata et al., 2012), and the large-scale OGB link prediction datasets (Hu et al., 2020): ogbl-collab, ogbl-ppa, ogbl-citation2 and ogbl-ddi. Statis- tics of these datasets are shown in Appendix C.
Partial-adaptive VSFs. GVN use end-to-end finetuning of vision encoder VE& to refine the VSFs. However, such end- to-end finetuning requires retaining all visualization images and thus lead to substantial memory overhead. To enhance scalability in terms of space, E-GVN first freezes the vision encoder extract static VSF v... Instead, those static VSFs {v.} can be stored and loaded as a fixed vector repository, significantly reducing the storage payload. After that, as we still want the VSFs to flexibly adapt to the different scenarios, we additionally append a trainable Adapter with
Baselines. Baseline methods used include 1) Link predic- tion heuristics: Common Neighbor counts (CN) (Barabási & Albert, 1999), Adamic-Adar (AA) (Adamic & Adar, 2003), and Resource Allocation (RA) (Zhou et al., 2009); 2) MPNNs: GraphSAGE (Hamilton et al., 2017) and Graph Convolutional Network (GCN) (Kipf & Welling, 2017); 3) Advanced SF-enhanced MPNNs: SEAL (Zhang & Chen, 2018) and NBFNet (Zhu et al., 2021) with path-based SFs,
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Open Your Eyes: Vision Enhances Message Passing Neural Networks in Link Prediction
Table 3. Link prediction performance (average score = standard deviation). "-" indicates that the training time is >> 12 hour/epoch (for GVN) or out of memory (for NBFnet). The best performance is shown in bold, and the second-best is underlined.
Cora @HR@ @ 100)
Citeseer (HR@ 100)
Pubmed (HR@ @ 100)
ogbl-collab (HR@50) 50)
ogbl-ppa (HR @ 100)
ogbl-citation2 (MRR)
ogbl-ddi
(HR@20)
CN
33.92#0.46
23.13:0.11
56.0000.00
27.65
51.47720.00
17.73=0.00
AA
39.85++1.8 1.34
19
27.38
64.35=0.00
32.45
51.8940.00
18.61+0.00
RA
41.07 40.48
33.56+0.17
27.03++0.35
64.00=0.00
40.33
+0.00
27.60=0.00
SAGE
55.022:4.03
37.71
39.66:1.72
48. 18
16.55+2.40
82.6010.36
53.90=4.74
GCN
66.79+1.0
67.08+2.94
53.02++1.9
44.75+1.07
18,67+1.32
84.74400.1
37.07+5.07
GVNGON
$1.13
83.93+0.97
73.17+1..u
B-GVNecN
80.01 11.05
82. 1..
71.94+1.87
62. 12
32.15+1.58
16.10+o.13
60.21+6.o7
Neo-GNN
80. 1.31
84.677+-2.6
73.93+1.199
57.52=0.37
19.13
87.26++0.84
63.57=3302
SEAL
81.71#1.30
83.89 22.15
75.54+1.32
64.71=0.43
48. 18.80+3.16
87.67+00.2
30.5643.80
NBFnet
71.65 27
1..07
58.7311.99
4.00
BUDDY
88.00:10.41
92.9310.27
74.10:10.78
65.94 58
1.28
87.5611.11
78.51
NCNC
89. 1936
93.47
81.29:10.95
66.61
61.42
89.12:10.4
84.1113.67
GVNNGNG
90.70=0..66
12.12
82.1770.77
B-GVNNCNC
91.47=0.38
94.44+0.53
84.02:0.55
68.14
63.4520.66
90.72.0.24
87.31=3.04
Neo-GNN (Yun et al., 2021), BUDDY (Chamberlain et al., 2023), and NCNC (Wang et al., 2024) that is the SOTA SF-enhanced MPNN.
indicates the MPNN model used within the frameworks. Our choice of MPNNs is based on the following consid- erations: First, using GCN, a classic and straightforward MPNN, within the proposed frameworks directly demon- strates the enhancement provided by vision awareness when compared MPNN alone. This allows us to clearly see the impact of incorporating the visual modality into MPNNs. Second, based on NCNC, a state-of-the-art MPNN en- hanced by advanced structural features, the comparison between / NCNC and NCNC will high- light the additional performance improvements from the vision awareness that are orthogonal to existing advanced methods. This demonstrates how visual features can comple- ment and enhance existing sophisticated models. Although we focus on these two MPNNs, the proposed GVN and E-GVN are compatible with most MPNN models.
Performance Evaluation. The use of evaluation metrics fol- lows (Chamberlain et al., 2023; Wang et al., 2024). Specifi- cally, for the Planetoid datasets, (HR @ 100), while for the OGB datasets, we use the metrics in their official documents," i.e., hit-ratio at 50 (HR 50) for ogbl-collab, HR @ 100 for ogbl-ppa, Mean Reciprocal Rank (MRR) for ogbl- ogbl-citation2, and hit-ratio at 20 (HR@) (2) for ogbl-ddi. 5 All results are reported as average and standard variation over 10 trials with different random seeds.
use the hit-ratio at 100
Implementation Details. All experiments are conducted on an NVIDIA A100 80G GPU. For GVN and E-GVN, the candidate hyperparameters include the visual perception scope (i.e., the subgraph visualization hop) k ranging from I to 3, the hidden dimension ranging from 512 to 2048, the number of MPNN layers and readout predictor layers varying from 1 to 3, the two separate learning rates for trainable VSFs and compatible feature integration among {10-7, 10-5, 0,001, 0.01), and the weight decay from 0 to 0.0001. The hyperparameters with the best validation accuracy are selected. For the model parameters, we utilize the Adam algorithm (Kingma, 2014) as the optimizer. As default settings, we use Graphviz (Gansner& & North, 2000) as the graph visualizer and use a pretrained ResNet50 (He et al., 2016) the vision encoder. More details on the experimental setup are in Appendix D.
Main Results. Table 3 compares the performance of the proposed methods with various baselines.
(i) By integrating visual structural features into GCN, GVN enhances GCN with relative improvements on link pre- diction performance (HR @ 100) by 21.47%, 25.13% and 38.00% on Cora, Citeseer and PubMed, respectively. Sim- ilarly, E-GVN achieves relative improvements of 19.79%, 23.51% and 35.68% upon GCN on these three datasets. Ad- ditionally, due to the efficient designs, E-GVN extends the visual benefits to large-scale graph datasets ogbl-collab, ogbl-ppa, ogbl-citation2 and ogbl-ddì, bringing relative improvements of 38.86% (HR@ (50, 72.20% (HR @ 100), 1.60% (MRR), and 62.42% (HR @ 20), respectively. There- fore, consistent results indicate that visual awareness has been effectively integrated into GCN by the proposed meth- ods and significantly enhances the link prediction perfor- mance of GCN.
Configurations of the Proposed Methods. We use four configurations of the GVN and E-GVN frameworks: GVNGON. NVNN E-GVNGON, and E-GVNNONC. as shown in Table 3. The subscript (i.e. 'GCN' or 'NCNC")
hhtpss//obb.stanfffii www.s/oooeeeedd//o/eeeeeeeeeeeee edw//ocs/leader Sine
(ii) Based SF-enhanced NCNC model, both GVNNCNC and E-GVNNGNC still show remarkable improvements.
Evaluation results other metrics are in Section 5.2.
7

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Open Your Eyes: Vision Enhances Message Passing Neural Networks in Link Prediction
Table 4. The performance comparison of the proposed methods against the strongest baseline NCNC across broader metrics.
Cora
Citeseer
Pubmed
Collab
PPA
Citation2
DDII
hit@1
GVNyowG
11
51 51.69
18 66
N-GV
8.66
59. 59.30 2s.5a
16.88
11.04
6.53
86.6221.04
0..2
NCNC
10.90
32.45 32.15
8.57
9.82
7.78
84.66:1.15
0.10
h
GVNNONG
26.66
59.97
32 23:23:
B.GVN
27. 27.55
66.76 6..76.4.20
31.21 23.95
26.31
18.88_1.21
94.2910.00
2.12
NCNC
25.04
40.40
17.58g6.57
21.07
16.58
22.37
0.59
hit@ 10
GVNN
58.83
25.28
40.34
CGVVNcNG
65.98
77. 17.12: :2.99
47 10:90 we
43, 43.12
31.16
97 97.07
50.8 60.88:11.85
NCNC
53.78
69.50
34.29 24.29
13.2220.19
26.67
96.9920.84
45.64g11.12
hit@20
GVNNONC
70.01
81.11
53.33222.77
E-GVN
69. 69.55
82.02 1.46
56. 56.92::a
56.87
98. 98.17 44.06=2.00
87.31 87.31
NCNC
67. 10
79.05=2.08
51.42=3..8
57.83
35.00+2.22
97. 97.22.
83.92_3.25
h0t@50
GVNN
82.06g1.04
88.88
71.66
E-GVN
82, 22.99.2295
20.97
71.55
68 14
52.58
99 00.00
95. 95.95
NCNC
11.36
88. 5..60
69.25 69.25
66.88
48.66 48.66
99.01 #0.53
94.85
hit@ 100
GVNNOwG
90.70
94.12+0.58
82.17 $2.17
B-GVN NENG
91 91.47=0.30
24.44
84.02 66
70.83++2.25
63.45_0.00
99.51
97. 27.99
NCNC
19.05
93.13g1.15
81.18 1.21
71.9610.14
62.02
99.37
97.60 22
mnr
GVNNONG
24.66::4.81
62.744s..s
26.32
B-GVNNENG
23.27
66.49 2353
27.1 27.11
18.044a.01 17.68
19.66-0.11
90.72.0.24
13.32
NCNC
23.50g9.07
45.0 45.64
15.63
29.06
89.1220.a 80
8.61g1.37
Although NCNC is a leading link prediction model by en- hancing MPNN with dedicated common neighbor structural features, adopting GVN and E-GVN brings additional im- provements over NCNC. These results demonstrate that the visual awareness provided by GVN or E-GVN own advan- tages not covered by existing methods and can be used in conjunction with current SOTA methods for better perfor- mance. Therefore, GVNNGNG and B-GVNNCNG surpass all baselines and established as more powerful link pre- diction approaches.
GVN achieves 39 best scores (in bold), GVN achieves 7 best scores, and our strongest baseline NCNC achieves 3 best scores. Therefore, GVNNCNG and L-GVNNcNe con- sistently outperform NCNC in more comprehensive metrics.
5.3. Ablation and Sensitivity Analysis
Visualization Style Consistency. Table 5 shows that incon- sistent styles degrade performance and emphasize keeping styles consistent. The inconsistent styles are sampled from a fixed range of node colors, shapes, and graph visualizers, as detailed in Appendix G. Appendix H, we include more comprehensive findings by studying the impacts of node colors (Appendix H.1), node shapes (Appendix H.2), and node labeling strategies (Appendix H.3).
(iii) Compared to GVN, the computationally efficient de- sign of E-GVN makes it more suitable for large-scale graphs. GVNGON is more powerful than E-GVNGGN. This may be because the visual structural awareness in GVN link- based, therefore explicitly revealing link pairwise relations such common neighbors or shortest path differences for distinguishing links with isomorphic nodes better. How- ever, when using SF-enhanced NCNC, the improvements brought by N-GVNNCNC surpass those of GVNN We attribute this to the fact that in GVNNCNG. both the link- centered visual awareness and the common-neighhor-basee SF can reveal the common neighbor information between the link nodes, which makes their effects partially overlap. In contrast, the pre-MPNN integration in E-GVN allows vision-aware structural information to be further aggregated during message passing, which provides more comprehen- sive visual awareness.
Visualization Scope Impact. Table 6 shows the perfor- mance with varying visualization scopes k. The results consistently show that & = 2 is enough for effective VSFs.
Graph Visualizer Selection. Table shows the perfor- mance with different graph visualizers. The results demon- strate stable performance across various graph visualizers.
Vision Encoder Selection. Table 8 shows the performance with different vision encoders. The results show stable performance across various vision encoders.
Feature Integration Strategies. Table 9 shows the perfor- mance when varying feature integration strategies in Sec- tion 4.3. Experimental results suggest that in most cases, the default attention-based integration (denoted "Attention" in Table 9) is more effective than concatenated integra- tion (denoted "Concat") and weighted integration (denoted "Weight").
5.2. Evaluation Broader Metrics
Besides the metrics listed in Table 3, the performances of proposed methods against the strongest baseline NCNC with broader metrics are presented in Table 4. In total, E-
8

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Open Your Eyes: Vision Enhances Message Passing Neural Networks in Link Prediction
VSF Adaptivity. Table 10 shows the impacts of VSF Adap- tivity, where "freeze" means using frozen vision encoder, making VSFs static, "partial" adopts the partial adaptive VSFs proposed in Section 4.4 that freezes the vision en- coder but supplements it with a learnable adapter to provide some adaptivity, and "full" means the models are fully fine- tuned. Results show that static VSFs lose adaptivity, leading to performance degradation. The "partial" strategy can provide comparable performance with the "full" strategy, demonstrating its effectiveness.
visualization time across link queries, E-GVN still exhibits computational overhead similar to the base models GCN and NCNC. Therefore, when leveraging the lightweight base models (e.g.. GCN or NCNC), E-GVN maintains efficiency for large-scale graphs.
GVN GVNwew E.VNNoc B-VV NCNC -CN
SEAL
NBFmm
10.
/GB
10'
Time is
10"
memory
Table 5. Performance comparison between consistent and incon- 1072
GPV
sistent visualization (HR @ 100).
10"3-
100
Cora
Citereer
10a
10
10
10
consistent
incresiitent
consistent
incomsistent
batch size
batch size
GVNNowe
90. 70.0.0.
94.12:0.38 $9.88
03.65
Figure 5. Inference time and the use of GPU memory of different methods on Cora.
E-GVN woxe
91.47au.3 se
90 29
94. a4
03.90amm
Table Performance comparison of the visualization scopes
Cone
Grewer
5.5. Comparison with Positional Encodings
h-1
k- 2
R-g 3
8-1
2-2
k-3
GVNscNe B-GVNSONG
92.51 53,20
94.12 94.44:035
92.33
In addition to comparing with heuristic SFs, we further demonstrate the effectiveness of VSFs by comparing them against four representative encoding mechanisms for nodes: 1) 2- 2-dimensional coordinates of nodes in the subgraph im- age, 2) Laplacian positional encoding, 3) Distances to other nodes, and 4) Node degree (centrality encoding). These positional encodings (PEs) are utilized as node features and processed by a 2-layer GCN followed by 2-layer MLP for link prediction. The comparison results of Hits @ 100 score among VSFs and these encoding mechanisms are pre- sented in Table 11. As observed, VSFs outperform the PFs across various datasets. Notably, directly encoding the 2- dimensional coordinates proves insufficient, highlighting the importance of employing a vision encoder to capture comprehensive structural information.
97.47:036 90
50,21
02.62:
Table 7. Performance comparison of different graph visualizers.
Cura
Clessvr Maplodibb
Graphriz
Maplodii
Igrpp
Graptviz
Igmaph
GVNN
90. 70
90 5.500e.a a
90 8a
94 ss
03.96gn e
94 28
97.47
31.31
94 44
91.3
$4.12
Table Performance comparison of different vision encoders.
Cora
Cieezeer VOG
ResNer15
VGG
ViT
ResNe150
VIT
GVNsese
80.90 70:000
50 00.00
47
$0.92 m 21.242006
94.44got
88 45
Table 9. Performance comparison of feature integration strategies.
Choweer Concat
Ancution
Concut
Weight
Attestion
Weight
GVN ooNe E-GVNwese
90.70...50
89 Lt
94.12
91.47:0.66
70.58
90 90.00a130
04 04:44:000
88 25a334
90.8111.1
Table 10, Performance comparison with varying VSF adaptivity.
Core
Cveneer paniill
puniia
froeze
full
Cora
Citeseer
Pubmed
GVN wone
80.07anes
30 22.22-0000
30 00.30
78.75a
12
VSF
71.32 1:2 0.70
60.96 1 0.68
48.27
0.51
R-GVNsowe
80 80.0020:4
91 17.47 av
91. 888 sn
02 72772 cs
94.444633
94 02
2-D Axis in Image
38.57 + 1.22
33.29 + 1.80
25.34 0.95
Laplacian PE
55.14 + 0.84
52.03 1.17
46.80 0.75
5.4. Scalability Analysis
Distance
42.03 + 0.82
56.65 + 0.43
44.21 0.36
Degree/Centrality
42.80 + 1.52
44.15 + 1.61
34.90 1.23
Figure 5 compares the inference time and GPU memory for inferring one batch of samples from Cora (including pre-processing time). Among all the methods in compari- son, GVN is the most time-consuming, followed by SEAL and NBFnet. These three methods also require consider- ably more memory than the others. This elevated resource consumption is due to the need for pre-processing and com- putation for each link, and the storage of intermediate vari- ables with respect to links. Particularly, GVN requires graph visualization, which introduces extra pre-processing time. Therefore, similar to SEAL and NBFnet, GVN is not well- suited for large-scale graph computations. In contrast, the visualization of E-GVN is node-dependent, which can be reused for diverse links. After amortizing the pre- pre-processing
Table 11. Link prediction effectiveness between VSFs and posi- tional encodings (Hits@ 100).
6. Conclusion
We propose GVN and E-GVN, novel frameworks that first reveal the vision potentials to enhance the link prediction ability for MPNNs. We provide key practices and address unexplored research questions in the integration of vision and MPNN. Comprehensive experiments demonstrate that the proposed methods significantly improve link prediction and are fully compatible with existing methods. GVN ex- hibits novel direction for link prediction, with the potential to extend to more graph learning tasks.

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Open Your Eyes: Vision Enhances Message Passing Neural Networks in Link Prediction
Impact Statement
Chen, D., O'Bray, L.., and Borgwardt, K. Structure-aware transformer for graph representation learning. In Interna- tional Conference on Machine Learning, pp. 3469-3489, 2022.
This work underscores the often-overlooked yet effective role of visual perception in graph learning. By drawing attention to this aspect, it is poised to generate discussion and interest within the community. Additionally, it may inspire the development of further research that combines graph neural networks with visual insights, leveraging their synergy across broader range of applications. For example, this approach could be extended to other graph tasks such as node classification, as well as applied to various types of graphs such as heterogeneous graphs and temporal graphs. We leave these for future works.
Chen, K. and Wei, Y. UPCS: Unbiased persona construction for dialogue generation. In International Conference on Acoustics, Speech and Signal Processing, pp. 1-5, 2025.
Chen, Z., Chen, L.,, Villar, S., and Bruna, J. Can graph neural networks count substructures? Advances in Neural Information Processing Systems, 13:10383-10395, 2020.
Chiang, W.-L., Liu, X., Si, S., Li, Y., Bengio, S., and Hsich, C.-J. Cluster-GCN: An efficient algorithm for training deep and large graph convolutional networks. In Inter- national Conference on Knowledge Discovery & Data Mining, pp. 257-266, 2019.
Acknowledgement
This work was supported by National Key Research and De- velopment Program of China (No. 2022ZD0160300), NSFC grant (No. 621 36005), and the Research Grants Council of the Hong Kong Special Administrative Region (Grants 16200021, 16202523, C7004-22G-1). We also acknowledge the authors of (Chen & Wei, 2025; Lu et al.; 2024; 2025).
Das, D., Gupta, I., Srivastava, J., and Kang, D. Which modality should I use Text, motif, or image?: Under- standing graphs with large language models. Preprint (ttV:2311.098622 2023.
Dijkstra, E. W. A note on two problems connexion with graphs. Numerische Mathematik, 1959.
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Open Your Eyes: Vision Enhances Message Passing Neural Networks in Link Prediction
A. Supplementary Algorithms
This section provides the algorithms for GVN and E-GVN.
A.1. Algorithm for GVN with Selective Integration Strategies
Algorithm 2 The GVN Framework.
Require: Graph G (V, F) with node attrihutes Xc, queried links Q = v(u, Ensure: Link existence probabilities (p(u,v) (u, v) E Q}
Yo t- MM,
2: for each (u, v)) E do
3: Step 1: Scopp-dccoupled Subgraph Visualization
4:
S + Extract k-hop subgraph around (u, v)
5:
Iu + GV(S)v)
6:
Step 2: Adaptive Extraction of VSFs
7:
+ VE,,,(/uu)
8:
Step 3: Compatible Features Integration
9:
yu.Yo yv +- YG(uu, Yo(v) if use Attention-based Integration then
10:
11:
Vuv -- Linear(v...)
12:
Yu:
CA(y,; Vuv); CA(ye, Vue)
p(u, v) + H(F...o)
14:
else if use Concatenated Integration then
15:
S. + Yu Ve Vue
16:
p(u, v) +- R.)
17:
else if use Weighted Integration then
Prisiun (u, v) <- VDDcoder(Vvel
19:
PMPPNN(P (, v) &- Ro)
20:
p(u,v) +- 8 prision u, v) (1 - 8) pMPPN((, v)
21:
end if
22:
Output p(u, v)
23:
end for
A.2. Algorithm for Efficient GVN (E-GVN)
Algorithm 3 The Efficient GVN (E-GVN) Framework.
Require: Graph G (V, E) with node attributes Xc, queried links v),
Ensure: Link existence probabilities (p(u, (u, v) E Q}
1: for each node E V do
2: Step I: Scope-dccoupled Subgraph Visualization
3:
St + Extract k-hop subgraph around (v)
4:
It GV(S*)
5:
Step 2: Adaptive Extraction of VSFs
6:
V. VE(I*)
7:
V. +- Adaptor.(v.)
8:
Step 3: Compatible Features Integration
9:
if use Attention-based Integration then
10:
t- I-CAxx,,e V.)
clse if use Concatenated Integration then
12:
&. < -V.
13:
else if use Weighted Integration then
14: X. 8Linear,, (x.)
Lincar (V.)
end if end for
17: Xo + {x,}
VG + M-NNNNG Xo)
19: for each (u, E Q do
Ju.Yo Yaluj, Ya[v]
21: p(u,v) + H.)
22: Output p(u,
23: end for
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Open Your Eyes: Vision Enhances Message Passing Neural Networks in Link Prediction
B. Time Complexity Analysis
Let be the number of nodes, be the maximum node degree, be the node feature dimension, F be dimension of node representation produced by MPNN, S be the dimension of visual structural features (VSFs), and I be the number of target links.
B.1. Time Complexity Analysis for GVN
The time complexity of GVN is determined by the following components:
1. Complexity of the base MPNN model, which includes the MPNN and its associated read-out function. For example, the complexity of GCN is O(ndF + nF + O(IF2). For the NCNC model (Wang et al., 2024) that incorporates common-neighbor SFs, the complexity is O(nFF + + + Old F + IdF²).. We denote this part by O(MPNN).
2. Complexity of generating visual images for the target links is O
3. Complexity of extracting visual structural features with Vision Encoder is / O(VE), where O(VE) is the complexity vision encoder.
4. Complexity of feature integration, which varies based on the integration strategy:
irrention-based Integration:
The linear projection that converts the S-dimensional VSFs Vue to the F'-dimensional Vav has a complexity of F').
TTee cross-attention mechanism has a complexity of O(L
Therefore, the total time complexity for attention-based integration is dominated by O(ISF' + 1F
Concatenated Integration:
Concatenating Vuv with Yu and y. has complexity of O(I(F' + +S), where (F' + S) is the dimension after
concatenation.
Therefore, the total time complexity for Concatenated integration is dominated as O(I(F" + +)).
Weighted Integration:
Using VExpert (an MLP) to process Vae has a complexity of O(LS²).
The weighted integration step has a complexity of O()).
Therefore, the total time complexity for Weighted integration is dominated as O(18²).
Thus, the total time complexity of GVN for each feature integration method is as follows:
Attention-based Integration:
O(MPNN) + 1 O(VB) + O((SF' F²))).
Concatenated Integration:
O(MPNN) + - OOLE) S)).
Weighted Integration:
((MPNN) + 1 O(VE) O(IS)).
B.2. Time Complexity Analysis for E-GVN
The time complexity components for E-GVN are as follows:
1. Complexity of generating visual images for all nodes: O(n).
2. Complexity of extracting visual structural features with Vision Encoder is n O(VE).
3. Complexity of processing VSFs with the Adaptor: O
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Open Your Eyes: Vision Enhances Message Passing Neural Networks in Link Prediction
4. Complexity of integrating VSFs into node attributes before MPNN:
Attention- baase Integration:
The attention mechanism now operates on nodes instead of links, and operates on F dimension node attributes instead of F' dimension MPNN-produced node representations, resulting in a complexity of O + =FF)..
Therefore, the total time complexity for attention-based integration in B-GVN O(nFF+nF3)
Concatenated Integration:
-Concatenating v. with x, for all nodes has a complexity ( + +S).
Therefore, the total time complexity for Concatenated integration in E-GVN is O(n(F +)).
Weighted Integration:
-Using separate Linear Experts to process x, and Va and for all nodes has a complexity of Ond 2 n252).
The weighted integration step has a complexity of O(z).
Therefore, the total time complexity for Weighted integration in E-GVN is O(nF² n.
5. Complexity of the base model: Remains O(MPNN).
Thus, the total time complexity of E-GVN for each feature integration method is as follows:
Attention-based Integration:
(MPPNN) + n O(VE) O SF
Concatenated Integration:
O(MPNN) + n O(VE) + O(n(S2 + F 8)).
Weighted Integration:
O(MPNN) + O(VE) + (s + F2)).
C. Dataset Statistics
The statistics of the datasets are shown in Table 12. Among these datasets, Collab, Collab, DDI and Citation2 belong to large-scale graphs and the link prediction on them are more challenging.
For the Planetoid datasets (Cora, Citeseer, and Pubmed), since the official data splits are not available, we adopt the common random splits of 70%/10%/20% for (Hu al., 2020), utilize the official fixed splits.
For the OGB benchmarks Collab, PPA, DDI, and Citation2
Table 12. Statistics of datasets.
Cora
Citeseer
Pubmed
Collab
PPA
DDI
Citation2
#Nodes
2,708
3,327
18,717
235,868
576,289
4,267
2,927,963
#Edges
5,278
4,676
44,327
1,285,465
30,326,273
1,334,889
30,561,187
data set splits
random 3.9
random
random 4.5
fixed
fixed
fixed
fixed
average degrce
2.74
5.45
52.62
312,84
10.44
D. Link Prediction Experimental Setups
In link prediction, links play dual roles: serving as supervision and acting message-passing paths. Following the standard practice in link prediction, training links fulfill both supervision labels and message- message-passing paths. In terms of supervision, the training, validation, and testing links are mutually exclusive. For message passing, we follow the common setting (Li et al., 2024) where the validation links in ogbl-collab additionally function as passsag--passing paths during test time.
For the baselines, we directly use the results reported in (Wang et al., 2024) since we adopt the same experimental setup.
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Open Your Eyes: Vision Enhances Message Passing Neural Networks in Link Prediction
E. Substructure Counting Experimental Details
The experimental settings of substructure counting in Table are detailed as follows.
Datasets Generation We follow the experimental setup in (Chen et al., 2020) to generate two synthetic datasets of random
unattributed graphs. The first one is set of 5000 Erdos-Renyi random graphs, where each graph contains 10 nodes and each edge exists with the probability p = 0.3. The second one is a set of 5000 random regular graphs, where the number of nodes m for each graph and the node degree d is uniformly sampled from {(m 10, d = 6), (m = 15, d = 6), (m 20, d = 5), (m 30, d = 5)}. As the ground-truth labels, we calculate the counts of two types of substructures, including "Triangle" and '3-Star', both are common patterns in graph topology. The dataset split ratio is set as 30%/20%/55% for rainiingvvalddationttssnnnn respectively.
Models We compare GCN (Kipf& & Welling, 2017), VSF+GCN, SAGE (Hamilton al., 2017), and VSF+SAGE. To predict the substructure count, we append 3-layer MLP decoder after GCN SAGE. For VSF+ "'GCN and VSF+SAGE, we concatenate the VSFs with the node representations produced by the MPNN, which are then used inputs to the MLP decoder. All models are trained for 100 epochs using the Adam optimizer (Kingma, 2014), with learning rates searched from {1, 0.1, 0.05, J. The depths of GCN and SAGE are searched from {2, 4, 5}. and the hidden dimensions are searched from {8, 32, 128, 256]. We select the best model based on the lowest MSE loss on the validation set to generate the results.
F. Graph Visualizer
In our implementation, the default graph visualization processes for both GVN and E-GVN are developed using Graphviz. Graphviz (Gansner & North, 2000) is powerful tool for creating visual representations of abstract graphs and networks. It allows for the customization of styles (e.g., shapes, colors, labels) of nodes and edges to tailor the visualization to specific requirements. By default, we use brown color to emphasize the centered link or node, white color for the hackground and to fill other nodes, and a rectangular shape for node outlines. We use the scalable force-directed placement algorithm (sfdp) as the default layout computation algorithm. All of these configurations are specified and implemented with Graphviz.
We also implement two other optional graph visualizers using Matplotlib (Tosi, 2009) and Igraph (Gabor Csardi, 2006). Matplotlib provides versatile plotting library that can be used for basic graph visualization, offering customization of node and edge properties and integration with other data visualizations. Igraph, on the other hand, is specifically designed for network analysis and visualization, featuring a wide range of layout algorithms and the ability to handle large graphs efficiently.
These graph visualizers produce images with distinct stylistic characteristics, as illustrated in Figure 6. Specifically, Graphviz generates images that are typically more structured and clean, making them suitable for detailed analysis and professional presentations. Matplotlib is known for its flexibility, allowing for creative and highly customized images, which are ideal for exploratory data analysis. Igraph, on the other hand, focuses revealing underlying patterns in complex networks, particularly excelling in handling large datasets with layout algorithms that effectively display the overall structure of the network.
(a)
(b)
(c)
Figure 6. Node-centered examples of the visualized images by various visualizers (a) Graphviz (b) Matplotlib (c) Igraph.
G. Style Consistency Ablation Experimental Details
In this section, we provide a detailed description of the experimental setup used in Table 5. This experiment demonstrates the negative impact of inconsistent styles on visualized subgraph images. Below, we outline the implementation details of
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Open Your Eyes: Vision Enhances Message Passing Neural Networks in Link Prediction
both consistent and inconsistent style settings.
The consistent style setting is achieved by using the default image style configuration as described in Appendix F. This involves maintaining uniformity in visual elements across all subgraph images, ensuring that each image adheres to the same stylistic parameters.
For the inconsistent style setting, configurations are randomly sampled from a predetermined range options. This includes variations in node colors, shapes, and graph visualizers. The specific details are as follows:
Node Colors: Colors are randomly selected from the set (White, Black, Brown, Yellow, Red, Green]. It is important to note that the centered link/node colored distinctly from the other nodes maintain focus.
Node Shapes: Shapes are randomly chosen from the set {ellipse, box, circle, pentagon).
Graph Visualizers: The visualizer is randomly selected from the set [Graphviz, Matplotlib, Igraph}.
By employing these variations, the inconsistent style setting introduces heterogeneity in the visual representation of subgraphs, allowing us to assess the impact style inconsistency on the overall analysis.
H. Impact Study for Image Styles
H.1. Impacts of Node Colors
In this section, we explore the effects of different color choices for node representations in graph images. We first alter the colors of central nodes while keeping surrounding nodes white and evaluate performance on the Cora and Citeseer datasets (Hits @ 100). The results are summarized in Table 13.
Table 13. Performance @Hits@ 100) with Different Central Node Colors
Center Node
GVN (Cora)
E-GVN (Cora)
GVN (Citeseer)
E-GVN (Citeseer)
Black
90.72+0.52
91.43=2..1
94.12+0.58
94.46+0.52
Brown
90.70#0.56
91.47+00.66
94.12+0.58
94.44+0.53
Dark Blue
90.71=0.48
91.45+0044
94.09=0.45
94.39+0.47
Red
90.6640.50
91.40=0.40
94.00+0.50
94.30+0.50
Green
90.6010.55
91.35+0045
93,95+0.55
94.25+0.55
Yellow
90.68+0.57
91.42+0.38
94.05+0.57
94.40+0.54
White 89.35+0.72
89.90+0.65
93.20+0.72
93.55+0.75
From the above results, we have several findings:
Findings 1 Only slight differences in performance when the model could distinguish central nodes from surrounding nodes. However, the model showed preference for darker colors.
When central nodes became white (indistinguishable from others), there was a noticeable performance degrada- tion. This highlights the significance of labeling the identification of center nodes.
Findings 2
To further illustrate Findings 2, we assign colors the nodes surrounding the central nodes. The results are presented in Table 14.
Table 14. Performance (Hits @ 100) with Different Surrounding Node Colors
Center Node
Surrounding Node
GVN (Cora)
E-GVN (Cora)
GVN (Citeseer)
E-GVN (Citeseer)
Black
Black (same color)
89.00+0.60
89.50=0.55
93.00+0.65
93.40=0.60
White
White (same color)
89.35+0.72 72
89.90=0.65
93.20+0.77 72
93.55+0.75
Black
Brown (near color)
90.20+0.50
90.70+0.45
93.80+0.55
94.10+0.50
Black
White (opposite color)
90.72+0.52
91.433+0.1
94.1 94.12+0.58
94.46+0.52
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Open Your Eyes: Vision Enhances Message Passing Neural Networks in Link Prediction
These results further reflect the preference of the model for more pronounced color differences between central and surrounding nodes, indicated in Findings 2. The performance is lower when colors the same or similar, and higher when there is a clear distinction.
H.2. Impacts of Node Shapes
In this section, investigate the impact of different node shapes model performance. We experimented with three different shapes: Box, Circle, and Ellipse.
Table 15. Performance (Hits@ @ 100) with Different Node Shapes
Center Node
GVN (Cora)
E-GVN (Cora)
GVN (Citeseer)
E-GVN (Citeseer)
Box
90.70=0.56
91.47=#0.6
94.12+0.58
94.44+0.53
Circle Ellipse
90.65=0.52
91.40+0.38 91.45+0.44
94.15+0.43 94.10
94,42+0.50
90.72=0.46
94.4622.55
According to Table 15, we find there is no obvious preference for a particular node shape.
H.3. Impacts of Node Labeling Strategies
1. SENSITIVE STUDY OF NODE LABELING STRATEGIES
Table 16. HR@ 100 performance with different node labeling strategies.
Cora Re-label
Cileseer Re-label
No-label
Unique
No-label
Unique
GVNNCNG E-GVNNeNC
00.50
89.8620.4
89.6720.60
94.12:1.55
94.01:0.49
94.08
20.47
89.73
$9.7520.83
94.4440.65
93.85+0.66
94.02=+0.91
In this experiment, we study different ways to label the nodes in the image: (i) "No-label", which shows the nodes without any labels; (ii) "Re-label", which maps all the nodes in the current subgraph to new labels starting from zero; (iii) "Unique". which labels the nodes with unique global indices. Example images for these visualization strategies are shown in Appendix H.3.2. Table 16 shows the HR @ 100 performance of GVNNCNG and E-GVN with these different labeling strategies on Cora and Citeseer. As can be seen, "no-label" performs best, indicating that purely using the structural information is preferred.
H.3.2. ILLUSTRATIONS FOR DIFFERENT LABELING STRATEGIES
Here, we present image examples for graph visualization used in both GVN and E-GVN with the three different labeling strategies.
Figures 7-9 show example of link-centered subgraph visualization in GVN with various labeling strategies, where the target link is (1, 158). This indicates the objective is to predict the existence of link between node 1 and node 158. Similarly, Figures 10-12 present node-centered subgraph visualization images with various labeling strategies, where the colored node is the center node.
In Figures 7 and 10, the "No-label" labeling strategy is applied. In this strategy, node labels are omitted, enabling the model to focus purely on the intrinsic graph topological structural information, which is beneficial for generalizability across different datasets settings.
Figures& 8 and 11 adopt the "Re-label" labeling strategy, where the nodes within the subgraph are reassigned labels starting from O. This local relabeling introduces some OCR noise, compelling the model to be more robust.
Finally, in Figures 9 and 12, which apply the "Unique" labeling strategy, nodes are labeled with their original IDs from the dataset. This might leverage the OCR capability to match nodes across various subgraphs due to the unique identifiers, which is beneficial for identifying node correspondences. However, this method may hamper generalizability and expose the model the loig-tail problem, where the model's performance degrades for nodes that appear infrequently in the data.
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Open Your Eyes: Vision Enhances Message Passing Neural Networks in Link Prediction
Figure 7. Link-centered subgraph visualization with "No-label" labeling scheme.
10
11
16
126
14
24
Figure Link-centered subgraph visualization with "Re-label" laheling scheme.
2427
1429
221
1097
1570
29033
2358
2478
264g
1575
$06
2891
20119
1625
1884
150
1587
509
Figure 9. link-centered subgraph visualization with "Unique" labeling scheme.
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Open Your Eyes: Vision Enhances Message Passing Neural Networks in Link Prediction
Figure 10. Node-centered subgraph visualization with "No-label" labeling scheme.
9
14
13
11
10
12
18
Figure 11. Node-centered subgraph visualization with "Re-label" labeling scheme.
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Open Your Eyes: Vision Enhances Message Passing Neural Networks in Link Prediction
1575
2478
2648
2919
221
1358
158
2427
1097
2933
150
559
2356
3228
2691
Figure 12, Node-centered subgraph visualization with "Unique" labeling scheme.
21


Reviews:
[{"review_id": "rQCQ6QgJz8", "reviewer": "Reviewer_1KMA", "summary": "This paper proposed to incorprate vision information into MPNN to enhance link prediction. Specfically, it designed two framework, Graph Vision Network(GVN),along with a more efficient variant (E-GVN).", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thanks for your insightful reviews.\n> 1. The discussion for RQ1 could be more convincing if some empirical study or theoretical analysis could be provided, instead of just intuition analysis.\n\nThanks for your advice. For RQ1, you can find the following supports for our discussion. \n1) For subgraph visualization, we have provided empirical ablation for **keeping style consistency** in Table 4 of Sec 5.3, where Appendix H provides more details. Appendices I.1 and I.2 provide the empirical study on color and shape influences on nodes, particularly demonstrating the significance of **highlighting the center nodes**. Appendix I.3 provides an ablation study on **node labeling strategies**, noting that eliminating node labels performs the best.\n2) For decoupled vision scope, we exemplified the actual cases in Figure 2 to support our claim about the vision scope and provide a sensitivity study in Table 5 of Sec 5.3. The theoretical analysis of decoupling subgraph scope from MPNN has been proven by [r1], and we omitted the details due to the page limit. We will add them in the revision. \n\n[r1] Decoupling the depth and scope of graph neural networks. NeurIPS 2021\n> 2. More link prediction methods that consider the graph sub-structures could be included in the comparison, such as Link-MOE (\"Mixture of Link Predictors on Graphs\").\n\nAs suggested, we have included Link-MOE in the comparison. Please note that Link-MOE integrates many MPNNs as experts to achieve good performance. Differently, as a plugin method outside MPNN, our proposed framework can be a supplement for enhancing **individual** MPNN to provide additional enhancements. Some results (i.e., Hits@50 for ogbl-collab, Hits@100 for ogbl-ppa) are shown in the following table, where we substitute the GCN and NCNC experts in Link-MOE as E-GVN(GCN) and E-GVN(NCNC). According to the results, we can see that incorporating VSFs can further enhance the performance of Link-MOE.\n\n||ogbl-collab|ogbl-ppa|\n|---|---|---|\n|Link-MOE|71.32 ± 0.99|69.39 ± 0.61|\n|Link-MOE+VSFs|71.84±0.85|70.06±0.56|", "claims_and_evidence": "This paper analyzes the potential benefits to incorporate vision awareness in link prediciton and provides some empirical evidences.\nThis paper also demonstrated the effectiveness of the proposed GVN and E-GVN across several link prediction datasets, and empirically show the vision awarness can bring orthogonal improvements to SOTA methods.", "methods_and_evaluation_criteria": "Yes, the empirical study can well support the effectiveness of the proposed method.", "theoretical_claims": "NA", "experimental_designs_or_analyses": "The experimental designs are overall thorough and convincing.", "relation_to_broader_scientific_literature": "This paper proposed that incorporating the vision modality into MPNN can enhance link prediction, and support it via emipiral observations and experrimental studies.", "essential_references_not_discussed": "NA", "other_strengths_and_weaknesses": "Pros:\n1. This paper proposed a novel idea to incorprate the vision modality into MPNN for link prediction, and demonstrate its rationality and effectiveness via empirical study.\n2. Most of the intuitions are well supported and discussed via empirical study and preliminary analysis.\n3. The experiments are carefully designed from different perspectives to support its design and motivations.\n\nCons:\n1. The discussion for RQ1 could be more convincing if some empirical study or theoretical analysis could be provided, instead of just intuition analysis.\n2. More link prediction methods that considering the graph sub-structures could be included in the comparison.", "other_comments_or_suggestions": "1. The discussion for RQ1 could be more convincing if some empirical study or theoretical analysis could be provided, instead of just intuition analysis.\n2. More link prediction methods that considering the graph sub-structures could be included in the comparison, such as Link-MOE (\"Mixture of Link Predictors on Graphs\").", "questions_for_authors": "NA", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "PBHfoy8Omw", "reviewer": "Reviewer_qvLH", "summary": "This paper proposes using visual structural features (VSFs) as a replacement for heuristic-based structural features (SFs) in graph learning tasks. The key contribution is the introduction of vision-based enhancements, which are empirically shown to improve message-passing neural network (MPNN) performance for link prediction.", "questions": "", "limitations": "", "rating": 1, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thanks for your insightful reviews. We here address your concerns point by point by merging and re-arranging relevant comments together: \n> The justification for why VSFs work better remains unclear, particularly in relation to existing expressive power analysis on models with SFs. \n> The expressive power of models incorporating VSFs remains unclear,  raises concerns about whether VSFs fundamentally improve representation power or simply introduce additional complexity without well-characterized benefits.\n> How well does VDecoder perform alone?\n\nFirst, we want to clarify that we **did not claim VSFs always have stronger expressive power than other SFs**, instead, our main claims for VSFs include\n1. **When used alone, VSFs benefits MPNNs**. (Qualitatively demonstrated in Sec. 4.2, remarks 4.1-4.4).\n2. **When used together with other SFs, VSFs still provide remarkable orthogonal improvements.** (Empirically demonstrated in Sec. 5). \n\nSecond, the proposed VSFs show different characteristics from classic SFs: 1) Classic link prediction SFs are typically derived from a single type of heuristic (e.g., SFs in SEAL only encode path distance, and SFs in BUDDY only focus on high-order common neighbors). However, VSFs encode the whole subgraph from images, containing **massive and hybrid types** of structural biases (as demonstrated in Fig.4). 2) With training on specific data, VSFs **can vary** to align the data requirements (Remark 4.4). Due to such characteristics, it is not easy to theoretically analyze the properties of VSFs precisely, and instead we conducted empirical demonstrations (Sec. 4.2 and 5) to describe properties of VSFs.\n\nLastly, **we provide the standalone performance of 2-hop VSFs from ResNet50 encoder in the following table, which is a direct comparison for the representation quality of different SFs on the link prediction task.** As illustrated, both individual link-based and node-based VSFs proposed in this paper outperform common neighbor SFs (i.e., CN, RA, and AA) and distance-based SFs (i.e., SPD) across various datasets, showing their superior structural representations beyond classic link prediction SFs.\n\n|SFs|Cora|Citeseer|Pubmed|\n|---|---|---|---|\n|CN|33.92±0.46|29.79±0.90|23.13±0.15|\n|AA|39.85±1.34|35.19±1.34|27.38±0.11|\n|RA|41.07±0.48|33.56±0.17|27.03±0.35|\n|SPD|29.97±0.76|41.37±0.81|40.21±0.59|\n|VSF(link)|**68.24±0.41**|**57.66±0.47**|**46.81±1.02**|\n|VSF(node)|65.98±0.72|55.51±0.91|45.24±0.44|\n> Implementation details and hyperparameter settings for Sec 5’s results are missing, which makes reproducing results difficult.\n> What are the vision model configurations and hyperparameters used in Table 3, Fig. 5 and other results. \n> Explicitly provide a direct runtime comparison of preprocessing VSFs vs. classical SFs.\n\nThanks for your suggestion.\n1. For hyperparameter configurations, please note that we have included **all the hyperparameters for the main results in ./scripts/ path of our submitted code repo. We also give the ranges and optimization approaches of the significant hyperparameters in Sec 5.1. Therefore, we think that it is easy to reproduce our results**. For the scalability analysis in Fig.5 and other experiments, the encoder is ResNet50 by default as mentioned in Sec. 4.2, and the default hop is 2.\n2. Pre-processing time compared with SFs: We provide the time comparison on pre-processing VSFs and classic SFs on cora and ogbl-ddi testing in the following table. As shown, **E-GVN can process VSFs in comparable time (in seconds) as classic SFs. For the dense graph like ogbl-ddi, it is even more efficient** because the number of nodes are much smaller than that of links.\n\n|Dataset|VSF(GVN)|VSF(E-GVN)|CN|RA|AA|SPD|\n|---|---|---|---|---|---|---|\n|Cora|2.91e1|5.02e-2|**1.69e-2**|1.81e-2|1.89e-2|3.06e-2|\n|DDI|4.39e4|**6.20e0**|1.46e2|1.95e2|2.07e2|4.46e1|\n> How does VSF handle hub nodes?\n\nAs exemplified in Fig 2, hub nodes are faithfully reflected in the image, revealing important cluster information.\n> Could the limited scope of visual perception cause nodes with non-isomorphic subgraphs to be mapped to non-distinguishable VSF?\n\nNo. For any hop k, non-isomorphic subgraphs are visualized as different images, resulting in distinguishable VSFs.  \n> Would node-centered visualization degenerate to standard MPNNs for nodes with isomorphic subgraphs? \n\nNo. Though we eliminated node labels for structural clarity in visualization, we constructed the adjacent matrix with ascending order of node labels. This makes the visualization for isomorphic subgraphs different in layout if their relative label orderings are not permutation-equivariant. \n> Several relevant works are missing from the discussion in Sec 4.3 and 4.4.\n\nThanks for your supplement. Incorporating these discussions can definitely make the discussion more comprehensive. We will add discussions with them in the revision.\n\nSincerely wish we could address your concerns. For any further clarification, please feel free to let us know.", "claims_and_evidence": "The paper investigates whether and how visual awareness of graph structures benefits MPNNs in link prediction. The authors provide empirical evidence demonstrating improvements over baseline models in Section 5. However, the justification for why VSFs work better remains unclear, particularly in relation to existing expressive power analysis on models with SFs.", "methods_and_evaluation_criteria": "The paper utilizes standard link prediction benchmarks for performance comparison, making its evaluation broadly relevant. However, more details on how hyperparameters and configurations were chosen would strengthen the evaluation.", "theoretical_claims": "The theoretical justification for VSFs in Section 4.2 is grounded in prior work on subgraph-based methods (e.g., SEAL and labeling tricks). However, the expressive power of models incorporating VSFs remains unclear, especially given their black-box nature and potential randomness in mapping and encoding. This raises concerns about whether VSFs fundamentally improve representation power or simply introduce additional complexity without well-characterized benefits.", "experimental_designs_or_analyses": "The scalability analysis is incomplete. While inference time and GPU memory usage are reported, key details such as the configuration of VSF and the actual preprocessing overhead of VSFs are missing. Figure 5 lacks clarity regarding which encoder and number of hops for VSF were used. Since the primary computational cost comes from VSFs, explicitly reporting their preprocessing runtime would provide a clearer picture of the method’s efficiency.", "relation_to_broader_scientific_literature": "This paper presents an interesting adaptation of visual features to enhance MPNN-based link prediction.", "essential_references_not_discussed": "Several relevant works are missing from the discussion in Sections 4.3 and 4.4:  \n• BUDDY [1] and Bloom-MPNN [2] explored different strategies for integrating SFs with MPNNs, but they are not cited in relevant sections.  \n• SUREL [3] introduced the idea of decomposing query-induced subgraphs into node-level subgraphs for efficiency, which directly relates to the node-centered visualization approach in E-GVN (Section 4.4).\n\n[1] Chamberlain, Benjamin Paul, et al. “Graph neural networks for link prediction with subgraph sketching.” ICLR’23.  \n[2] Zhang, Tianyi, et al. “Learning Scalable Structural Representations for Link Prediction with Bloom Signatures.” WWW’24.  \n[3] Yin, Haoteng, et al. “Algorithm and system co-design for efficient subgraph-based graph representation learning.” VLDB’22.", "other_strengths_and_weaknesses": "• Strengths: The idea of leveraging vision models for structural feature extraction is straightforward and empirically effective based on the reported results.  \n• Weaknesses: The paper lacks a clear justification linking the empirical improvements of VSFs to existing analyses of SF-based methods. Additionally, the increased computational complexity—due to large vision models such as ViTs—raises concerns about whether the performance gains justify the additional overhead.", "other_comments_or_suggestions": "N/A", "questions_for_authors": "1. How does VSF handle hub nodes, such as influencers in social networks or highly cited papers? Could the limited scope of visual perception cause nodes with non-isomorphic subgraphs to be mapped to non-distinguishable VSF?\n2. How well does VDecoder perform as a standalone model on benchmark datasets?\n3. Considering VSF requires style consistency, wouldn’t node-centered subgraph visualization degenerate back to standard MPNNs for nodes with isomorphic subgraphs?\n4. Could the authors provide a direct runtime comparison of preprocessing VSFs vs. classical SFs? Additionally, what are the vision model configurations and hyperparameters used in Table 3, Figure 5, and other results in Section 5?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "PugbUGlfi0", "reviewer": "Reviewer_w7VD", "summary": "This paper proposes a novel framework called Graph Vision Network (GVN) and its efficient variant (E-GVN) to enhance link prediction in graph neural networks by integrating visual perception. The authors argue that while message-passing graph neural networks (MPNNs) and structural features (SFs) are dominant in link prediction tasks, the potential of visual perception has been overlooked.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your insightful feedback. \n\n> I believe the authors should concentrate on the efficient GVN within the paper's architecture, as it can achieve better performance with NCNC and is significantly more efficient.\n\nWe sincerely appreciate your suggestion. We will focus on highlighting the efficient GVN in the revision.\n\nThanks again for recognizing our work.", "claims_and_evidence": "The claims made in the paper are well-supported by extensive empirical evidence:\n1. **Enhancement through Visual Awareness**: The authors claim that incorporating visual perception enhances link prediction performance. This is supported by experimental results showing significant improvements over baseline MPNNs and SF-enhanced MPNNs across multiple datasets.\n2. **Compatibility with Existing Methods**: The paper demonstrates that GVN and E-GVN can be seamlessly integrated with existing models like GCN and NCNC, achieving new state-of-the-art results. This supports the claim that visual features provide orthogonal enhancements.\n3. **Scalability**: The efficiency of E-GVN is demonstrated through reduced computational complexity and memory usage compared to GVN, making it suitable for large-scale graphs.", "methods_and_evaluation_criteria": "The proposed methods and evaluation criteria are appropriate for the problem:\n1. **GVN Framework**: The method involves converting subgraphs into visual representations using graph visualization tools and extracting visual structural features (VSFs) using a vision encoder. The integration of VSFs with MPNNs is explored through multiple strategies (attention-based, concatenated, and weighted). This approach is logical and well-motivated.\n2. **Evaluation Criteria**: The authors use standard metrics (e.g., hit-ratio, MRR) for link prediction and evaluate on diverse datasets (Planetoid, OGB benchmarks). This ensures the robustness of their claims across different graph types and scales.", "theoretical_claims": "Not applicable.", "experimental_designs_or_analyses": "The experimental designs are sound and comprehensive:\n1. **Datasets**: The use of both small-scale (Planetoid) and large-scale (OGB) datasets ensures the evaluation covers a wide range of graph sizes and complexities.\n2. **Baselines**: The comparison with strong baselines (e.g., GCN, NCNC) and various integration strategies provides a thorough analysis of the proposed methods' effectiveness.\n3. **Ablation Studies**: The paper includes ablation studies on visualization styles, scopes, and adaptivity of VSFs, providing insights into the design choices and their impacts.", "relation_to_broader_scientific_literature": "None", "essential_references_not_discussed": "None", "other_strengths_and_weaknesses": "Strength: Good performance and efficiency\nWeakness: Since the method is a plugin outside the MPNN, the novelty of GNN structure is limited but not fatal. I will still give a positive score.", "other_comments_or_suggestions": "I think the authors should focus on the efficient GVN in the paper architecture, since it can get better performances with NCNC and much more efficient.", "questions_for_authors": "None.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "fiY5KbCpOB", "reviewer": "Reviewer_cLaP", "summary": "The paper introduces a new GNN framework for link prediction tasks that can be used to extend existing architectures. The main idea is that the GNN can access image embeddings of visualizations of the (extended) neighborhoods. These are meant to enrich the representations with more context on where nodes are positioned in the graph and ultimately improve predictive performance. The paper claims that using this technique, state-of-the-art results can be achieved on common link prediction benchmarks.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thanks for your insightful reviews. **Please note that all the new tables and figures mentioned here are put in https://anonymous.4open.science/r/GVN-CLap/README.md**.\n> compares assigning the visualized node positions as node features. \n> compares more standard node positional encoding (PE) mechanisms like Laplacian-based and distance-based ones.\n\nAs you adviced, we compared VSFs for nodes with 4 representative encoding mechanisms: 1) 2-d axis position of nodes in subgraph image, 2) Laplacian PE, 3) Distances to other nodes, and 4) Node degree (centrality encoding). These PEs were used as node features and decoded by 2-layer GCN+2-lyaer MLP for link prediction. The results in Table A show that **VSFs outperform those PEs across datasets**. Notably, directly encoding the 2-d axis is not effective enough, underscoring **the importance of using a vision encoder for comprehensive structural information**.\n> Why does the paper only consider link prediction tasks?\n\nAs the title indicates, this work focuses on link prediction within the context of MPNN because:\n1. Link prediction is one of the cornerstone tasks in graph learning, with 1) long history, 2) significant applications, and 3) well-established experimental settings, making it vital and representative. \n2. As a first exploratory work for incorporating vision to MPNN, we faced many factors to explore. For example, we have revealed the effects on style consistency, node coloring, node labeling, image scopes, feature integration strategies, node shapes, visualizer, and encoder, etc. Efforts on those findings cost 8 months. Therefore, multiple efforts on other tasks are impractical for this starting work given limited resource. \n\nMoreover, we provide results in Table B, which demonstrate that **the benefits of VSF are promising for the node classification task**. We will study such extensions in future works.\n> Is there any reason to believe that the methods do not scale linearly with increasing batch size? \n\nWhile logarithmic axis labels are utilized in Fig. 5, the time actually scales linearly to the batch size. A version of Fig 5 with linear axis labels is provided in Fig. A.\n>  O(VE) should be exemplified.\n>  Welcome to analyzing the scalability on larger graphs by increasing the graph but not the batch size.\n\nAs you advised, we here supplement another scalability analysis on randomly generated Erdos-Renyi graphs (edge possibility=0.2) with increasing numbers of nodes from 100 to 5000. The total training times for training 200 epochs of GCN/GVN/E-GVN/SEAL are provided in Table C, and the contributions of O(VE) are explicitly listed in parentheses. As shown, the O(VE) time of GVN scale quadratically w.r.t. the node size, making it unavailable for large graphs. Instead, E-GVN can handle large graphs in time comparable to GCN and its O(VE) time scales nearly linearly.\n> Remark 4.1 is not really surprising, as the method also completely breaks permutation equivariance.\n> GVs don’t usually yield unique and permutation equivariant representations.\n\nWe acknowledge that VSFs are not permutation-equivariant. However, our performances have surpassed many permutation-equivariant SF-MPNNs, demonstrating it is not fatal. We think that there are two main reasons: 1) the learnable VSFs can provide some specific information, e.g., important structure patterns/motifs (Remark 4.2). 2) Visualization also imports meaningful data augmentations on permutation (e.g., varying layouts), which forces the decoder model to become less sensitive to node order, potentially alleviating the drawbacks. We will add these discussions with revisions.\n> Should mention representative works about 1) general positional encoder, 2）GNNs with language embeddings, 3) graph drawing techniques and their optimization targets \n\nIncorporating these discussions would definitely provide a more comprehensive background. We will add the discussion with them in the revision.\n> Matplotlib and igraph are not graph drawing frameworks. which doesn’t sufficiently describe what method was used\n\nMatplotlib is used to render images, while networkx handles the structures. For Igraph, it provides a built-in graph visualization function. We will add details about them in the revision.\n> Is there any reason for selecting fdp for graphviz?\n\nWe choose fdp since a preliminary experiment comparing E-GVN with different layout algorithms on Cora (Table D) shows dot and fdp are better. Then we select fdp but not dot with reasons:\n1. The force-based layout algorithm in fdp highlights node clustering, which is important for link prediction.\n2. The tree-based layout in dot often results in a flattened image where the length exceeds the width, leading to a waste of the canvas.\n\nThanks again for your kind reviews. We sincerely hope we have addressed your concerns. If you have any question, please feel free to discuss with us.", "claims_and_evidence": "One core claim the paper makes is that using image representations and embeddings from vision models (and the resulting “vision awareness”) improves performance. However, the paper never properly compares to other encoding techniques, like assigning the position of nodes in the visualization directly as features to nodes. The paper also fails to set the vision embeddings into context with other positional encodings commonly used for GNNs. While the performance seems to be good with the image embeddings, it’s not clear where these gains are coming from and whether one really needs to use vision models instead of some more simple and straight-forward encoding techniques.", "methods_and_evaluation_criteria": "The paper proposes an MPNN architecture extension that could be used for any graph learning task. The paper does not convincingly explain why it chooses link prediction as the only task for evaluation. However, the datasets that are used in the evaluation are common and make sense.", "theoretical_claims": "The only theoretical claims are based around the runtime analysis and expressiveness of the model. Here, the paper does not mention the running time of O(VE), which, while dependent on the used visualizer, seems to be one of the major contributors and could be exemplified at least for the visualization method that is used in the final testing. Regarding the expressiveness (Remark 4.1): This result is not really surprising, as the method also completely breaks permutation equivariance. This fact is not really highlighted as a downside of the method, but would be important in this context.", "experimental_designs_or_analyses": "* The scalability analysis is generally a welcome addition, but the tests are only done on the smallest graph used in the benchmarking. Moreover, the scaling behavior is only analyzed by increasing the batch size. I’m really wondering: Is there any reason to believe that the methods do not scale linearly with increasing batch size? If the paper wants to analyze the scaling behavior to larger graphs, then one should increase the graph and not the batch size. This could (for example) be facilitated by sampling random graphs of increasing sizes and running the methods on them (for the scalability analysis it doesn’t really matter that much whether there is meaningful ground-truth data to learn). \n\n* A comparison to other (more standard) encoding mechanisms for the node positions would be welcome, as well as a comparison to other standard positional encodings used for example for graph transformers.", "relation_to_broader_scientific_literature": "The paper is grounded in the broader work on link prediction and extends existing methods to obtain better results.", "essential_references_not_discussed": "In my opinion, this is one of the main weaknesses of the paper. The paper doesn’t mention any recent positional embeddings (for example, the very widely used Laplacian-based features) or other embeddings that were popularized together with graph transformers. Multimodal GNNs, such as those using language embeddings, could also be mentioned. Furthermore, and more importantly, the paper does not discuss graph visualization techniques and how they work. As this is at the core of this paper, I think it would be hugely important to explain what the employed visualization techniques try to optimize. This is its own research area and commonly referred to as “graph drawing”. The paper should mention some algorithms, at least the current state-of-the-art (which also includes some GNN models), and especially those that were used in the paper. The paper could also consider different optimization criteria like stress, edge crossings, angles, overlap between nodes, … and explain which ones were used for the visualizations. In the ablation study for different visualization techniques, the paper refers to them as “graphviz, matplotlib, and igraph”, which really doesn’t sufficiently describe what method was used, as graphviz alone has at least 7 very different algorithms to draw graphs. matplotlib and igraph are not even graph drawing frameworks, so it’s questionable what was used here. The Appendix claims that fdp was used for graphviz, is there any reason for this specific choice? Were the other methods compared to this?", "other_strengths_and_weaknesses": "* GVs don’t usually yield unique and permutation equivariant representations\n\n* It is not clear whether the visualization as an image brings any advantage over encoding the node positions (in the visualization) as features", "other_comments_or_suggestions": "I don't have more suggestions than the ones already mentioned.", "questions_for_authors": "* Why does the paper only consider link prediction tasks?\n* How do the vision embeddings perform in comparison to other positional encodings (like Laplacian-based ones, distance-based ones, and so on)?\n\n## update after rebuttal\nI appreciate the authors' responses and want to maintain my positive rating. At the same time, I still feel that limiting the evaluation to link prediction significantly weakens the paper, which is why I don't want to go higher.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: This paper introduces Graph Vision Network (GVN, link-centered visualization) and its efficient variant E-GVN (node-centered visualization), which integrate visual structural features into MPNNs to enhance link prediction. This is the first work to leverage graph visualizations as input to vision models (e.g., ResNet, ViT) for structural feature extraction and show improvement to state-of-the-art link prediction methods by achieving SOTA results on 7 LP benchmarks, demonstrating orthogonal improvements when combined with existing methods (e.g., GCN, NCNC). Some light concerns are raised regarding theoretical expressivity, comparison to recent PE methods, break of permutation equivariance, etc. 

I think this work opens a new direction for multimodal GNNs, and its empirical gains warrant attention despite methodological gaps. I encourage the authors to add discussions on 1) positional encoding comparisons (Laplacian, distance-based), 2) permutation equivariance trade-offs and other limitations of the current strategy, and 3) make E-GVN the main focus due to its better efficiency and performance.
Decision: Accept (poster)