Graph neural network: Difference between revisions

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{{Short description|Class of artificial neural networks}}

{{Machine learning|Artificial neural network}}

{{Use dmy dates|date=July 2025}}

'''Graph neural networks''' ('''GNN''') are specialized [[artificial neural network]]s that are designed for tasks whose inputs are [[Graph (abstract data type)|graphs]].<ref name="wucuipeizhao2022" /><ref name="scarselli2009" /><ref name="micheli2009" /><ref name="sanchez2021" /><ref name="daigavane2021" />

One prominent example is molecular drug design.<ref>{{Cite journal |last1=Stokes |first1=Jonathan M. |last2=Yang |first2=Kevin |last3=Swanson |first3=Kyle |last4=Jin |first4=Wengong |last5=Cubillos-Ruiz |first5=Andres |last6=Donghia |first6=Nina M. |last7=MacNair |first7=Craig R. |last8=French |first8=Shawn |last9=Carfrae |first9=Lindsey A. |last10=Bloom-Ackermann |first10=Zohar |last11=Tran |first11=Victoria M. |last12=Chiappino-Pepe |first12=Anush |last13=Badran |first13=Ahmed H. |last14=Andrews |first14=Ian W. |last15=Chory |first15=Emma J. |date=2020-02-20 February 2020 |title=A Deep Learning Approach to Antibiotic Discovery |journal=Cell |volume=180 |issue=4 |pages=688–702.e13 |doi=10.1016/j.cell.2020.01.021 |issn=1097-4172 |pmc=8349178 |pmid=32084340}}</ref><ref>{{Citationcite arXiv|last1=Yang |first1=Kevin |title=Analyzing Learned Molecular Representations for Property Prediction |date=2019-11-20 November 2019 |arxiveprint=1904.01561 |last2=Swanson |first2=Kyle |last3=Jin |first3=Wengong |last4=Coley |first4=Connor |last5=Eiden |first5=Philipp |last6=Gao |first6=Hua |last7=Guzman-Perez |first7=Angel |last8=Hopper |first8=Timothy |last9=Kelley |first9=Brian|class=cs.LG }}</ref><ref>{{Cite journal |last=Marchant |first=Jo |date=2020-02-20 February 2020 |title=Powerful antibiotics discovered using AI |url=https://www.nature.com/articles/d41586-020-00018-3 |journal=Nature |language=en |doi=10.1038/d41586-020-00018-3|pmid=33603175 |url-access=subscription }}</ref> Each input sample is a graph representation of a molecule, where atoms form the nodes and chemical bonds between atoms form the edges. In addition to the graph representation, the input also includes known chemical properties for each of the atoms. Dataset samples may thus differ in length, reflecting the varying numbers of atoms in molecules, and the varying number of bonds between them. The task is to predict the efficacy of a given molecule for a specific medical application, like eliminating [[Escherichia coli|''E. coli'']] bacteria.

The key design element of GNNs is the use of ''pairwise message passing'', such that graph nodes iteratively update their representations by exchanging information with their neighbors. Several GNN architectures have been proposed,<ref name="scarselli2009" /><ref name="micheli2009" /><ref name="kipf2016" /><ref name="hamilton2017" /><ref name="velickovic2018" /> which implement different flavors of message passing,<ref name="bronstein2021" /><ref name="hajij2022" /> started by recursive<ref name="scarselli2009" /> or convolutional constructive<ref name="micheli2009" /> approaches. {{As of|2022}}, it is an open question whether it is possible to define GNN architectures "going beyond" message passing, or instead every GNN can be built on message passing over suitably defined graphs.<ref name="velickovic2022" />

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In the more general subject of "geometric [[deep learning]]", certain existing neural network architectures can be interpreted as GNNs operating on suitably defined graphs.<ref name=bronstein2021 /> A [[convolutional neural network]] layer, in the context of [[computer vision]], can be considered a GNN applied to graphs whose nodes are [[pixel]]s and only adjacent pixels are connected by edges in the graph. A [[Transformer (machine learning model)|transformer]] layer, in [[natural language processing]], can be considered a GNN applied to [[complete graph]]s whose nodes are [[words]] or tokens in a passage of [[natural language]] text.

Relevant application domains for GNNs include [[Natural Language Processing|natural language processing]],<ref name="wuchen2023" /> [[social networks]],<ref name="ying2018" /> [[Citation graph|citation networks]],<ref name="stanforddata" /> [[molecular biology]],<ref>{{cite journal |last1=Zhang |first1=Weihang |last2=Cui |first2=Yang |last3=Liu |first3=Bowen |last4=Loza |first4=Martin |last5=Park |first5=Sung-Joon |last6=Nakai |first6=Kenta |date=5 April 2024 |title=HyGAnno: Hybrid graph neural network-based cell type annotation for single-cell ATAC sequencing data |url=https://academic.oup.com/bib/article/25/3/bbae152/7641197 |journal=Briefings in Bioinformatics |volume=25 |issue=3 |pages=bbae152 |doi=10.1093/bib/bbae152|pmid=38581422 |pmc=10998639 }}</ref> chemistry,<ref name="gilmer2017" /><ref>{{Cite journal |last1=Coley |first1=Connor W. |last2=Jin |first2=Wengong |last3=Rogers |first3=Luke |last4=Jamison |first4=Timothy F. |last5=Jaakkola |first5=Tommi S. |last6=Green |first6=William H. |last7=Barzilay |first7=Regina |last8=Jensen |first8=Klavs F. |date=2 January 2019-01-02 |title=A graph-convolutional neural network model for the prediction of chemical reactivity |journal=Chemical Science |language=en |volume=10 |issue=2 |pages=370–377 |doi=10.1039/C8SC04228D |pmid=30746086 |pmc=6335848 |issn=2041-6539|doi-access=free }}</ref> [[physics]]<ref name=qasim2019 /> and [[NP-hard]] [[combinatorial optimization]] problems.<ref name="li2018" />

[[Open source]] [[Library (computing)|libraries]] implementing GNNs include PyTorch Geometric<ref name=fey2019 /> ([[PyTorch]]), TensorFlow GNN<ref name=tfgnn2022 /> ([[TensorFlow]]), Deep Graph Library<ref>{{Cite web |last= |title=Deep Graph Library (DGL) |url=https://www.dgl.ai/ |access-date=2024-09-12 September 2024 |website=}}</ref> (framework agnostic), jraph<ref name=jraph2022/> ([[Google JAX]]), and GraphNeuralNetworks.jl<ref name=Lucibello2021GNN/>/GeometricFlux.jl<ref>{{Citation |title=FluxML/GeometricFlux.jl |date=2024-01-31 January 2024 |url=https://github.com/FluxML/GeometricFlux.jl |access-date=3 February 2024-02-03 |publisher=FluxML}}</ref> ([[Julia (programming language)|Julia]], [[Flux (machine-learning framework)|Flux]]).

== Architecture ==

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# <em>Global pooling</em>: a global pooling layer, also known as ''readout'' layer, provides fixed-size representation of the whole graph. The global pooling layer must be permutation invariant, such that permutations in the ordering of graph nodes and edges do not alter the final output.<ref name="lui2022" /> Examples include element-wise sum, mean or maximum.

It has been demonstrated that GNNs cannot be more expressive than the [[Weisfeiler Leman graph isomorphism test|Weisfeiler–Leman Graph Isomorphism Test]].<ref name="douglas2011" /><ref name="xu2019" /> In practice, this means that there exist different graph structures (e.g., [[molecules]] with the same [[atoms]] but different [[Chemical bond|bonds]]) that cannot be distinguished by GNNs. More powerful GNNs operating on higher-dimension geometries such as [[simplicial complex]]es can be designed.<ref name=bronstein2021-2 /><ref name=grady2011discrete /><ref name=hajij2022>< /ref> {{As of|2022}}, whether or not future architectures will overcome the message passing primitive is an open research question.<ref name=velickovic2022 />

[[File:GNN representational limits.png|thumb|[[Graph isomorphism|Non-isomorphic]] graphs that cannot be distinguished by a GNN due to the limitations of the Weisfeiler-Lehman Graph Isomorphism Test. Colors indicate node [[Feature (machine learning)|features]].]]

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== Local pooling layers ==

Local pooling layers coarsen the graph via downsampling. We present hereSubsequently, several learnable local pooling strategies that have been proposed are presented.<ref name=lui2022 /> For each case, the input is the initial graph is represented by a matrix <math>\mathbf{X}</math> of node features, and the graph adjacency matrix <math>\mathbf{A}</math>. The output is the new matrix <math>\mathbf{X}'</math>of node features, and the new graph adjacency matrix <math>\mathbf{A}'</math>.

=== Top-k pooling ===

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:<math>\mathbf{A}' = \mathbf{A}_{\mathbf{i}, \mathbf{i}}</math>

where <math>\mathbf{i} = \text{top}_k(\mathbf{y})</math> is the subset of nodes with the top-k highest projection scores, <math>\odot</math> denotes [[Hadamard product (matrices) | element-wise matrix multiplication]].

The self-attention pooling layer can be seen as an extension of the top-k pooling layer. Differently from top-k pooling, the self-attention scores computed in self-attention pooling account both for the graph features and the graph topology.

== Heterophilic Graph Learning ==

[[Homophily]] principle, i.e., nodes with the same labels or similar attributes are more likely to be connected, has been commonly believed to be the main reason for the superiority of Graph Neural Networks (GNNs) over traditional Neural Networks (NNs) on graph-structured data, especially on node-level tasks.<ref name=":0">{{Citationcite |last1=LuanarXiv |first1eprint=Sitao |title=The Heterophilic Graph Learning Handbook: Benchmarks, Models, Theoretical Analysis, Applications and Challenges |date=2024-07-12 |url=https://arxiv.org/abs/2407.09618 |access-datelast1=2025-02-02Luan |arxivfirst1=2407.09618Sitao |last2=Hua |first2=Chenqing |last3=Lu |first3=Qincheng |last4=Ma |first4=Liheng |last5=Wu |first5=Lirong |last6=Wang |first6=Xinyu |last7=Xu |first7=Minkai |last8=Chang |first8=Xiao-Wen |last9=Precup |first9=Doina |last10=Ying |first10=Rex |last11=Li |first11=Stan Z. |last12=Tang |first12=Jian |last13=Wolf |first13=Guy |last14=Jegelka |first14=Stefanie |title=The Heterophilic Graph Learning Handbook: Benchmarks, Models, Theoretical Analysis, Applications and Challenges |date=2024 |class=cs.LG }}</ref> However, recent work has identified a non-trivial set of datasets where GNN’s performance compared to the NN’s is not satisfactory.<ref>{{Cite journalbook |last1=Luan |first1=Sitao |last2=Hua |first2=Chenqing |last3=Lu |first3=Qincheng |last4=Zhu |first4=Jiaqi |last5=Chang |first5=Xiao-Wen |last6=Precup |first6=Doina |chapter=When do We Need Graph Neural Networks for Node Classification? |date=2024 |editor-last=Cherifi |editor-first=Hocine |editor2-last=Rocha |editor2-first=Luis M. |editor3-last=Cherifi |editor3-first=Chantal |editor4-last=Donduran |editor4-first=Murat |title=WhenComplex DoNetworks We& NeedTheir GraphApplications Neural Networks for Node Classification?XII |chapter-url=https://link.springer.com/chapter/10.1007/978-3-031-53468-3_4 |journal=Complex Networks & Their Applications XII |series=Studies in Computational Intelligence |volume=1141 |language=en |___location=Cham |publisher=Springer Nature Switzerland |pages=37–48|doi=10.1007/978-3-031-53468-3_4 |isbn=978-3-031-53467-6 }}</ref> [[Heterophily]], i.e., low homophily, has been considered the main cause of this empirical observation.<ref name=":1">{{Cite journal |last1=Luan |first1=Sitao |last2=Hua |first2=Chenqing |last3=Lu |first3=Qincheng |last4=Zhu |first4=Jiaqi |last5=Zhao |first5=Mingde |last6=Zhang |first6=Shuyuan |last7=Chang |first7=Xiao-Wen |last8=Precup |first8=Doina |date=6 December 2022-12-06 |title=Revisiting Heterophily For Graph Neural Networks |url=https://proceedings.neurips.cc/paper_files/paper/2022/hash/092359ce5cf60a80e882378944bf1be4-Abstract-Conference.html |journal=Advances in Neural Information Processing Systems |language=en |volume=35 |pages=1362–1375|arxiv=2210.07606 }}</ref> People have begun to revisit and re-evaluate most existing graph models in the heterophily scenario across various kinds of graphs, e.g., [[Heterogeneous network|heterogeneous graphs]], [[Temporal network|temporal graphs]] and [[Hypergraph|hypergraphshypergraph]]s. Moreover, numerous graph-related applications are found to be closely related to the heterophily problem, e.g. [[Fraud detection|graph fraud/anomaly detection]], [[Adversarial attack|graph adversarial attacks and robustness]], privacy, [[federated learning]] and [[Point cloud|point cloud segmentation]], [[Clusteringcluster analysis|graph clustering]], [[Recommenderrecommender system|recommender systems]]s, [[Generativegenerative model|generative models]]s, [[link prediction]], [[Graph isomorphism|graph classification]] and [[Graph coloring|coloring]], etc. In the past few years, considerable effort has been devoted to studying and addressing the heterophily issue in graph learning.<ref name=":0" /><ref name=":1" /><ref>{{Cite journal |last1=Luan |first1=Sitao |last2=Hua |first2=Chenqing |last3=Xu |first3=Minkai |last4=Lu |first4=Qincheng |last5=Zhu |first5=Jiaqi |last6=Chang |first6=Xiao-Wen |last7=Fu |first7=Jie |last8=Leskovec |first8=Jure |last9=Precup |first9=Doina |date=2023-12-15 December 2023 |title=When Do Graph Neural Networks Help with Node Classification? Investigating the Homophily Principle on Node Distinguishability |url=https://proceedings.neurips.cc/paper_files/paper/2023/hash/5ba11de4c74548071899cf41dec078bf-Abstract-Conference.html |journal=Advances in Neural Information Processing Systems |language=en |volume=36 |pages=28748–28760}}</ref>

== Applications ==

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=== Cyber security ===

{{See also|Intrusion detection system}}

When viewed as a graph, a network of computers can be analyzed with GNNs for anomaly detection. Anomalies within provenance graphs often correlate to malicious activity within the network. GNNs have been used to identify these anomalies on individual nodes<ref>{{Cite journal |last1=Wang |first1=Su |last2=Wang |first2=Zhiliang |last3=Zhou |first3=Tao |last4=Sun |first4=Hongbin |last5=Yin |first5=Xia |last6=Han |first6=Dongqi |last7=Zhang |first7=Han |last8=Shi |first8=Xingang |last9=Yang |first9=Jiahai |date=2022 |title=Threatrace: Detecting and Tracing Host-Based Threats in Node Level Through Provenance Graph Learning |url=https://ieeexplore.ieee.org/document/9899459/;jsessionid=NzAXdLahhjEX-xmrFzOROk4qxoaz40aJFvKcZRgjck8-zCOucJi7!380715771 |journal=IEEE Transactions on Information Forensics and Security |volume=17 |pages=3972–3987 |doi=10.1109/TIFS.2022.3208815 |issn=1556-6021|arxiv=2111.04333 |bibcode=2022ITIF...17.3972W |s2cid=243847506 }}</ref> and within paths<ref>{{Cite journal |last1=Wang |first1=Qi |last2=Hassan |first2=Wajih Ul |last3=Li |first3=Ding |last4=Jee |first4=Kangkook |last5=Yu |first5=Xiao |date=2020 |title=You Are What You Do: Hunting Stealthy Malware via Data Provenance Analysis. |journal=Network and Distributed Systems Security (NDSS) Symposium|doi=10.14722/ndss.2020.24167 |isbn=978-1-891562-61-7 |s2cid=211267791 |doi-access=free }}</ref> to detect malicious processes, or on the edge level<ref>{{Cite journal |last1=King |first1=Isaiah J. |last2=Huang |first2=H. Howie |date=2022 |title=Euler: Detecting Network Lateral Movement via Scalable Temporal Link Prediction |url=https://www.ndss-symposium.org/wp-content/uploads/2022-107A-paper.pdf |journal=In Proceedings of the 29th Network and Distributed Systems Security Symposium (NDSS)|doi=10.14722/ndss.2022.24107 |s2cid=248221601 }}</ref> to detect [[Network Lateral Movement|lateral movement]].

=== Water distribution networks ===

{{See also|Water distribution system}}

Water distribution systems can be modelled as graphs, being then a straightforward application of GNN. This kind of algorithm has been applied to water demand forecasting,<ref>{{cite journal |url=https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2022WR032299|title=Graph Convolutional Recurrent Neural Networks for Water Demand Forecasting|last=Zanfei|first=Ariele |display-authors=etal |date=2022|journal=Water Resources Research|volume=58 |issue=7 |article-number=e2022WR032299 |publisher=AGU|doi=10.1029/2022WR032299 |bibcode=2022WRR....5832299Z |access-date=June 11, June 2024}}</ref> interconnecting District Measuring Areas to improve the forecasting capacity. Other application of this algorithm on water distribution modelling is the development of metamodels.<ref>{{cite journal |url=https://www.sciencedirect.com/science/article/abs/pii/S0043135423007005|title=Shall we always use hydraulic models? A graph neural network metamodel for water system calibration and uncertainty assessment|last=Zanfei|first=Ariele |journal=Water Research |display-authors=etal |date=2023|volume=242 |article-number=120264 |doi=10.1016/j.watres.2023.120264 |pmid=37393807 |bibcode=2023WatRe.24220264Z |access-date=June 11, June 2024|url-access=subscription }}</ref>

=== Computer Vision ===

{{See also|Computer vision}}

To represent an image as a graph structure, the image is first divided into multiple patches, each of which is treated as a node in the graph. Edges are then formed by connecting each node to its nearest neighbors based on spatial or feature similarity. This graph-based representation enables the application of graph learning models to visual tasks. The relational structure helps to enhance feature extraction and improve performance on image understanding.<ref>{{cite arXiv |eprint=2206.00272 |last1=Han |first1=Kai |last2=Wang |first2=Yunhe |last3=Guo |first3=Jianyuan |last4=Tang |first4=Yehui |last5=Wu |first5=Enhua |title=Vision GNN: An Image is Worth Graph of Nodes |date=2022 |class=cs.CV }}</ref>

=== Text and NLP ===

{{See also|Natural language processing}}

Graph-based representation of text helps to capture deeper semantic relationships between words. Many studies have used graph networks to enhance performance in various text processing tasks such as text classification, question answering, Neural Machine Translation (NMT), event extraction, fact verification, etc.<ref>{{Cite journal |last1=Zhou |first1=Jie |last2=Cui |first2=Ganqu |last3=Hu |first3=Shengding |last4=Zhang |first4=Zhengyan |last5=Yang |first5=Cheng |last6=Liu |first6=Zhiyuan |last7=Wang |first7=Lifeng |last8=Li |first8=Changcheng |last9=Sun |first9=Maosong |date=1 January 2020 |title=Graph neural networks: A review of methods and applications |journal=AI Open |volume=1 |pages=57–81 |doi=10.1016/j.aiopen.2021.01.001 |issn=2666-6510|doi-access=free }}</ref>

==References==

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<ref name="bronstein2021">{{cite arXiv |last1=Bronstein |first1=Michael M. |last2=Bruna |first2=Joan |last3=Cohen |first3=Taco |last4=Veličković |first4=Petar |title=Geometric Deep Learning: Grids, Groups, Graphs Geodesics and Gauges |date=May 4, May 2021 |class=cs.LG |eprint=2104.13478}}</ref>

<ref name=douglas2011>{{cite arXiv|last=Douglas|first=B. L.|date=2011-01-27 January 2011|title=The Weisfeiler–Lehman Method and Graph Isomorphism Testing|class=math.CO|eprint=1101.5211}}</ref>

<ref name=xu2019>{{Cite arXiv|last1=Xu|first1=Keyulu|last2=Hu|first2=Weihua|last3=Leskovec|first3=Jure |last4=Jegelka|first4=Stefanie|author4-link=Stefanie Jegelka|date=2019-02-22 February 2019|title=How Powerful are Graph Neural Networks? |eprint=1810.00826 |class=cs.LG}}</ref>

<ref name=velickovic2022>{{cite arXiv |last1=Veličković |first1=Petar |title=Message passing all the way up |year=2022 |class=cs.LG |eprint=2202.11097}}</ref>

<ref name=qasim2019>{{cite journal |last1=Qasim |first1=Shah Rukh |last2=Kieseler |first2=Jan |last3=Iiyama |first3=Yutaro |last4=Pierini |first4=Maurizio Pierini |title=Learning representations of irregular particle-detector geometry with distance-weighted graph networks |journal=The European Physical Journal C |date=2019 |volume=79 |issue=7 |page=608 |doi=10.1140/epjc/s10052-019-7113-9|s2cid=88518244 |doi-access=free |arxiv=1902.07987 |bibcode=2019EPJC...79..608Q }}</ref>

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<ref name=grady2011discrete>{{cite book |last1=Grady |first1=Leo |last2=Polimeni |first2=Jonathan |title=Discrete Calculus: Applied Analysis on Graphs for Computational Science |url=http://leogrady.net/wp-content/uploads/2017/01/grady2010discrete.pdf |date=2011 |publisher=Springer }}</ref>

<ref name=xu2018>{{cite arXiv |last1=Xu |first1=Keyulu |last2=Li |first2=Chengtao |last3=Tian |first3=Yonglong |last4=Sonobe |first4=Tomohiro |last5=Kawarabayashi |first5=Ken-ichi |last6=Jegelka |first6=Stefanie|author6-link=Stefanie Jegelka |title=Representation Learning on Graphs with Jumping Knowledge Networks |date=2018 |class=cs.LG |eprint=1806.03536}}</ref>

<ref name=Lucibello2021GNN>{{cite web |last=Lucibello |first=Carlo |title=GraphNeuralNetworks.jl |website=[[GitHub]] |url=https://github.com/CarloLucibello/GraphNeuralNetworks.jl |year=2021 |access-date=2023-09-21 September 2023}}</ref>

}}

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[[Category:Artificial neural networks]]

[[Category:Graph algorithms]]

[[Category:2009 in artificial intelligence]]