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'''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 |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>{{cite arXiv|last1=Yang |first1=Kevin |title=Analyzing Learned Molecular Representations for Property Prediction |date=2019-11-20 |eprint=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 |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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<ref name="wucuipeizhao2022">{{Cite journal|last1=Wu|first1=Lingfei|last2=Cui|first2=Peng|last3=Pei |first3=Jian|last4=Zhao|first4=Liang|date=2022|title=Graph Neural Networks: Foundations, Frontiers, and Applications|url=https://graph-neural-networks.github.io/|journal=Springer Singapore|pages=725|url-access=<!--WP:URLACCESS-->}}</ref>
<ref name="scarselli2009">{{Cite journal|last1=Scarselli|first1=Franco|last2=Gori|first2=Marco|last3=Tsoi |first3=Ah Chung|last4=Hagenbuchner|first4=Markus|last5=Monfardini|first5=Gabriele|date=2009|title=The Graph Neural Network Model|url=https://ieeexplore.ieee.org/document/4700287|journal=IEEE Transactions on Neural Networks|volume=20|issue=1|pages=61–80|doi=10.1109/TNN.2008.2005605 |pmid=19068426|s2cid=206756462|issn=1941-0093}}</ref>
<ref name="micheli2009">{{Cite journal|last1=Micheli|first1=Alessio|title=Neural Network for Graphs: A Contextual Constructive Approach|url=https://ieeexplore.ieee.org/document/4700287|journal=IEEE Transactions on Neural Networks|year=2009 |volume=20|issue=3|pages=498–511|doi=10.1109/TNN.2008.2010350 |pmid=19193509|s2cid=17486263|issn=1045-9227|url-access=subscription}}</ref>
<ref name="sanchez2021">{{Cite journal|last1=Sanchez-Lengeling|first1=Benjamin|last2=Reif|first2=Emily |last3=Pearce|first3=Adam|last4=Wiltschko|first4=Alex|date=2021-09-02|title=A Gentle Introduction to Graph Neural Networks|url=https://distill.pub/2021/gnn-intro|journal=Distill|volume=6|issue=9|pages=e33 |doi=10.23915/distill.00033|issn=2476-0757|doi-access=free}}</ref>
<ref name="daigavane2021">{{Cite journal|last1=Daigavane|first1=Ameya|last2=Ravindran|first2=Balaraman |last3=Aggarwal|first3=Gaurav|date=2021-09-02|title=Understanding Convolutions on Graphs |url=https://distill.pub/2021/understanding-gnns|journal=Distill|volume=6|issue=9|pages=e32 |doi=10.23915/distill.00032|s2cid=239678898|issn=2476-0757|doi-access=free}}</ref>
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