{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T02:36:18Z","timestamp":1780626978533,"version":"3.54.1"},"reference-count":42,"publisher":"MIT Press","issue":"1","content-domain":{"domain":["direct.mit.edu"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2023,1,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Graph convolutional network (GCN) is a powerful deep model in dealing with graph data. However, the explainability of GCN remains a difficult problem since the training behaviors for graph neural networks are hard to describe. In this work, we show that for GCN with wide hidden feature dimension, the output for semisupervised problem can be described by a simple differential equation. In addition, the dynamics of the behavior of output is decided by the graph convolutional neural tangent kernel (GCNTK), which is stable when the width of hidden feature tends to be infinite. And the solution of node classification can be explained directly by the differential equation for a semisupervised problem. The experiments on some toy models speak to the consistency of the GCNTK model and GCN.<\/jats:p>","DOI":"10.1162\/neco_a_01548","type":"journal-article","created":{"date-parts":[[2022,10,25]],"date-time":"2022-10-25T19:42:31Z","timestamp":1666726951000},"page":"1-26","update-policy":"https:\/\/doi.org\/10.1162\/mitpressjournals.corrections.policy","source":"Crossref","is-referenced-by-count":4,"title":["On the Explainability of Graph Convolutional Network With GCN Tangent Kernel"],"prefix":"10.1162","volume":"35","author":[{"given":"Xianchen","family":"Zhou","sequence":"first","affiliation":[{"name":"National University of Defense Technology, Changsha 410073, P.R.C. zhouxianchen13@nudt.edu.cn"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hongxia","family":"Wang","sequence":"additional","affiliation":[{"name":"National University of Defense Technology, Changsha 410073, P.R.C. wanghongxia@nudt.edu.cn"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"281","published-online":{"date-parts":[[2023,1,1]]},"reference":[{"key":"2023032023360999800_","first-page":"242","article-title":"A convergence theory for deep learning via over-parameterization","volume-title":"Proceedings of the International Conference on Machine Learning","author":"Allen-Zhu","year":"2019"},{"key":"2023032023360999800_","first-page":"8139","volume-title":"Advances in neural information processing systems, 32","author":"Arora","year":"2019"},{"key":"2023032023360999800_","author":"Baldassarre","year":"2019","journal-title":"Explainability techniques for graph convolutional networks"},{"key":"2023032023360999800_","first-page":"521","article-title":"Gradient descent with identity initialization efficiently learns positive definite linear transformations by deep residual networks","volume-title":"Proceedings of theInternational Conference on Machine Learning","author":"Bartlett","year":"2018"},{"key":"2023032023360999800_","author":"Chen","year":"2019","journal-title":"On the equivalence between graph isomorphism testing and function approximation with GNNs."},{"key":"2023032023360999800_","article-title":"Gaussian process behaviour in wide deep neural networks","volume-title":"Proceedings of the International Conference on Learning Representations.","author":"de G. Matthews","year":"2018"},{"key":"2023032023360999800_","first-page":"1675","article-title":"Gradient descent finds global minima of deep neural networks","volume-title":"Proceedings of the International Conference on Machine Learning","author":"Du","year":"2019"},{"key":"2023032023360999800_","first-page":"5723","volume-title":"Advances in neural information processing systems","author":"Du","year":"2019"},{"key":"2023032023360999800_","author":"Franceschi","year":"2021","journal-title":"A neural tangent kernel perspective of GANs."},{"key":"2023032023360999800_","author":"Funke","year":"2021","journal-title":"Hard masking for explaining graph neural networks."},{"key":"2023032023360999800_","first-page":"3419","article-title":"Generalization and representational limits of graph neural networks","volume-title":"Proceedings of the International Conference on Machine Learning","author":"Garg","year":"2020"},{"key":"2023032023360999800_","author":"Huang","year":"2020","journal-title":"Local interpretable model explanations for graph neural networks."},{"key":"2023032023360999800_","author":"Huang","year":"2021","journal-title":"Towards deepening graph neural networks: A GNTK-based optimization perspective."},{"key":"2023032023360999800_","first-page":"8580","volume-title":"Advances in neural information processing systems, 32","author":"Jacot","year":"2018"},{"key":"2023032023360999800_","author":"Kipf","year":"2016","journal-title":"Semi-supervised classification with graph convolutional networks."},{"key":"2023032023360999800_","article-title":"Deep neural networks as gaussian processes","volume-title":"Proceedings of the International Conference on Learning Representations.","author":"Lee","year":"2018"},{"key":"2023032023360999800_","first-page":"8572","volume-title":"Advances in neural information processing systems","author":"Lee","year":"2019"},{"key":"2023032023360999800_","author":"Li","year":"2021","journal-title":"The future is log-gaussian: ReNets and their infinite-depth-and-width limit at initialization"},{"key":"2023032023360999800_","volume-title":"Advances in neural information processing systems","author":"Littwin","year":"2020"},{"key":"2023032023360999800_","volume-title":"Advances in neural information processing systems","author":"Liu","year":"2020"},{"key":"2023032023360999800_","author":"Loukas","year":"2020","journal-title":"How hard is to distinguish graphs with graph neural networks?"},{"key":"2023032023360999800_","author":"Luo","year":"2020","journal-title":"Parameterized explainer for graph neural network."},{"issue":"71","key":"2023032023360999800_","first-page":"1","article-title":"Phase diagram for two-layer ReLU neural networks at infinite-width limit","volume":"22","author":"Luo","year":"2021","journal-title":"Journal of Machine Learning Research"},{"key":"2023032023360999800_","volume-title":"Bayesian learning for neural networks","author":"Neal","year":"1995"},{"key":"2023032023360999800_","first-page":"5042","article-title":"The effect of network width on stochastic gradient descent and generalization: an empirical study","volume-title":"Proceedings of the International Conference on Machine Learning","author":"Park","year":"2019"},{"key":"2023032023360999800_","first-page":"10772","article-title":"Explainability methods for graph convolutional neural networks","volume-title":"Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition","author":"Pope","year":"2019"},{"key":"2023032023360999800_","doi-asserted-by":"publisher","first-page":"248","DOI":"10.1016\/j.neunet.2018.08.010","article-title":"The Vapnik\u2013Chervonenkis dimension of graph and recursive neural networks","volume":"108","author":"Scarselli","year":"2018","journal-title":"Neural Networks"},{"key":"2023032023360999800_","author":"Schlichtkrull","year":"2020","journal-title":"Interpreting graph neural networks for NLP with differentiable edge masking"},{"key":"2023032023360999800_","author":"Schnake","year":"2020","journal-title":"Higher-order explanations of graph neural networks via relevant walks"},{"key":"2023032023360999800_","author":"Schwarzenberg","year":"2019","journal-title":"Layer-wise relevance visualization in convolutional text graph classifiers"},{"key":"2023032023360999800_","author":"Sohl-Dickstein","year":"2020","journal-title":"On the infinite width limit of neural networks with a standard parameterization."},{"key":"2023032023360999800_","unstructured":"Vershynin, R. (2010). Introduction to the non-asymptotic analysis of random matrices. arXiv preprint arXiv:1011.3027."},{"key":"2023032023360999800_","author":"Vu","year":"2020","journal-title":"PGM-explainer: Probabilistic graphical model explanations for graph neural networks"},{"key":"2023032023360999800_","first-page":"6861","article-title":"Simplifying graph convolutional networks","volume-title":"Proceedings of the International Conference on Machine Learning","author":"Wu","year":"2019"},{"key":"2023032023360999800_","doi-asserted-by":"publisher","first-page":"4","DOI":"10.1109\/Tnnls.2020.2978386","article-title":"A comprehensive survey on graph neural networks","volume-title":"IEEE Transactions on Neural Networks and Learning Systems","author":"Wu","year":"2021"},{"key":"2023032023360999800_","author":"Xu","year":"2018","journal-title":"How powerful are graph neural networks?"},{"key":"2023032023360999800_","author":"Xu","year":"2020","journal-title":"How neural networks extrapolate: From feedforward to graph neural networks"},{"key":"2023032023360999800_","author":"Yang","year":"2019","journal-title":"Scaling limits of wide neural networks with weight sharing: Gaussian process behavior, gradient independence, and neural tangent kernel derivation."},{"key":"2023032023360999800_","volume-title":"Advances in neural information processing systems","author":"Ying","year":"2019"},{"key":"2023032023360999800_","author":"Yuan","year":"2020","journal-title":"Explainability in graph neural networks: A taxonomic survey."},{"key":"2023032023360999800_","doi-asserted-by":"crossref","first-page":"1042","DOI":"10.1145\/3461702.3462562","article-title":"RelEx: A model-agnostic relational model explainer","volume-title":"Proceedings of the 2021 AAAI\/ACM Conference on AI, Ethics, and Society","author":"Zhang","year":"2021"},{"key":"2023032023360999800_","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1016\/j.aiopen.2021.01.001","article-title":"Graph neural networks: A review of methods and applications","volume":"1","author":"Zhou","year":"2020","journal-title":"AI Open"}],"container-title":["Neural Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/direct.mit.edu\/neco\/article-pdf\/35\/1\/1\/2075421\/neco_a_01548.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/direct.mit.edu\/neco\/article-pdf\/35\/1\/1\/2075421\/neco_a_01548.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,29]],"date-time":"2023-11-29T15:11:28Z","timestamp":1701270688000},"score":1,"resource":{"primary":{"URL":"https:\/\/direct.mit.edu\/neco\/article\/35\/1\/1\/113354\/On-the-Explainability-of-Graph-Convolutional"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,1]]},"references-count":42,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,1,1]]},"published-print":{"date-parts":[[2023,1,1]]}},"URL":"https:\/\/doi.org\/10.1162\/neco_a_01548","relation":{},"ISSN":["0899-7667","1530-888X"],"issn-type":[{"value":"0899-7667","type":"print"},{"value":"1530-888X","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2023,1]]},"published":{"date-parts":[[2023,1,1]]}}}