{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:45:36Z","timestamp":1740134736245,"version":"3.37.3"},"reference-count":43,"publisher":"Informa UK Limited","issue":"4","funder":[{"DOI":"10.13039\/501100000930","name":"NSF","doi-asserted-by":"publisher","award":["CCF-1740551"],"award-info":[{"award-number":["CCF-1740551"]}],"id":[{"id":"10.13039\/501100000930","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000930","name":"NSF","doi-asserted-by":"publisher","award":["CCF-2019844"],"award-info":[{"award-number":["CCF-2019844"]}],"id":[{"id":"10.13039\/501100000930","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000930","name":"NSF","doi-asserted-by":"publisher","award":["DMS-2134012"],"award-info":[{"award-number":["DMS-2134012"]}],"id":[{"id":"10.13039\/501100000930","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.tandfonline.com"],"crossmark-restriction":true},"short-container-title":["Journal of Computational and Graphical Statistics"],"published-print":{"date-parts":[[2023,10,2]]},"DOI":"10.1080\/10618600.2022.2163649","type":"journal-article","created":{"date-parts":[[2023,1,4]],"date-time":"2023-01-04T21:34:00Z","timestamp":1672868040000},"page":"1237-1247","update-policy":"https:\/\/doi.org\/10.1080\/tandf_crossmark_01","source":"Crossref","is-referenced-by-count":0,"title":["Revisiting Convolutional Neural Networks from the Viewpoint of Kernel-Based Methods"],"prefix":"10.1080","volume":"32","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7363-0431","authenticated-orcid":false,"given":"Corinne","family":"Jones","sequence":"first","affiliation":[{"name":"Swiss Data Science Center, \u00c9cole polytechnique f\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6526-5235","authenticated-orcid":false,"given":"Vincent","family":"Roulet","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Washington, Seattle, WA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1186-1343","authenticated-orcid":false,"given":"Zaid","family":"Harchaoui","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Washington, Seattle, WA"}]}],"member":"301","published-online":{"date-parts":[[2023,2,16]]},"reference":[{"key":"e_1_3_5_2_1","first-page":"8139","article-title":"\u201cOn Exact Computation with an Infinitely Wide Neural Net,\u201d in","author":"Arora S.","year":"2019","unstructured":"Arora, S., Du, S. S., Hu, W., Li, Z., Salakhutdinov, R., and Wang, R. (2019), \u201cOn Exact Computation with an Infinitely Wide Neural Net,\u201d in Advances in Neural Information Processing Systems, pp. 8139\u20138148.","journal-title":"Advances in Neural Information Processing Systems"},{"key":"e_1_3_5_3_1","first-page":"1","article-title":"\u201cGroup Invariance, Stability to Deformations, and Complexity of Deep Convolutional Representations,\u201d","volume":"20","author":"Bietti A.","year":"2019","unstructured":"Bietti, A., and Mairal, J. (2019), \u201cGroup Invariance, Stability to Deformations, and Complexity of Deep Convolutional Representations,\u201d Journal of Machine Learning Research, 20, 1\u201349.","journal-title":"Journal of Machine Learning Research"},{"key":"e_1_3_5_4_1","first-page":"135","article-title":"\u201cEfficient Match Kernel between Sets of Features for Visual Recognition,\u201d","author":"Bo L.","year":"2009","unstructured":"Bo, L., and Sminchisescu, C. (2009), \u201cEfficient Match Kernel between Sets of Features for Visual Recognition,\u201d in Advances in Neural Information Processing Systems, pp. 135\u2013143.","journal-title":"in Advances in Neural Information Processing Systems"},{"key":"e_1_3_5_5_1","doi-asserted-by":"publisher","DOI":"10.1109\/MSP.2017.2693418"},{"key":"e_1_3_5_6_1","first-page":"2253","article-title":"\u201cToward Deeper Understanding of Neural Networks: The Power of Initialization and a Dual View on Expressivity,\u201d in","author":"Daniely A.","year":"2016","unstructured":"Daniely, A., Frostig, R., and Singer, Y. (2016), \u201cToward Deeper Understanding of Neural Networks: The Power of Initialization and a Dual View on Expressivity,\u201d in Advances in Neural Information Processing Systems, pp. 2253\u20132261.","journal-title":"Advances in Neural Information Processing Systems"},{"key":"e_1_3_5_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/0096-3003(76)90020-5"},{"key":"e_1_3_5_8_1","first-page":"7710","volume-title":"Advances in Neural Information Processing Systems","author":"Fan Z.","year":"2020","unstructured":"Fan, Z., and Wang, Z. (2020), \u201cSpectra of the Conjugate Kernel and Neural Tangent Kernel for Linear-Width Neural Networks,\u201d in Advances in Neural Information Processing Systems (Vol. 33), eds. H. Larochelle, M. Ranzato, R. Hadsell, M. Balcan, and H. Lin, pp. 7710\u20137721."},{"key":"e_1_3_5_9_1","doi-asserted-by":"publisher","DOI":"10.1109\/JPROC.2020.3048020"},{"key":"e_1_3_5_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF00342633"},{"key":"e_1_3_5_11_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF00344251"},{"key":"e_1_3_5_12_1","volume-title":"International Conference on Learning Representations","author":"Garriga-Alonso A.","year":"2019","unstructured":"Garriga-Alonso, A., Aitchison, L., and Rasmussen, C. E. (2019), \u201cDeep Convolutional Networks as Shallow Gaussian Processes,\u201d in International Conference on Learning Representations."},{"key":"e_1_3_5_13_1","volume-title":"Deep Learning, Adaptive Computation and Machine Learning","author":"Goodfellow I. J.","year":"2016","unstructured":"Goodfellow, I. J., Bengio, Y., and Courville, A. C. (2016), Deep Learning, Adaptive Computation and Machine Learning. Cambridge, MA: MIT Press."},{"key":"e_1_3_5_14_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00365-021-09543-4"},{"key":"e_1_3_5_15_1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1019150005407"},{"key":"e_1_3_5_16_1","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898717778"},{"key":"e_1_3_5_17_1","doi-asserted-by":"publisher","DOI":"10.1113\/jphysiol.1962.sp006837"},{"key":"e_1_3_5_18_1","first-page":"8580","article-title":"\u201cNeural Tangent Kernel: Convergence and Generalization in Neural Networks,","author":"Jacot A.","year":"2018","unstructured":"Jacot, A., Hongler, C., and Gabriel, F. (2018), \u201cNeural Tangent Kernel: Convergence and Generalization in Neural Networks,\u201d in Advances in Neural Information Processing Systems, pp. 8580\u20138589.","journal-title":"in Advances in Neural Information Processing Systems"},{"key":"e_1_3_5_19_1","unstructured":"Jones C. Roulet V. and Harchaoui Z. (2021a) \u201cyesweckn: Software Package for the Training of Convolutional Kernel Networks \u201d available at https:\/\/github.com\/cjones6\/yesweckn."},{"key":"e_1_3_5_20_1","unstructured":"Jones C. Roulet V. and Harchaoui Z. (2021b) \u201cTraining a CKN Counterpart to a LeNet5 ConvNet on MNIST \u201d available at https:\/\/colab.research.google.com\/drive\/11HJpi7no0PRk0vNlJq8rtHF-g49ZWaYJ?usp=sharing."},{"key":"e_1_3_5_21_1","volume-title":"Nonlinear Systems","author":"Khalil H. K.","year":"1992","unstructured":"Khalil, H. K. (1992), Nonlinear Systems, New York, NY: Macmillan Publishing Company."},{"key":"e_1_3_5_22_1","article-title":"\u201cOne Weird Trick for Parallelizing Convolutional Neural Networks,\u201d","author":"Krizhevsky A.","year":"2014","unstructured":"Krizhevsky, A. (2014), \u201cOne Weird Trick for Parallelizing Convolutional Neural Networks,\u201d CoRR, abs\/1404.5997.","journal-title":"CoRR, abs\/1404.5997"},{"key":"e_1_3_5_24_1","first-page":"1106","article-title":"\u201cImageNet Classification with Deep Convolutional Neural Networks,\u201d","author":"Krizhevsky A.","year":"2012","unstructured":"Krizhevsky, A., Sutskever, I., and Hinton, G. E. (2012), \u201cImageNet Classification with Deep Convolutional Neural Networks,\u201d in Advances in Neural Information Processing Systems, pp. 1106\u20131114.","journal-title":"in Advances in Neural Information Processing Systems"},{"key":"e_1_3_5_25_1","first-page":"244","volume-title":"International Conference on Machine Learning","author":"Le Q.","year":"2013","unstructured":"Le, Q., Sarlos, T., and Smola, A. (2013), \u201cFastfood - Computing Hilbert Space Expansions in Loglinear Time,\u201d in International Conference on Machine Learning, pp. 244\u2013252."},{"key":"e_1_3_5_26_1","first-page":"21","volume-title":"Proceedings of the 1988 Connectionist Models Summer School","author":"LeCun Y.","year":"1988","unstructured":"LeCun, Y. (1988), \u201cA Theoretical Framework for Back-Propagation,\u201d in Proceedings of the 1988 Connectionist Models Summer School, pp. 21\u201328."},{"key":"e_1_3_5_27_1","first-page":"306","volume-title":"Intelligent Signal Processing","author":"LeCun Y.","year":"2001","unstructured":"LeCun, Y., Bottou, L., Bengio, Y., and Haffner, P. (2001), \u201cGradient-based Learning Applied to Document Recognition,\u201d in Intelligent Signal Processing, pp. 306\u2013351, IEEE Press."},{"key":"e_1_3_5_28_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01589116"},{"key":"e_1_3_5_29_1","first-page":"1399","article-title":"\u201cEnd-to-End Kernel Learning with Supervised Convolutional Kernel Networks,\u201d","author":"Mairal J.","year":"2016","unstructured":"Mairal, J. (2016), \u201cEnd-to-End Kernel Learning with Supervised Convolutional Kernel Networks,\u201d in Advances in Neural Information Processing Systems, pp. 1399\u20131407.","journal-title":"in Advances in Neural Information Processing Systems"},{"key":"e_1_3_5_30_1","first-page":"2627","article-title":"\u201cConvolutional Kernel Networks,\u201d","author":"Mairal J.","year":"2014","unstructured":"Mairal, J., Koniusz, P., Harchaoui, Z., and Schmid, C. (2014), \u201cConvolutional Kernel Networks,\u201d in Advances in Neural Information Processing Systems, pp. 2627\u20132635.","journal-title":"in Advances in Neural Information Processing Systems"},{"key":"e_1_3_5_31_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF00336963"},{"key":"e_1_3_5_32_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0745-0"},{"key":"e_1_3_5_33_1","volume-title":"International Conference on Learning Representations","author":"Novak R.","year":"2019","unstructured":"Novak, R., Xiao, L., Bahri, Y., Lee, J., Yang, G., Abolafia, D. A., Pennington, J., and Sohl-dickstein, J. (2019), \u201cBayesian Deep Convolutional Networks with Many Channels are Gaussian Processes,\u201d in International Conference on Learning Representations."},{"key":"e_1_3_5_34_1","first-page":"2652","volume-title":"International Conference on Machine Learning","author":"Oglic D.","year":"2017","unstructured":"Oglic, D., and G\u00e4rtner, T. (2017), \u201cNystr\u00f6m Method with Kernel k-means++ Samples as Landmarks,\u201d in International Conference on Machine Learning, pp. 2652\u20132660."},{"key":"e_1_3_5_35_1","first-page":"1375","volume-title":"International Conference on Artificial Intelligence and Statistics","author":"Que Q.","year":"2016","unstructured":"Que, Q., and Belkin, M. (2016), \u201cBack to the Future: Radial Basis Function Networks Revisited,\u201d in International Conference on Artificial Intelligence and Statistics, pp. 1375\u20131383."},{"key":"e_1_3_5_36_1","first-page":"1177","article-title":"\u201cRandom Features for Large-Scale Kernel Machines,\u201d in Advances in","author":"Rahimi A.","year":"2007","unstructured":"Rahimi, A., and Recht, B. (2007), \u201cRandom Features for Large-Scale Kernel Machines,\u201d in Advances in Neural Information Processing Systems, pp. 1177\u20131184.","journal-title":"Neural Information Processing Systems"},{"key":"e_1_3_5_37_1","first-page":"63","volume-title":"Summer School on Machine Learning","author":"Rasmussen C. E.","year":"2003","unstructured":"Rasmussen, C. E. (2003), \u201cGaussian Processes in Machine Learning,\u201d in Summer School on Machine Learning, eds. O. Bousquet, U. Luxburg, and G. R\u00e4tsch, pp. 63\u201371, Berlin: Springer."},{"key":"e_1_3_5_38_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-28650-9_4"},{"key":"e_1_3_5_39_1","unstructured":"Roulet V. Jones C. and Harchaoui Z. (2021) \u201cyesweckn: Visualizing Filters of CKNs and ConvNets \u201d Available at https:\/\/share.streamlit.io\/vroulet\/ckn_visualization\/interactive_visualization.py."},{"key":"e_1_3_5_40_1","first-page":"3215","article-title":"\u201cGeneralization Properties of Learning with Random Features,\u201d in","author":"Rudi A.","year":"2017","unstructured":"Rudi, A., and Rosasco, L. (2017), \u201cGeneralization Properties of Learning with Random Features,\u201d in Advances in Neural Information Processing Systems, pp. 3215\u20133225.","journal-title":"Advances in Neural Information Processing Systems"},{"key":"e_1_3_5_41_1","volume-title":"Adaptive Computation and Machine Learning Series","author":"Sch\u00f6lkopf B.","year":"2002","unstructured":"Sch\u00f6lkopf, B., and Smola, A. J. (2002), Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond. Adaptive Computation and Machine Learning Series. Cambridge, MA: MIT Press."},{"key":"e_1_3_5_42_1","article-title":"\u201cStriving for Simplicity: The All Convolutional Net,\u201d","author":"Springenberg J. T.","year":"2015","unstructured":"Springenberg, J. T., Dosovitskiy, A., Brox, T., and Riedmiller, M. (2015), \u201cStriving for Simplicity: The All Convolutional Net,\u201d in arXiv:1412.6806, also appeared at ICLR 2015 Workshop Track.","journal-title":"in arXiv:1412.6806"},{"key":"e_1_3_5_43_1","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970128"},{"key":"e_1_3_5_44_1","first-page":"295","article-title":"\u201cComputing with Infinite Networks,\u201d in Advances in","author":"Williams C. K. I.","year":"1996","unstructured":"Williams, C. K. I. (1996), \u201cComputing with Infinite Networks,\u201d in Advances in Neural Information Processing Systems, pp. 295\u2013301.","journal-title":"Neural Information Processing Systems"},{"key":"e_1_3_5_45_1","first-page":"682","article-title":"\u201cUsing the Nystr\u00f6m Method to Speed Up Kernel Machines,\u201d in Advances in","author":"Williams C. K. I.","year":"2000","unstructured":"Williams, C. K. I., and Seeger, M. W. (2000), \u201cUsing the Nystr\u00f6m Method to Speed Up Kernel Machines,\u201d in Advances in Neural Information Processing Systems, pp. 682\u2013688.","journal-title":"Neural Information Processing Systems"}],"container-title":["Journal of Computational and Graphical Statistics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.tandfonline.com\/doi\/pdf\/10.1080\/10618600.2022.2163649","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,11,20]],"date-time":"2024-11-20T17:49:53Z","timestamp":1732124993000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.tandfonline.com\/doi\/full\/10.1080\/10618600.2022.2163649"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,16]]},"references-count":43,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2023,10,2]]}},"alternative-id":["10.1080\/10618600.2022.2163649"],"URL":"https:\/\/doi.org\/10.1080\/10618600.2022.2163649","relation":{},"ISSN":["1061-8600","1537-2715"],"issn-type":[{"type":"print","value":"1061-8600"},{"type":"electronic","value":"1537-2715"}],"subject":[],"published":{"date-parts":[[2023,2,16]]},"assertion":[{"value":"The publishing and review policy for this title is described in its Aims & Scope.","order":1,"name":"peerreview_statement","label":"Peer Review Statement"},{"value":"http:\/\/www.tandfonline.com\/action\/journalInformation?show=aimsScope&journalCode=ucgs20","URL":"http:\/\/www.tandfonline.com\/action\/journalInformation?show=aimsScope&journalCode=ucgs20","order":2,"name":"aims_and_scope_url","label":"Aim & Scope"},{"value":"2021-03-26","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2022-12-14","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2023-02-16","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}