{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T15:07:26Z","timestamp":1742915246492,"version":"3.40.3"},"publisher-location":"Cham","reference-count":43,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030616151"},{"type":"electronic","value":"9783030616168"}],"license":[{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020]]},"DOI":"10.1007\/978-3-030-61616-8_19","type":"book-chapter","created":{"date-parts":[[2020,10,16]],"date-time":"2020-10-16T23:07:42Z","timestamp":1602889662000},"page":"229-240","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["The Effect of Batch Normalization in the Symmetric Phase"],"prefix":"10.1007","author":[{"given":"Shiro","family":"Takagi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuki","family":"Yoshida","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Masato","family":"Okada","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,10,14]]},"reference":[{"issue":"2","key":"19_CR1","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1162\/089976698300017746","volume":"10","author":"S Amari","year":"1998","unstructured":"Amari, S.: Natural gradient works efficiently in learning. Neural Comput. 10(2), 251\u2013276 (1998)","journal-title":"Neural Comput."},{"issue":"1","key":"19_CR2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1162\/neco_a_01029","volume":"30","author":"S Amari","year":"2018","unstructured":"Amari, S., Ozeki, T., Karakida, R., Yoshida, Y., Okada, M.: Dynamics of learning in MLP: natural gradient and singularity revisited. Neural Comput. 30(1), 1\u201333 (2018)","journal-title":"Neural Comput."},{"issue":"5","key":"19_CR3","doi-asserted-by":"publisher","first-page":"1007","DOI":"10.1162\/neco.2006.18.5.1007","volume":"18","author":"S Amari","year":"2006","unstructured":"Amari, S., Park, H., Ozeki, T.: Singularities affect dynamics of learning in neuromanifolds. Neural Comput. 18(5), 1007\u20131065 (2006)","journal-title":"Neural Comput."},{"key":"19_CR4","unstructured":"Arora, S., Li, Z., Lyu, K.: Theorical analysis of auto rate-tuning by batch normalization. arXiv preprint arXiv:1812.03981 (2018)"},{"key":"19_CR5","unstructured":"Arpit, D., et al.: A closer look at memorization in deep networks. In: Proceedings of the 34th International Conference on Machine Learning (2017)"},{"issue":"3","key":"19_CR6","doi-asserted-by":"publisher","first-page":"643","DOI":"10.1088\/0305-4470\/28\/3\/018","volume":"28","author":"M Biehl","year":"1995","unstructured":"Biehl, M., Schwarze, H.: Learning by on-line gradient descent. J. Phys. A: Math. Gen. 28(3), 643 (1995)","journal-title":"J. Phys. A: Math. Gen."},{"key":"19_CR7","unstructured":"Bjorck, J., Gomes, G., Selman, B., Weinberger, K.Q.: Understanding batch normalization. In: Advances in Neural Information Processing Systems, vol. 31 (2018)"},{"key":"19_CR8","doi-asserted-by":"crossref","unstructured":"Chaudhari, P., Soatto, S.: Stochastic gradient descent performs variational inference, converges to limit cycles for deep networks. In: 6th International Conference on Learning Representations (2018)","DOI":"10.1109\/ITA.2018.8503224"},{"issue":"8","key":"19_CR9","doi-asserted-by":"publisher","first-page":"1313","DOI":"10.1109\/TNN.2008.2000391","volume":"19","author":"F Cousseau","year":"2008","unstructured":"Cousseau, F., Ozeki, T., Amari, S.: Dynamics of learning in multilayer perceptrons near singularities. IEEE Trans. Neural Netw. 19(8), 1313\u20131328 (2008)","journal-title":"IEEE Trans. Neural Netw."},{"issue":"5","key":"19_CR10","doi-asserted-by":"publisher","first-page":"871","DOI":"10.1016\/0893-6080(95)00119-0","volume":"9","author":"K Fukumizu","year":"1996","unstructured":"Fukumizu, K.: A regularity condition of the information matrix of a multilayer perception network. Neural Netw. 9(5), 871\u2013879 (1996)","journal-title":"Neural Netw."},{"key":"19_CR11","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1016\/S0893-6080(00)00009-5","volume":"13","author":"K Fukumizu","year":"2000","unstructured":"Fukumizu, K., Amari, S.: Local minima and plateaus in hierarchical structures of multilayer perceptrons. Neural Netw. 13, 317\u2013327 (2000)","journal-title":"Neural Netw."},{"key":"19_CR12","doi-asserted-by":"crossref","unstructured":"Goldt, S., Advani, M.S., Saxe, A.M., Krzakala, F., Zdeborova, L.: Dynamics of stochastic gradient descent for two-layer neural networks in the teacher-student setup. In: Advances in Neural Information Processing Systems, vol. 32 (2019)","DOI":"10.1088\/1742-5468\/abc61e"},{"key":"19_CR13","doi-asserted-by":"crossref","unstructured":"Goldt, S., Mezard, M., Krzakala, F., Zdeborova, L.: Modelling the influence of data structure on learning in neural networks: the hidden manifold model. arXiv preprint arXiv:1909.11500 (2019)","DOI":"10.1103\/PhysRevX.10.041044"},{"key":"19_CR14","doi-asserted-by":"crossref","unstructured":"Gunasekar, S., Woodworth, B.E., Bhojanapalli, S., Neyshabur, B., Srebro, N.: Implicit regularization in matrix factorization. In: Advances in Neural Information Processing Systems, vol. 30 (2017)","DOI":"10.1109\/ITA.2018.8503198"},{"key":"19_CR15","unstructured":"Han, S., Pool, J., Tran, J., Dally, W.: Learning both weights and connections for efficient neural network. In: Advances in Neural Information Processing Systems, vol. 28 (2015)"},{"key":"19_CR16","unstructured":"Hassibi, B., Stork, D.G.: Second order derivatives for network pruning: optimal brain surgeon. In: Advances in Neural Information Processing Systems, vol. 6 (1993)"},{"issue":"1","key":"19_CR17","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1162\/neco.1997.9.1.1","volume":"9","author":"S Hochreiter","year":"1997","unstructured":"Hochreiter, S., Schmidhuber, J.: Flat minima. Neural Comput. 9(1), 1\u201342 (1997)","journal-title":"Neural Comput."},{"key":"19_CR18","unstructured":"Ioffe, S., Szegedy, C.: Batch normalization: accelerating deep network training by reducing internal covariate shift. In: Proceedings of the 32nd International Conference on Machine Learning (2015)"},{"key":"19_CR19","unstructured":"Jastrzebski, S., et al.: Three factors influencing minima in SGD. arXiv preprint arXiv:1711.04623 (2017)"},{"key":"19_CR20","unstructured":"Karakida, R., Akaho, S., Amari, S.: The normalization method for alleviating pathological sharpness in wide neural networks. In: Advances in Neural Information Processing Systems, vol. 32 (2019)"},{"key":"19_CR21","unstructured":"Karakida, R., Akaho, S., Amari, S.: Universal statistics of fisher information in deep neural networks: mean field approach. In: Chaudhuri, K., Sugiyama, M. (eds.) Proceedings of Machine Learning Research, 16\u201318 April 2019, vol. 89, pp. 1032\u20131041. PMLR (2019)"},{"key":"19_CR22","unstructured":"Keskar, N.S., Mudigere, D., Nocedal, J., Smelyanskiy, M., Tang, P.T.P.: On large-batch training for deep learning: generalization gap and sharp minima. In: 5th International Conference on Learning Representations (2017)"},{"key":"19_CR23","unstructured":"Kohler, J., Daneshmand, H., Lucchi, A., Zhou, M., Neymeyr, K., Hofmann, T.: Exponential convergence rates for batch normalization: the power of length-direction decoupling in non-convex optimization. arXiv preprint arXiv:1805.10694 (2018)"},{"key":"19_CR24","unstructured":"LeCun, Y., Denker, J.S., Solla, S.A.: Optimal brain damage. In: Advances in Neural Information Processing Systems, vol. 3 (1990)"},{"key":"19_CR25","unstructured":"Li, H., Kadav, A., Durdanovic, I., Samet, H., Graf, H.P.: Pruning filters for efficient convnets. arXiv preprint arXiv:1608.08710 (2016)"},{"key":"19_CR26","unstructured":"Luo, P., Wang, X., Shao, W., Peng, Z.: Towards understanding regularization in batch normalization. arXiv preprint arXiv:1809.00846 (2018)"},{"key":"19_CR27","unstructured":"Mandt, S., Hoffman, M., Blei, D.: A variational analysis of stochastic gradient algorithms. In: Proceedings of the 33nd International Conference on Machine Learning (2016)"},{"key":"19_CR28","unstructured":"Neyshabur, B., Tomioka, R., Salakhutdinov, R., Srebro, N.: Geometry of optimization and implicit regularization in deep learning. arXiv preprint arXiv:1705.03071 (2017)"},{"key":"19_CR29","unstructured":"Neyshabur, B., Tomioka, R., Srebro, N.: In search of the real inductive bias: on the role of implicit regularization in deep learning. In: 3rd International Conference on Learning Representations (2015)"},{"key":"19_CR30","doi-asserted-by":"publisher","first-page":"L507","DOI":"10.1088\/0305-4470\/28\/20\/002","volume":"28","author":"P Riegler","year":"1995","unstructured":"Riegler, P., Biehl, M.: On-line backpropagation in two-layered neural networks. J. Phys. A 28, L507\u2013L513 (1995)","journal-title":"J. Phys. A"},{"key":"19_CR31","unstructured":"Saad, D., Solla, S.A.: Dynamics of on-line gradient descent learning for multilayer neural networks. In: Advances in Neural Information Processing Systems, vol. 8 (1995)"},{"issue":"41","key":"19_CR32","doi-asserted-by":"publisher","first-page":"4337","DOI":"10.1103\/PhysRevLett.74.4337","volume":"74","author":"D Saad","year":"1995","unstructured":"Saad, D., Solla, S.A.: Exact solution for on-line learning in multilayer neural networks. Phys. Rev. Lett. 74(41), 4337\u20134340 (1995)","journal-title":"Phys. Rev. Lett."},{"issue":"4","key":"19_CR33","doi-asserted-by":"publisher","first-page":"4225","DOI":"10.1103\/PhysRevE.52.4225","volume":"52","author":"D Saad","year":"1995","unstructured":"Saad, D., Solla, S.A.: On-line learning in soft committee machines. Phys. Rev. E 52(4), 4225\u20134243 (1995)","journal-title":"Phys. Rev. E"},{"key":"19_CR34","unstructured":"Santurkar, S., Tsipras, D., Ilyas, A., Mardy, A.: How does batch normalization help optimization? arXiv preprint arXiv:1805.11604 (2018)"},{"key":"19_CR35","doi-asserted-by":"publisher","first-page":"5781","DOI":"10.1088\/0305-4470\/26\/21\/017","volume":"26","author":"H Schwarze","year":"1993","unstructured":"Schwarze, H.: Learning a rule in a multilayer neural network. J. Phys. A 26, 5781\u20135794 (1993)","journal-title":"J. Phys. A"},{"issue":"8","key":"19_CR36","doi-asserted-by":"publisher","first-page":"6056","DOI":"10.1103\/PhysRevA.45.6056","volume":"45","author":"HS Seung","year":"1992","unstructured":"Seung, H.S., Somopolinsky, H., Tishby, N.: Statistical mechanics of learning from examples. Phys. Rev. A 45(8), 6056\u20136091 (1992)","journal-title":"Phys. Rev. A"},{"issue":"8","key":"19_CR37","doi-asserted-by":"publisher","first-page":"1049","DOI":"10.1016\/S0893-6080(01)00069-7","volume":"14","author":"S Watanabe","year":"2001","unstructured":"Watanabe, S.: Algebraic geometrical methods for hierarchical learning machines. Neural Netw. 14(8), 1049\u20131060 (2001)","journal-title":"Neural Netw."},{"issue":"5","key":"19_CR38","doi-asserted-by":"publisher","first-page":"1011","DOI":"10.1162\/089976603765202640","volume":"15","author":"S Watanabe","year":"2003","unstructured":"Watanabe, S., Amari, S.: Learning coefficients of layered models when the true distribution mismatches the singularities. Neural Comput. 15(5), 1011\u20131033 (2003)","journal-title":"Neural Comput."},{"issue":"7","key":"19_CR39","doi-asserted-by":"publisher","first-page":"989","DOI":"10.1016\/j.neunet.2008.06.017","volume":"21","author":"H Wei","year":"2008","unstructured":"Wei, H., Amari, S.: Dynamics of learning near singularities in radial basis function networks. Neural Netw. 21(7), 989\u20131005 (2008)","journal-title":"Neural Netw."},{"issue":"3","key":"19_CR40","doi-asserted-by":"publisher","first-page":"813","DOI":"10.1162\/neco.2007.12-06-414","volume":"20","author":"H Wei","year":"2008","unstructured":"Wei, H., Zhang, J., Cousseau, F., Ozeki, T., Amari, S.: Dynamics of learning in multilayer perceptrons near singularities. Neural Comput. 20(3), 813\u2013842 (2008)","journal-title":"Neural Comput."},{"key":"19_CR41","unstructured":"West, A.H.L., Saad, D., Nabney, I.T.: The learning dynamics of a universal approximator. In: Advances in Neural Information Processing Systems, vol. 9 (1996)"},{"issue":"18","key":"19_CR42","doi-asserted-by":"publisher","first-page":"184002","DOI":"10.1088\/1751-8121\/ab0669","volume":"52","author":"Y Yoshida","year":"2019","unstructured":"Yoshida, Y., Karakida, R., Okada, M., Amari, S.: Statistical mechanical analysis of learning dynamics of two-layer perceptron with multiple output units. J. Phys. A 52(18), 184002 (2019)","journal-title":"J. Phys. A"},{"key":"19_CR43","unstructured":"Yoshida, Y., Okada, M.: Data-dependence of plateau phenomenon in learning with neural network \u2013 statistical mechanical analysis. In: Advances in Neural Information Processing Systems, vol. 32 (2019)"}],"container-title":["Lecture Notes in Computer Science","Artificial Neural Networks and Machine Learning \u2013 ICANN 2020"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-61616-8_19","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,24]],"date-time":"2021-04-24T10:14:20Z","timestamp":1619259260000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-61616-8_19"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020]]},"ISBN":["9783030616151","9783030616168"],"references-count":43,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-61616-8_19","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2020]]},"assertion":[{"value":"14 October 2020","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"ICANN","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Artificial Neural Networks","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Bratislava","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Slovakia","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2020","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"15 September 2020","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"18 September 2020","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"29","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"icann2020","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/e-nns.org\/icann2020\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"OCS","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"249","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"139","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"0","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"56% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"2.5","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"*The conference was postponed to 2021 due to the COVID-19 pandemic.","order":10,"name":"additional_info_on_review_process","label":"Additional Info on Review Process","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}