{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T15:36:33Z","timestamp":1742916993103,"version":"3.40.3"},"publisher-location":"Cham","reference-count":19,"publisher":"Springer Nature Switzerland","isbn-type":[{"type":"print","value":"9783031812408"},{"type":"electronic","value":"9783031812415"}],"license":[{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025]]},"DOI":"10.1007\/978-3-031-81241-5_9","type":"book-chapter","created":{"date-parts":[[2024,12,31]],"date-time":"2024-12-31T13:45:47Z","timestamp":1735652747000},"page":"121-135","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Combined First- and\u00a0Second-Order Directions for\u00a0Deep Neural Networks Training"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4826-1114","authenticated-orcid":false,"given":"\u00c1ngeles","family":"Mart\u00ednez","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2140-8094","authenticated-orcid":false,"given":"Marco","family":"Viola","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2937-9654","authenticated-orcid":false,"given":"Mahsa","family":"Yousefi","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,1,1]]},"reference":[{"key":"9_CR1","unstructured":"Anil, R., Gupta, V., Koren, T., Regan, K., Singer, Y.: Scalable second order optimization for deep learning. arXiv preprint arXiv:2002.09018 (2021)"},{"issue":"2","key":"9_CR2","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1137\/16M1080173","volume":"60","author":"L Bottou","year":"2018","unstructured":"Bottou, L., Curtis, F.E., Nocedal, J.: Optimization methods for large-scale machine learning. SIAM Rev. 60(2), 223\u2013311 (2018). https:\/\/doi.org\/10.1137\/16M1080173","journal-title":"SIAM Rev."},{"key":"9_CR3","unstructured":"Defazio, A., Bach, F., Lacoste-Julien, S.: SAGA: a fast incremental gradient method with support for non-strongly convex composite objectives. In: Advances in Neural Information Processing Systems, pp. 1646\u20131654 (2014)"},{"issue":"3","key":"9_CR4","doi-asserted-by":"publisher","first-page":"460","DOI":"10.1080\/10556788.2019.1624747","volume":"35","author":"JB Erway","year":"2020","unstructured":"Erway, J.B., Griffin, J., Marcia, R.F., Omheni, R.: Trust-region algorithms for training responses: machine learning methods using indefinite Hessian approximations. Optimiz. Methods Softw. 35(3), 460\u2013487 (2020)","journal-title":"Optimiz. Methods Softw."},{"key":"9_CR5","unstructured":"Glorot, X., Bengio, Y.: Understanding the difficulty of training deep feedforward neural networks. In: Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, pp. 249\u2013256. JMLR Workshop and Conference Proceedings (2010)"},{"key":"9_CR6","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1007\/s10107-020-01506-0","volume":"188","author":"RM Gower","year":"2021","unstructured":"Gower, R.M., Richt\u00e1rik, P., Bach, F.: Stochastic quasi-gradient methods: variance reduction via Jacobian sketching. Math. Program. 188, 135\u2013192 (2021)","journal-title":"Math. Program."},{"key":"9_CR7","unstructured":"Griffin, J.D., Jahani, M., Takac, M., Yektamaram, S., Zhou, W.: A minibatch stochastic quasi-newton method adapted for nonconvex deep learning problems. Optimization Online preprint (2022). https:\/\/optimization-online.org\/?p=18601"},{"key":"9_CR8","doi-asserted-by":"crossref","unstructured":"He, K., Zhang, X., Ren, S., Sun, J.: Deep residual learning for image recognition. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 770\u2013778 (2016)","DOI":"10.1109\/CVPR.2016.90"},{"key":"9_CR9","first-page":"315","volume":"26","author":"R Johnson","year":"2013","unstructured":"Johnson, R., Zhang, T.: Accelerating stochastic gradient descent using predictive variance reduction. Adv. Neural. Inf. Process. Syst. 26, 315\u2013323 (2013)","journal-title":"Adv. Neural. Inf. Process. Syst."},{"key":"9_CR10","unstructured":"Kingma, D.P., Ba, J.: Adam: a method for stochastic optimization. In: 3rd International Conference on Learning Representations, ICLR 2015 - Conference Track Proceedings (2015)"},{"key":"9_CR11","unstructured":"Krizhevsky, A., Hinton, G., et\u00a0al.: Learning multiple layers of features from tiny images (2009). https:\/\/www.cs.toronto.edu\/~kriz\/cifar.html"},{"key":"9_CR12","unstructured":"Nguyen, L.M., Liu, J., Scheinberg, K., Tak\u00e1\u010d, M.: SARAH: a novel method for machine learning problems using stochastic recursive gradient. In: International Conference on Machine Learning, pp. 2613\u20132621. PMLR (2017)"},{"key":"9_CR13","unstructured":"Nguyen, L.M., Liu, J., Scheinberg, K., Tak\u00e1\u010d, M.: Stochastic recursive gradient algorithm for nonconvex optimization. arXiv preprint arXiv:1705.07261 (2017)"},{"key":"9_CR14","unstructured":"Nocedal, J., Wright, S.: Numerical optimization. In: Springer Series in Operations Research and Financial Engineering. Springer (2006)"},{"key":"9_CR15","unstructured":"Reddi, S.J., Hefny, A., Sra, S., Poczos, B., Smola, A.: Stochastic variance reduction for nonconvex optimization. In: International Conference on Machine Learning, pp. 314\u2013323. PMLR (2016)"},{"key":"9_CR16","volume":"409","author":"D di Serafino","year":"2021","unstructured":"di Serafino, D., Toraldo, G., Viola, M.: Using gradient directions to get global convergence of Newton-type methods. Appl. Math. Comput. 409, 125612 (2021)","journal-title":"Appl. Math. Comput."},{"key":"9_CR17","unstructured":"Xiao, H., Rasul, K., Vollgraf, R.: Fashion-MNIST: a novel image dataset for benchmarking machine learning algorithms. arXiv preprint arXiv:1708.07747 (2017)"},{"key":"9_CR18","doi-asserted-by":"publisher","unstructured":"Yousefi, M., Mart\u00ednez, A.: Deep neural networks training by stochastic quasi-Newton trust-region methods. Algorithms 16(10) (2023). https:\/\/doi.org\/10.3390\/a16100490","DOI":"10.3390\/a16100490"},{"key":"9_CR19","doi-asserted-by":"publisher","unstructured":"Yousefi, M., Mart\u00ednez\u00a0Calomardo, \u00c1.: A Matlab-based tutorial on implementing custom loops for training a deep neural network (2022). https:\/\/doi.org\/10.13140\/RG.2.2.33008.94720","DOI":"10.13140\/RG.2.2.33008.94720"}],"container-title":["Lecture Notes in Computer Science","Numerical Computations: Theory and Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-81241-5_9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,12,31]],"date-time":"2024-12-31T14:03:17Z","timestamp":1735653797000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-81241-5_9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"ISBN":["9783031812408","9783031812415"],"references-count":19,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-81241-5_9","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2025]]},"assertion":[{"value":"1 January 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"NUMTA","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Numerical Computations: Theory and Algorithms","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Pizzo Calabro","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Italy","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2023","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"14 June 2023","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"20 June 2023","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"4","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"numta2023","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/www.numta.org\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}