{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T10:04:43Z","timestamp":1777629883247,"version":"3.51.4"},"reference-count":48,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T00:00:00Z","timestamp":1771891200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100010067","name":"Government of Arag\u00f3n","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100010067","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100014440","name":"Spain Ministry of Science Innovation and Universities","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100014440","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Information Sciences"],"published-print":{"date-parts":[[2026,6]]},"DOI":"10.1016\/j.ins.2026.123275","type":"journal-article","created":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T16:14:13Z","timestamp":1771863253000},"page":"123275","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Bregman Proximal Gradient with extrapolation to train a Reservoir Computing network for a binary classification task"],"prefix":"10.1016","volume":"742","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3431-0926","authenticated-orcid":false,"given":"Carmen","family":"Mayora-Cebollero","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4802-2511","authenticated-orcid":false,"given":"Ana","family":"Mayora-Cebollero","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1184-5901","authenticated-orcid":false,"given":"\u00c1lvaro","family":"Lozano","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8089-343X","authenticated-orcid":false,"given":"Roberto","family":"Barrio","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"issue":"2","key":"10.1016\/j.ins.2026.123275_bib0005","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1007\/s40305-020-00309-6","article-title":"Optimization for deep learning: an overview","volume":"8","author":"Sun","year":"2020","journal-title":"J. Oper. Res. Soc. China"},{"key":"10.1016\/j.ins.2026.123275_bib0010","series-title":"Deep Learning","author":"Goodfellow","year":"2016"},{"key":"10.1016\/j.ins.2026.123275_bib0015","first-page":"26","article-title":"Lecture 6.5-RMSProp: divide the gradient by a running average of its recent magnitude","volume":"4","author":"Hinton","year":"2012","journal-title":"COURSERA: Neural networks for machine learning"},{"key":"10.1016\/j.ins.2026.123275_bib0020","author":"Kingma"},{"key":"10.1016\/j.ins.2026.123275_bib0025","series-title":"International Conference on Machine Learning","first-page":"560","article-title":"signSGD: compressed optimisation for non-convex problems","author":"Bernstein","year":"2018"},{"issue":"192","key":"10.1016\/j.ins.2026.123275_bib0030","first-page":"1","article-title":"A Bregman learning framework for sparse neural networks","volume":"23","author":"Bungert","year":"2022","journal-title":"J. Mach. Learn. Res."},{"issue":"12","key":"10.1016\/j.ins.2026.123275_bib0035","doi-asserted-by":"crossref","first-page":"9508","DOI":"10.1109\/TPAMI.2024.3423382","article-title":"Adan: adaptive nesterov momentum algorithm for faster optimizing deep models","volume":"46","author":"Xie","year":"2024","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"issue":"5","key":"10.1016\/j.ins.2026.123275_bib0040","doi-asserted-by":"crossref","first-page":"678","DOI":"10.1109\/TKDE.2005.77","article-title":"Epsilon-SSVR: a smooth support vector machine for epsilon-insensitive regression","volume":"17","author":"Lee","year":"2005","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"10.1016\/j.ins.2026.123275_bib0045","series-title":"2018 IEEE International Conference on Data Mining Workshops (ICDMW)","first-page":"1217","article-title":"Smoothed hinge loss and\u21131support vector machines","author":"Hajewski","year":"2018"},{"issue":"3","key":"10.1016\/j.ins.2026.123275_bib0050","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1007\/s10994-014-5436-1","article-title":"An efficient primal dual prox method for non-smooth optimization","volume":"98","author":"Yang","year":"2015","journal-title":"Mach. Learn."},{"key":"10.1016\/j.ins.2026.123275_bib0055","doi-asserted-by":"crossref","DOI":"10.1016\/j.chaos.2021.111754","article-title":"An efficient primal-dual method for solving non-smooth machine learning problem","volume":"155","author":"Lyaqini","year":"2022","journal-title":"Chaos Solitons Fract."},{"issue":"3\u20134","key":"10.1016\/j.ins.2026.123275_bib0060","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1561\/2200000058","article-title":"Non-convex optimization for machine learning","volume":"10","author":"Jain","year":"2017","journal-title":"Found. Trends Mach. Learn."},{"key":"10.1016\/j.ins.2026.123275_bib0065","doi-asserted-by":"crossref","first-page":"126515","DOI":"10.1109\/ACCESS.2019.2937005","article-title":"Bregman proximal gradient algorithm with extrapolation for a class of nonconvex nonsmooth minimization problems","volume":"7","author":"Zhang","year":"2019","journal-title":"IEEE Access"},{"key":"10.1016\/j.ins.2026.123275_bib0070","series-title":"Proceedings of the 28th International Conference on Machine Learning (ICML-11)","first-page":"1033","article-title":"Learning recurrent neural networks with hessian-free optimization","author":"Martens","year":"2011"},{"issue":"5","key":"10.1016\/j.ins.2026.123275_bib0075","doi-asserted-by":"crossref","first-page":"1668","DOI":"10.1080\/10556788.2021.1977806","article-title":"Quasi-Newton methods for machine learning: forget the past, just sample","volume":"37","author":"Berahas","year":"2022","journal-title":"Optim. Methods Softw."},{"key":"10.1016\/j.ins.2026.123275_bib0080","author":"Osawa"},{"key":"10.1016\/j.ins.2026.123275_bib0085","author":"Anil"},{"issue":"4","key":"10.1016\/j.ins.2026.123275_bib0090","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1214\/15-STS530","article-title":"Proximal algorithms in statistics and machine learning","volume":"30","author":"Polson","year":"2015","journal-title":"Statist. Sci."},{"key":"10.1016\/j.ins.2026.123275_bib0095","series-title":"OPT 2022: Optimization for Machine Learning (NeurIPS 2022 Workshop)","article-title":"A better way to decay: proximal gradient training algorithms for neural nets","author":"Yang","year":"2022"},{"key":"10.1016\/j.ins.2026.123275_bib0100","series-title":"Bregman Proximal Minimization Algorithms, Analysis and Applications","author":"Mukkamala","year":"2021"},{"key":"10.1016\/j.ins.2026.123275_bib0105","series-title":"International Conference on Machine Learning","first-page":"1139","article-title":"On the importance of initialization and momentum in deep learning","author":"Sutskever","year":"2013"},{"key":"10.1016\/j.ins.2026.123275_bib0110","series-title":"Proceedings of the 4th International Conference on Learning Representations, Workshop Track","first-page":"1","article-title":"Incorporating Nesterov momentum into Adam","author":"Dozat","year":"2016"},{"issue":"1","key":"10.1016\/j.ins.2026.123275_bib0115","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1109\/4235.585893","article-title":"No free lunch theorems for optimization","volume":"1","author":"Wolpert","year":"1997","journal-title":"IEEE Trans. Evol. Comput."},{"issue":"7","key":"10.1016\/j.ins.2026.123275_bib0120","article-title":"Adaptive subgradient methods for online learning and stochastic optimization","volume":"12","author":"Duchi","year":"2011","journal-title":"J. Mach. Learn. Res."},{"key":"10.1016\/j.ins.2026.123275_bib0125","first-page":"543","article-title":"A method for unconstrained convex minimization problem with the rate of convergence o(1\/k2)","volume":"269","author":"Nesterov","year":"1983","journal-title":"Dokl. Akad. Nauk. SSSR"},{"issue":"3","key":"10.1016\/j.ins.2026.123275_bib0130","doi-asserted-by":"crossref","first-page":"2131","DOI":"10.1137\/17M1138558","article-title":"First order methods beyond convexity and Lipschitz gradient continuity with applications to quadratic inverse problems","volume":"28","author":"Bolte","year":"2018","journal-title":"SIAM J. Optim."},{"key":"10.1016\/j.ins.2026.123275_bib0135","series-title":"Advances in Neural Information Processing Systems 32","first-page":"8024","article-title":"PyTorch: an imperative style, high-performance deep learning library","author":"Paszke","year":"2019"},{"issue":"3","key":"10.1016\/j.ins.2026.123275_bib0140","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1016\/j.neunet.2007.04.003","article-title":"An experimental unification of reservoir computing methods","volume":"20","author":"Verstraeten","year":"2007","journal-title":"Neural Netw."},{"issue":"3","key":"10.1016\/j.ins.2026.123275_bib0145","doi-asserted-by":"crossref","DOI":"10.1088\/2634-4386\/ac7db7","article-title":"Hands-on reservoir computing: a tutorial for practical implementation","volume":"2","author":"Cucchi","year":"2022","journal-title":"Neuromorph. Comput. Eng."},{"key":"10.1016\/j.ins.2026.123275_bib0150","series-title":"The \u201cEcho State\u201d Approach to Analysing and Training Recurrent Neural Networks-With an Erratum Note, Bonn, Germany: German National Research Center for Information Technology GMD Technical Report","author":"Jaeger","year":"2001"},{"issue":"11","key":"10.1016\/j.ins.2026.123275_bib0155","doi-asserted-by":"crossref","first-page":"2531","DOI":"10.1162\/089976602760407955","article-title":"Real-time computing without stable states: a new framework for neural computation based on perturbations","volume":"14","author":"Maass","year":"2002","journal-title":"Neural Comput."},{"key":"10.1016\/j.ins.2026.123275_bib0160","series-title":"2004 IEEE International Joint Conference on Neural Networks (IEEE Cat. No. 04CH37541)","first-page":"843","article-title":"Backpropagation-decorrelation: online recurrent learning with o(n) complexity","volume":"vol. 2","author":"Steil","year":"2004"},{"issue":"12","key":"10.1016\/j.ins.2026.123275_bib0165","doi-asserted-by":"crossref","DOI":"10.1063\/1.5010300","article-title":"Using machine learning to replicate chaotic attractors and calculate Lyapunov exponents from data","volume":"27","author":"Pathak","year":"2017","journal-title":"Chaos: Interdiscip. J. Nonlinear Sci."},{"key":"10.1016\/j.ins.2026.123275_bib0170","article-title":"Prediction of chaotic time series using recurrent neural networks and reservoir computing techniques: a comparative study","volume":"8","author":"Shahi","year":"2022","journal-title":"Mach. Learn. Appl."},{"key":"10.1016\/j.ins.2026.123275_bib0175","series-title":"Neural Networks: Tricks of the Trade: Second Edition. Lecture Notes in Computer Science (LNCS)","first-page":"659","article-title":"A practical guide to applying echo state networks","volume":"vol. 7700","author":"Luko\u0161evi\u010dius","year":"2012"},{"issue":"1","key":"10.1016\/j.ins.2026.123275_bib0180","doi-asserted-by":"crossref","first-page":"6086","DOI":"10.1038\/s41598-024-56706-x","article-title":"Evaluation metrics and statistical tests for machine learning","volume":"14","author":"Rainio","year":"2024","journal-title":"Sci. Rep."},{"key":"10.1016\/j.ins.2026.123275_bib0185","series-title":"Experiment Tracking with Weights and Biases","author":"Biewald","year":"2020"},{"issue":"1","key":"10.1016\/j.ins.2026.123275_bib0190","first-page":"1","article-title":"An introduction to the bootstrap","volume":"57","author":"Tibshirani","year":"1993","journal-title":"Monogr. Stat. Appl. Probab."},{"issue":"1","key":"10.1016\/j.ins.2026.123275_bib0195","article-title":"Effect sizes for nonparametric tests","volume":"36","author":"Peres","year":"2025","journal-title":"Biochem. Med."},{"issue":"2","key":"10.1016\/j.ins.2026.123275_bib0200","doi-asserted-by":"crossref","first-page":"738","DOI":"10.1137\/21M1453311","article-title":"Scheduled restart momentum for accelerated stochastic gradient descent","volume":"15","author":"Wang","year":"2022","journal-title":"SIAM J. Imaging Sci."},{"key":"10.1016\/j.ins.2026.123275_bib0205","doi-asserted-by":"crossref","first-page":"100670","DOI":"10.52202\/079017-3193","article-title":"Adaptive proximal gradient method for convex optimization","volume":"37","author":"Malitsky","year":"2024","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"10.1016\/j.ins.2026.123275_bib0210","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1175\/1520-0469(1963)020<0130:DNF>2.0.CO;2","article-title":"Deterministic nonperiodic flow","volume":"20","author":"Lorenz","year":"1963","journal-title":"J. Atmos. Sci."},{"issue":"3","key":"10.1016\/j.ins.2026.123275_bib0215","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1016\/0167-2789(85)90011-9","article-title":"Determining Lyapunov exponents from a time series","volume":"16","author":"Wolf","year":"1985","journal-title":"Phys. D"},{"issue":"6","key":"10.1016\/j.ins.2026.123275_bib0220","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/j.physrep.2008.01.001","article-title":"Chaotic transients in spatially extended systems","volume":"460","author":"T\u00e9l","year":"2008","journal-title":"Phys. Rep."},{"issue":"7","key":"10.1016\/j.ins.2026.123275_bib0225","doi-asserted-by":"crossref","DOI":"10.1063\/5.0143876","article-title":"Deep Learning for chaos detection","volume":"33","author":"Barrio","year":"2023","journal-title":"Chaos: Interdiscip. J. Nonlinear Sci."},{"key":"10.1016\/j.ins.2026.123275_bib0230","series-title":"The European Symposium on Artificial Neural Networks","article-title":"A public domain dataset for human activity recognition using smartphones","author":"Anguita","year":"2013"},{"key":"10.1016\/j.ins.2026.123275_bib0235","series-title":"Human Activity Recognition Using Smartphones","author":"Reyes-Ortiz","year":"2013"},{"key":"10.1016\/j.ins.2026.123275_bib0240","author":"LeCun"}],"container-title":["Information Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0020025526002069?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0020025526002069?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T02:42:52Z","timestamp":1777430572000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0020025526002069"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6]]},"references-count":48,"alternative-id":["S0020025526002069"],"URL":"https:\/\/doi.org\/10.1016\/j.ins.2026.123275","relation":{},"ISSN":["0020-0255"],"issn-type":[{"value":"0020-0255","type":"print"}],"subject":[],"published":{"date-parts":[[2026,6]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Bregman Proximal Gradient with extrapolation to train a Reservoir Computing network for a binary classification task","name":"articletitle","label":"Article Title"},{"value":"Information Sciences","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.ins.2026.123275","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 The Authors. Published by Elsevier Inc.","name":"copyright","label":"Copyright"}],"article-number":"123275"}}