{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T22:01:51Z","timestamp":1779919311397,"version":"3.53.1"},"reference-count":63,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Neurocomputing"],"published-print":{"date-parts":[[2026,8]]},"DOI":"10.1016\/j.neucom.2026.133808","type":"journal-article","created":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T23:08:27Z","timestamp":1777590507000},"page":"133808","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Low-rank surrogate modeling and stochastic zero-order optimization for training of neural networks with black-box layers"],"prefix":"10.1016","volume":"691","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9990-6598","authenticated-orcid":false,"given":"Andrei","family":"Chertkov","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Artem","family":"Basharin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mikhail","family":"Saygin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Evgeny","family":"Frolov","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9810-1958","authenticated-orcid":false,"given":"Stanislav","family":"Straupe","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ivan","family":"Oseledets","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"issue":"6","key":"10.1016\/j.neucom.2026.133808_bib0005","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s42979-021-00815-1","article-title":"Deep learning: a comprehensive overview on techniques, taxonomy, applications and research directions","volume":"2","author":"Sarker","year":"2021","journal-title":"SN Comput. Sci."},{"key":"10.1016\/j.neucom.2026.133808_bib0010","first-page":"1","article-title":"The potential of multidimensional photonic computing","author":"Bente","year":"2025","journal-title":"Nat. Rev. Phys."},{"issue":"10","key":"10.1016\/j.neucom.2026.133808_bib0015","doi-asserted-by":"crossref","first-page":"3243","DOI":"10.1109\/JLT.2022.3171831","article-title":"Neuromorphic silicon photonics and hardware-aware deep learning for high-speed inference","volume":"40","author":"Moralis-Pegios","year":"2022","journal-title":"J. Light. Technol."},{"issue":"1","key":"10.1016\/j.neucom.2026.133808_bib0020","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1038\/s41467-024-55220-y","article-title":"Quantum-limited stochastic optical neural networks operating at a few quanta per activation","volume":"16","author":"Ma","year":"2025","journal-title":"Nat. Commun."},{"issue":"8058","key":"10.1016\/j.neucom.2026.133808_bib0025","doi-asserted-by":"crossref","first-page":"368","DOI":"10.1038\/s41586-025-08854-x","article-title":"Universal photonic artificial intelligence acceleration","volume":"640","author":"Ahmed","year":"2025","journal-title":"Nature"},{"issue":"2","key":"10.1016\/j.neucom.2026.133808_bib0030","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1038\/s41566-020-00754-y","article-title":"Photonics for artificial intelligence and neuromorphic computing","volume":"15","author":"Shastri","year":"2021","journal-title":"Nat. Photonics"},{"issue":"7","key":"10.1016\/j.neucom.2026.133808_bib0035","doi-asserted-by":"crossref","first-page":"2001","DOI":"10.1021\/acsphotonics.2c01516","article-title":"Integrated photonic neural networks: opportunities and challenges","volume":"10","author":"Liao","year":"2023","journal-title":"ACS Photonics"},{"issue":"3","key":"10.1016\/j.neucom.2026.133808_bib0040","article-title":"Fundamentals and recent developments of free-space optical neural networks","volume":"136","author":"McNeil","year":"2024","journal-title":"J. Appl. Phys."},{"issue":"1","key":"10.1016\/j.neucom.2026.133808_bib0045","doi-asserted-by":"crossref","first-page":"5468","DOI":"10.1038\/s41467-024-49768-y","article-title":"Perfect linear Optics using silicon photonics","volume":"15","author":"Moralis-Pegios","year":"2024","journal-title":"Nat. Commun."},{"issue":"1","key":"10.1016\/j.neucom.2026.133808_bib0050","doi-asserted-by":"crossref","first-page":"1432","DOI":"10.1038\/s41467-024-45846-3","article-title":"Deep photonic network platform enabling arbitrary and broadband optical functionality","volume":"15","author":"Amiri","year":"2024","journal-title":"Nat. Commun."},{"issue":"10","key":"10.1016\/j.neucom.2026.133808_bib0055","doi-asserted-by":"crossref","first-page":"1076","DOI":"10.1038\/s41566-024-01494-z","article-title":"Nonlinear processing with linear Optics","volume":"18","author":"Yildirim","year":"2024","journal-title":"Nat. Photonics"},{"issue":"2","key":"10.1016\/j.neucom.2026.133808_bib0060","doi-asserted-by":"crossref","DOI":"10.1109\/JPHOT.2025.3547948","article-title":"Photonics breakthroughs 2024: nonlinear photonic computing at scale","volume":"17","author":"Wang","year":"2025","journal-title":"IEEE Photonics J."},{"issue":"1","key":"10.1016\/j.neucom.2026.133808_bib0065","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1007\/s10543-013-0454-0","article-title":"A projector-splitting integrator for dynamical low-rank approximation","volume":"54","author":"Lubich","year":"2014","journal-title":"BIT Numer. Math."},{"key":"10.1016\/j.neucom.2026.133808_bib0070","author":"Chen"},{"key":"10.1016\/j.neucom.2026.133808_bib0075","series-title":"Proceedings of the 29th ACM Conference on User Modeling, Adaptation and Personalization","first-page":"262","article-title":"Dynamic modeling of user preferences for stable recommendations","author":"Olaleke","year":"2021"},{"key":"10.1016\/j.neucom.2026.133808_bib0080","author":"Zhao"},{"issue":"1","key":"10.1016\/j.neucom.2026.133808_bib0085","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1038\/s42005-025-02255-2","article-title":"Genetically programmable optical random neural networks","volume":"8","author":"\u00c7arp\u0131nl\u0131o\u011flu","year":"2025","journal-title":"Commun. Phys."},{"issue":"8079","key":"10.1016\/j.neucom.2026.133808_bib0090","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1038\/s41586-025-09384-2","article-title":"Training of physical neural networks","volume":"645","author":"Momeni","year":"2025","journal-title":"Nature"},{"key":"10.1016\/j.neucom.2026.133808_bib0095","article-title":"Zeroth-order stochastic variance reduction for nonconvex optimization","volume":"31","author":"Liu","year":"2018","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"10.1016\/j.neucom.2026.133808_bib0100","first-page":"53038","article-title":"Fine-tuning language models with just forward passes","volume":"36","author":"Malladi","year":"2023","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"10.1016\/j.neucom.2026.133808_bib0105","author":"Chen"},{"key":"10.1016\/j.neucom.2026.133808_bib0110","author":"Chaubard"},{"key":"10.1016\/j.neucom.2026.133808_bib0115","first-page":"54905","article-title":"Lora-ga: low-rank adaptation with gradient approximation","volume":"37","author":"Wang","year":"2024","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"10.1016\/j.neucom.2026.133808_bib0120","series-title":"ICASSP 2020-2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)","first-page":"3017","article-title":"Low-rank gradient approximation for memory-efficient on-device training of deep neural network","author":"Gooneratne","year":"2020"},{"key":"10.1016\/j.neucom.2026.133808_bib0125","series-title":"International Conference on Machine Learning","first-page":"10249","article-title":"Can forward gradient match backpropagation?","author":"Fournier","year":"2023"},{"key":"10.1016\/j.neucom.2026.133808_bib0130","author":"Refael"},{"key":"10.1016\/j.neucom.2026.133808_bib0135","doi-asserted-by":"crossref","DOI":"10.1016\/j.neunet.2025.107504","article-title":"Interpretable unsupervised neural network structure for data clustering via differentiable reconstruction of ONMF and sparse autoencoder","author":"Gai","year":"2025","journal-title":"Neural Netw."},{"key":"10.1016\/j.neucom.2026.133808_bib0140","article-title":"Dual-space topological isomorphism and maximization of predictive diversity for unsupervised domain adaptation","author":"Wang","year":"2025","journal-title":"IEEE Trans. Image Process."},{"key":"10.1016\/j.neucom.2026.133808_bib0145","author":"Refael"},{"issue":"1","key":"10.1016\/j.neucom.2026.133808_bib0150","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1038\/s41467-022-35772-7","article-title":"Photonic machine learning with on-chip diffractive Optics","volume":"14","author":"Fu","year":"2023","journal-title":"Nat. Commun."},{"key":"10.1016\/j.neucom.2026.133808_bib0155","series-title":"Advances in Neural Information Processing Systems","first-page":"8649","article-title":"L2ight: enabling on-chip learning for optical neural networks via efficient in-situ subspace optimization","volume":"vol. 34","author":"Gu","year":"2021"},{"key":"10.1016\/j.neucom.2026.133808_bib0160","series-title":"Tensor-compressed back-propagation-free training for (physics-informed) neural networks","author":"Zhao","year":"2023"},{"key":"10.1016\/j.neucom.2026.133808_bib0165","series-title":"Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, KDD \u201922, ACM","first-page":"1441","article-title":"P-meta: towards on-device deep model adaptation","author":"Qu","year":"2022"},{"issue":"6643","key":"10.1016\/j.neucom.2026.133808_bib0170","doi-asserted-by":"crossref","first-page":"398","DOI":"10.1126\/science.ade8450","article-title":"Experimentally realized in situ backpropagation for deep learning in photonic neural networks","volume":"380","author":"Pai","year":"2023","journal-title":"Science"},{"issue":"6","key":"10.1016\/j.neucom.2026.133808_bib0175","doi-asserted-by":"crossref","first-page":"940","DOI":"10.1364\/PRJ.389553","article-title":"In situ optical backpropagation training of diffractive optical neural networks","volume":"8","author":"Zhou","year":"2020","journal-title":"Photon. Res."},{"issue":"20","key":"10.1016\/j.neucom.2026.133808_bib0180","doi-asserted-by":"crossref","first-page":"5752","DOI":"10.1364\/OL.401675","article-title":"Fully reconfigurable coherent optical vector\u2013matrix multiplication","volume":"45","author":"Spall","year":"2020","journal-title":"Opt. Lett."},{"issue":"12","key":"10.1016\/j.neucom.2026.133808_bib0185","doi-asserted-by":"crossref","first-page":"1335","DOI":"10.1038\/s41566-024-01567-z","article-title":"Single-chip photonic deep neural network with forward-only training","volume":"18","author":"Bandyopadhyay","year":"2024","journal-title":"Nat. Photonics"},{"key":"10.1016\/j.neucom.2026.133808_bib0190","series-title":"Streamlined optical training of large-scale modern deep learning architectures with direct feedback alignment","author":"Wang","year":"2025"},{"key":"10.1016\/j.neucom.2026.133808_bib0195","author":"Hinton"},{"issue":"20","key":"10.1016\/j.neucom.2026.133808_bib0200","doi-asserted-by":"crossref","first-page":"5249","DOI":"10.1364\/OL.496884","article-title":"Forward\u2013forward training of an optical neural network","volume":"48","author":"Oguz","year":"2023","journal-title":"Opt. Lett."},{"issue":"2","key":"10.1016\/j.neucom.2026.133808_bib0205","article-title":"Multiplexed gradient descent: fast online training of modern datasets on hardware neural networks without backpropagation","volume":"1","author":"McCaughan","year":"2023","journal-title":"APL Mach. Learn."},{"key":"10.1016\/j.neucom.2026.133808_bib0210","author":"Pai"},{"issue":"1","key":"10.1016\/j.neucom.2026.133808_bib0215","doi-asserted-by":"crossref","first-page":"5918","DOI":"10.1038\/s41598-019-42408-2","article-title":"Highly parallel simulation and optimization of photonic circuits in time and frequency domain based on the deep-learning framework pytorch","volume":"9","author":"Laporte","year":"2019","journal-title":"Sci. Rep."},{"key":"10.1016\/j.neucom.2026.133808_bib0220","series-title":"Conference on Neural Information Processing Systems (NeurIPS)","article-title":"L2ight: enabling on-chip learning for optical neural networks via efficient in-situ subspace optimization","author":"Gu","year":"2021"},{"key":"10.1016\/j.neucom.2026.133808_bib0225","author":"Yin"},{"key":"10.1016\/j.neucom.2026.133808_bib0230","first-page":"1","article-title":"Dual adaptive training of photonic neural networks","author":"Zheng","year":"2023","journal-title":"Nat. Mach. Intell."},{"issue":"8","key":"10.1016\/j.neucom.2026.133808_bib0235","doi-asserted-by":"crossref","first-page":"2425","DOI":"10.1109\/JLT.2023.3234689","article-title":"A coherent photonic crossbar for scalable universal linear Optics","volume":"41","author":"Giamougiannis","year":"2023","journal-title":"J. Light. Technol."},{"issue":"6","key":"10.1016\/j.neucom.2026.133808_bib0240","doi-asserted-by":"crossref","first-page":"312","DOI":"10.1109\/JSTQE.2016.2573583","article-title":"Microring weight banks","volume":"22","author":"Tait","year":"2016","journal-title":"IEEE J. Sel. Top. Quantum Electron."},{"issue":"198","key":"10.1016\/j.neucom.2026.133808_bib0245","article-title":"Two-dimensional matrix multiplication using coherent optical techniques","volume":"18","author":"Tamura","year":"1979","journal-title":"Opt. Eng."},{"key":"10.1016\/j.neucom.2026.133808_bib0250","series-title":"Monarch: expressive structured matrices for efficient and accurate training","author":"Dao","year":"2022"},{"key":"10.1016\/j.neucom.2026.133808_bib0255","author":"Qiu"},{"issue":"12","key":"10.1016\/j.neucom.2026.133808_bib0260","doi-asserted-by":"crossref","first-page":"1460","DOI":"10.1364\/OPTICA.3.001460","article-title":"Optimal design for universal multiport interferometers","volume":"3","author":"Clements","year":"2016","journal-title":"Optica"},{"key":"10.1016\/j.neucom.2026.133808_bib0265","doi-asserted-by":"crossref","DOI":"10.1038\/s41467-022-34308-3","article-title":"Asymptotically fault-tolerant programmable photonics","volume":"13","author":"Hamerly","year":"2022","journal-title":"Nat. Commun."},{"key":"10.1016\/j.neucom.2026.133808_bib0270","article-title":"Programmable Photonic Integrated Meshes for Modular Generation of Optical Entanglement Links, NPJ Quantum Information","volume":"9","author":"Dong","year":"2023"},{"key":"10.1016\/j.neucom.2026.133808_bib0275","series-title":"Learning multiple layers of features from tiny images","author":"Krizhevsky","year":"2009"},{"issue":"1","key":"10.1016\/j.neucom.2026.133808_bib0280","first-page":"1","article-title":"A comparative study of convolutional neural networks and cybernetic approaches on CIFAR-10 dataset","volume":"1","author":"Vinay","year":"2023","journal-title":"Int. J. Mach. Learn. Cybern. (IJMLC)"},{"key":"10.1016\/j.neucom.2026.133808_bib0285","doi-asserted-by":"crossref","first-page":"258","DOI":"10.1016\/j.isprsjprs.2025.09.013","article-title":"Arctic sea ice motion retrieval from multisource SAR images using a keypoint-free feature tracking algorithm","volume":"230","author":"Gao","year":"2025","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"10.1016\/j.neucom.2026.133808_bib0290","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1016\/j.isprsjprs.2025.02.032","article-title":"SFA-net: a SAM-guided focused attention network for multimodal remote sensing image matching","volume":"223","author":"Gao","year":"2025","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"10.1016\/j.neucom.2026.133808_bib0295","first-page":"1","article-title":"SAR\u2013optical image matching with semantic position probability distribution","volume":"61","author":"Li","year":"2023","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"10.1016\/j.neucom.2026.133808_bib0300","series-title":"Proceedings of the 22nd ACM International Conference on Multimedia","first-page":"1041","article-title":"A dataset and taxonomy for urban sound research","author":"Salamon","year":"2014"},{"key":"10.1016\/j.neucom.2026.133808_bib0305","author":"Desplanques"},{"issue":"8","key":"10.1016\/j.neucom.2026.133808_bib0310","first-page":"9","article-title":"Language models are unsupervised multitask learners","volume":"1","author":"Radford","year":"2019","journal-title":"OpenAI blog"},{"key":"10.1016\/j.neucom.2026.133808_bib0315","series-title":"The Thirty-Eight Conference on Neural Information Processing Systems Datasets and Benchmarks Track","article-title":"The fineweb datasets: decanting the web for the finest text data at scale","author":"Penedo","year":"2024"}],"container-title":["Neurocomputing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0925231226012051?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0925231226012051?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T21:02:25Z","timestamp":1779915745000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0925231226012051"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8]]},"references-count":63,"alternative-id":["S0925231226012051"],"URL":"https:\/\/doi.org\/10.1016\/j.neucom.2026.133808","relation":{},"ISSN":["0925-2312"],"issn-type":[{"value":"0925-2312","type":"print"}],"subject":[],"published":{"date-parts":[[2026,8]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Low-rank surrogate modeling and stochastic zero-order optimization for training of neural networks with black-box layers","name":"articletitle","label":"Article Title"},{"value":"Neurocomputing","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.neucom.2026.133808","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"133808"}}