{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T15:47:41Z","timestamp":1762530461278,"version":"build-2065373602"},"reference-count":70,"publisher":"Springer Science and Business Media LLC","issue":"15","license":[{"start":{"date-parts":[[2025,9,22]],"date-time":"2025-09-22T00:00:00Z","timestamp":1758499200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,9,22]],"date-time":"2025-09-22T00:00:00Z","timestamp":1758499200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"National Key Research and Development Program of China","award":["2022YFA1004700"],"award-info":[{"award-number":["2022YFA1004700"]}]},{"DOI":"10.13039\/501100013076","name":"National Major Science and Technology Projects of China","doi-asserted-by":"publisher","award":["2021SHZDZX0100"],"award-info":[{"award-number":["2021SHZDZX0100"]}],"id":[{"id":"10.13039\/501100013076","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the National Natural Science Foundation of China under Grant","award":["62403360, 72171172, 92367101, 62088101"],"award-info":[{"award-number":["62403360, 72171172, 92367101, 62088101"]}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Appl Intell"],"published-print":{"date-parts":[[2025,10]]},"DOI":"10.1007\/s10489-025-06875-7","type":"journal-article","created":{"date-parts":[[2025,9,22]],"date-time":"2025-09-22T12:36:13Z","timestamp":1758544573000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Towards understanding the optimization mechanisms in deep learning"],"prefix":"10.1007","volume":"55","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5832-1884","authenticated-orcid":false,"given":"Binchuan","family":"Qi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei","family":"Gong","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Li","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,9,22]]},"reference":[{"key":"6875_CR1","unstructured":"Yun C, Sra S, Jadbabaie A (2018) Small nonlinearities in activation functions create bad local minima in neural networks. In: International conference on learning representations. https:\/\/api.semanticscholar.org\/CorpusID:52893515"},{"key":"6875_CR2","unstructured":"Du SS, Zhai X, P\u00f3czos B et\u00a0al (2018) Gradient descent provably optimizes over-parameterized neural networks. ArXiv arXiv:1810.02054https:\/\/api.semanticscholar.org\/CorpusID:52920808"},{"key":"6875_CR3","unstructured":"Chizat L, Oyallon E, Bach FR (2018) On lazy training in differentiable programming. In: Neural information processing systems. https:\/\/api.semanticscholar.org\/CorpusID:189928159"},{"key":"6875_CR4","unstructured":"Arjevani Y, Field M (2022) Annihilation of spurious minima in two-layer relu networks. ArXiv arXiv:2210.06088https:\/\/api.semanticscholar.org\/CorpusID:252846371"},{"key":"6875_CR5","unstructured":"Jacot A, Gabriel F, Hongler C (2018) Neural tangent kernel: Convergence and generalization in neural networks. ArXiv arXiv:1806.07572https:\/\/api.semanticscholar.org\/CorpusID:49321232"},{"key":"6875_CR6","unstructured":"Du SS, Lee J, Li H et al (2018) Gradient descent finds global minima of deep neural networks. ArXiv arXiv:1811.03804https:\/\/api.semanticscholar.org\/CorpusID:53250419"},{"key":"6875_CR7","unstructured":"Zou D, Cao Y, Zhou D et al (2018) Stochastic gradient descent optimizes over-parameterized deep relu networks. ArXiv arXiv:1811.08888https:\/\/api.semanticscholar.org\/CorpusID:53752874"},{"key":"6875_CR8","unstructured":"Arora S, Du SS, Hu W et\u00a0al (2019) Fine-grained analysis of optimization and generalization for overparameterized two-layer neural networks. ArXiv arXiv:1901.08584https:\/\/api.semanticscholar.org\/CorpusID:59222746"},{"key":"6875_CR9","unstructured":"Mohamadi MA, Bae W, Sutherland DJ (2023) A fast, well-founded approximation to the empirical neural tangent kernel. In: International conference on machine learning, PMLR, pp 25061\u201325081"},{"key":"6875_CR10","unstructured":"Wang Y, Li D, Sun R (2023) Ntk-sap: Improving neural network pruning by aligning training dynamics. arXiv preprint arXiv:2304.02840"},{"key":"6875_CR11","unstructured":"Sirignano JA, Spiliopoulos KV (2018) Mean field analysis of neural networks: A central limit theorem. Stochastic Processes and their Applications. https:\/\/api.semanticscholar.org\/CorpusID:88523128"},{"key":"6875_CR12","doi-asserted-by":"crossref","unstructured":"Mei S, Montanari A, Nguyen PM (2018) A mean field view of the landscape of two-layer neural networks. Proc National Academy Sci USA 115:E7665 \u2013 E7671. https:\/\/api.semanticscholar.org\/CorpusID:4932688","DOI":"10.1073\/pnas.1806579115"},{"key":"6875_CR13","unstructured":"Chizat L, Bach FR (2018) On the global convergence of gradient descent for over-parameterized models using optimal transport. ArXiv arXiv:1805.09545https:\/\/api.semanticscholar.org\/CorpusID:43945764"},{"issue":"3","key":"6875_CR14","doi-asserted-by":"publisher","first-page":"201","DOI":"10.4171\/msl\/42","volume":"6","author":"PM Nguyen","year":"2023","unstructured":"Nguyen PM, Pham HT (2023) A rigorous framework for the mean field limit of multilayer neural networks. Math Stat Learn 6(3):201\u2013357","journal-title":"Math Stat Learn"},{"key":"6875_CR15","unstructured":"Seleznova M, Kutyniok G (2021) Analyzing finite neural networks: Can we trust neural tangent kernel theory? In: Bruna J, Hesthaven JS, Zdeborov\u00e1 L (eds) Mathematical and Scientific Machine Learning, 16-19 August 2021, Virtual Conference \/ Lausanne, Switzerland, Proceedings of Machine Learning Research, vol 145. PMLR, pp 868\u2013895. https:\/\/proceedings.mlr.press\/v145\/seleznova22a.html"},{"issue":"35","key":"6875_CR16","first-page":"1","volume":"21","author":"M Blondel","year":"2020","unstructured":"Blondel M, Martins AF, Niculae V (2020) Learning with fenchel-young losses. J Mach Learn Res 21(35):1\u201369","journal-title":"J Mach Learn Res"},{"key":"6875_CR17","unstructured":"Lee J, Simchowitz M, Jordan MI et\u00a0al (2016) Gradient descent only converges to minimizers. In: Annual conference computational learning theory. https:\/\/api.semanticscholar.org\/CorpusID:5378616"},{"key":"6875_CR18","unstructured":"Jentzen A, Kuckuck B, Neufeld A et\u00a0al (2018) Strong error analysis for stochastic gradient descent optimization algorithms. Ima Journal of Numerical Analysis. https:\/\/api.semanticscholar.org\/CorpusID:53603316"},{"key":"6875_CR19","unstructured":"Ahmad N, \u00d6fverstedt J, Tarai S et\u00a0al (2024a) Interpretable uncertainty-aware deep regression with cohort saliency analysis for three-slice CT imaging studies. In: Burgos N, Petitjean C, Vakalopoulou M et\u00a0al (eds) Medical Imaging with Deep Learning, 3-5 July 2024, Paris, France, Proceedings of Machine Learning Research, vol 250. PMLR, pp 17\u201332. https:\/\/proceedings.mlr.press\/v250\/ahmad24a.html"},{"key":"6875_CR20","doi-asserted-by":"publisher","unstructured":"Ahmad N, Dahlberg H, J\u00f6nsson H et al (2024) Voxel-wise body composition analysis using image registration of a three-slice CT imaging protocol: Methodology and proof-of-concept studies. BioMedical Eng OnLine 23(1):42. https:\/\/doi.org\/10.1186\/s12938-024-01235-x","DOI":"10.1186\/s12938-024-01235-x"},{"key":"6875_CR21","doi-asserted-by":"publisher","unstructured":"Ahmad N, Strand R, Sparres\u00e4ter B et al (2023) Automatic segmentation of large-scale CT image datasets for detailed body composition analysis. BMC Bioinform 24(1):346. https:\/\/doi.org\/10.1186\/S12859-023-05462-2","DOI":"10.1186\/S12859-023-05462-2"},{"key":"6875_CR22","doi-asserted-by":"publisher","unstructured":"Hayat M, Ahmad N, Nasir A et al (2024) Hybrid deep learning efficientnetv2 and vision transformer (effnetv2-vit) model for breast cancer histopathological image classification. IEEE Access 12:184119\u2013184131. https:\/\/doi.org\/10.1109\/ACCESS.2024.3503413","DOI":"10.1109\/ACCESS.2024.3503413"},{"issue":"8","key":"6875_CR23","doi-asserted-by":"publisher","first-page":"2751","DOI":"10.1007\/S00371-021-02153-Y","volume":"38","author":"N Ahmad","year":"2022","unstructured":"Ahmad N, Asghar S, Gillani SA (2022) Transfer learning-assisted multi-resolution breast cancer histopathological images classification. Vis Comput 38(8):2751\u2013277. https:\/\/doi.org\/10.1007\/S00371-021-02153-Y","journal-title":"Vis Comput"},{"key":"6875_CR24","doi-asserted-by":"crossref","unstructured":"Neal RM, Neal RM (1996) Priors for infinite networks. Bayesian learning for neural networks pp 29\u201353","DOI":"10.1007\/978-1-4612-0745-0_2"},{"key":"6875_CR25","unstructured":"Williams CKI (1996) Computing with infinite networks. In: Neural information processing systems. https:\/\/api.semanticscholar.org\/CorpusID:16883702"},{"key":"6875_CR26","unstructured":"Winther O (2000) Computing with finite and infinite networks. In: Neural Information Processing Systems. https:\/\/api.semanticscholar.org\/CorpusID:12052666"},{"key":"6875_CR27","unstructured":"Neal RM (2012) Bayesian learning for neural networks, vol 118. Springer Science & Business Media"},{"key":"6875_CR28","unstructured":"Lee J, Bahri Y, Novak R et\u00a0al (2017) Deep neural networks as gaussian processes. ArXiv arXiv:1711.00165https:\/\/api.semanticscholar.org\/CorpusID:3708505"},{"key":"6875_CR29","unstructured":"Li Y, Liang Y (2018) Learning overparameterized neural networks via stochastic gradient descent on structured data. ArXiv arXiv:1808.01204https:\/\/api.semanticscholar.org\/CorpusID:51920936"},{"key":"6875_CR30","unstructured":"Allen-Zhu Z, Li Y, Liang Y (2018a) Learning and generalization in overparameterized neural networks, going beyond two layers. In: Neural information processing systems. https:\/\/api.semanticscholar.org\/CorpusID:53287096"},{"key":"6875_CR31","unstructured":"Allen-Zhu Z, Li Y, Song Z (2018b) A convergence theory for deep learning via over-parameterization. ArXiv arXiv:1811.03962https:\/\/api.semanticscholar.org\/CorpusID:53250107"},{"key":"6875_CR32","unstructured":"Vyas N, Bansal Y, Nakkiran P (2022) Limitations of the ntk for understanding generalization in deep learning. arXiv preprint arXiv:2206.10012"},{"key":"6875_CR33","doi-asserted-by":"crossref","unstructured":"Oneto L, Ridella S, Anguita D (2023) Do we really need a new theory to understand over-parameterization? Neurocomputing 543:126227. https:\/\/api.semanticscholar.org\/CorpusID:258399088","DOI":"10.1016\/j.neucom.2023.126227"},{"key":"6875_CR34","doi-asserted-by":"crossref","unstructured":"Edwards L, Veale M (2017) Slave to the algorithm? why a right to explanationn is probably not the remedy you are looking for. SSRN Electronic J 16(1)","DOI":"10.2139\/ssrn.2972855"},{"key":"6875_CR35","doi-asserted-by":"publisher","unstructured":"Gunning D, Stefik M, Choi J et\u00a0al (2019) Xai\u2014explainable artificial intelligence. Sci Robotics 4(37):eaay7120.https:\/\/doi.org\/10.1126\/scirobotics.aay7120https:\/\/www.science.org\/doi\/abs\/10.1126\/scirobotics.aay7120https:\/\/www.science.org\/doi\/pdf\/10.1126\/scirobotics.aay7120","DOI":"10.1126\/scirobotics.aay7120"},{"key":"6875_CR36","doi-asserted-by":"publisher","first-page":"52138","DOI":"10.1109\/ACCESS.2018.2870052","volume":"6","author":"A Adadi","year":"2018","unstructured":"Adadi A, Berrada M (2018) Peeking inside the black-box: A survey on explainable artificial intelligence (xai). IEEE Access 6:52138\u201352160. https:\/\/doi.org\/10.1109\/ACCESS.2018.2870052","journal-title":"IEEE Access"},{"key":"6875_CR37","doi-asserted-by":"publisher","unstructured":"Finlay C, Oberman AM (2021) Scaleable input gradient regularization for adversarial robustness. Mach Learn Appl 3:1000177. https:\/\/doi.org\/10.1016\/j.mlwa.2020.100017","DOI":"10.1016\/j.mlwa.2020.100017"},{"issue":"12","key":"6875_CR38","doi-asserted-by":"publisher","first-page":"3197","DOI":"10.1007\/S10115-022-01756-8","volume":"64","author":"H Xiong","year":"2022","unstructured":"Xiong H, Li X, Li X et al (2022) Interpretable deep learning: interpretation, interpretability, trustworthiness, and beyond. Knowl Inf Syst 64(12):3197\u2013323. https:\/\/doi.org\/10.1007\/S10115-022-01756-8","journal-title":"Knowl Inf Syst"},{"key":"6875_CR39","doi-asserted-by":"crossref","unstructured":"Zhou B, Khosla A, Lapedriza A et\u00a0al (2016) Learning deep features for discriminative localization. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp 2921\u20132929","DOI":"10.1109\/CVPR.2016.319"},{"key":"6875_CR40","doi-asserted-by":"crossref","unstructured":"Selvaraju RR, Cogswell M, Das A et\u00a0al (2017) Grad-cam: Visual explanations from deep networks via gradient-based localization. In: Proceedings of the IEEE international conference on computer vision, pp 618\u2013626","DOI":"10.1109\/ICCV.2017.74"},{"key":"6875_CR41","doi-asserted-by":"crossref","unstructured":"Chattopadhay A, Sarkar A, Howlader P et\u00a0al (2018) Grad-cam++: Generalized gradient-based visual explanations for deep convolutional networks. In: 2018 IEEE winter conference on applications of computer vision (WACV), IEEE, pp 839\u2013847","DOI":"10.1109\/WACV.2018.00097"},{"key":"6875_CR42","doi-asserted-by":"publisher","unstructured":"Wang Z, Liu Y, Thiruselvi AA et\u00a0al (2024a) Xaiport: A service framework for the early adoption of XAI in AI model development. In: Proceedings of the 2024 ACM\/IEEE 44th international conference on software engineering: new ideas and emerging results, NIER@ICSE 2024, Lisbon, Portugal, April 14-20, 2024. ACM, pp 67\u20137. https:\/\/doi.org\/10.1145\/3639476.3639759","DOI":"10.1145\/3639476.3639759"},{"issue":"2","key":"6875_CR43","doi-asserted-by":"publisher","first-page":"762","DOI":"10.1109\/TCC.2024.3398609","volume":"12","author":"Z Wang","year":"2024","unstructured":"Wang Z, Liu Y, Huang J (2024) An open API architecture to discover the trustworthy explanation of cloud AI services. IEEE Trans Cloud Comput 12(2):762\u201377. https:\/\/doi.org\/10.1109\/TCC.2024.3398609","journal-title":"IEEE Trans Cloud Comput"},{"key":"6875_CR44","doi-asserted-by":"crossref","unstructured":"Todd MJ (2003) Convex analysis and nonlinear optimization: Theory and examples. jonathan m. borwein and adrian s. lewis, springer, new york, 2000. Int J Robust Nonlinear Control 13:92\u201393. https:\/\/api.semanticscholar.org\/CorpusID:120161819","DOI":"10.1002\/rnc.701"},{"key":"6875_CR45","doi-asserted-by":"publisher","DOI":"10.1017\/9781108755528","volume-title":"Foundations of data science","author":"A Blum","year":"2020","unstructured":"Blum A, Hopcroft J, Kannan R (2020) Foundations of data science. Cambridge University Press"},{"key":"6875_CR46","unstructured":"Fazlyab M, Robey A, Hassani H et\u00a0al (2019) Efficient and accurate estimation of lipschitz constants for deep neural networks. In: NeurIPS, pp 11423\u201311434"},{"issue":"1","key":"6875_CR47","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/TAC.2020.3046193","volume":"67","author":"M Fazlyab","year":"2022","unstructured":"Fazlyab M, Morari M, Pappas GJ (2022) Safety verification and robustness analysis of neural networks via quadratic constraints and semidefinite programming. IEEE Trans Autom Control 67(1):1\u201315","journal-title":"IEEE Trans Autom Control"},{"issue":"11","key":"6875_CR48","doi-asserted-by":"publisher","first-page":"14233","DOI":"10.1007\/s10489-022-04207-7","volume":"53","author":"BJ Kim","year":"2023","unstructured":"Kim BJ, Choi H, Jang H et al (2023) Smooth momentum: improving lipschitzness in gradient descent. Appl Intell 53(11):14233\u201314248","journal-title":"Appl Intell"},{"key":"6875_CR49","unstructured":"Wu X, Ward RA, Bottou L (2018) Wngrad: Learn the learning rate in gradient descent. CoRR arXiv:1803.02865"},{"key":"6875_CR50","doi-asserted-by":"crossref","unstructured":"Ghadimi S, Lan G (2013) Stochastic first- and zeroth-order methods for nonconvex stochastic programming. SIAM J Optim 23:2341\u20132368. https:\/\/api.semanticscholar.org\/CorpusID:14112046","DOI":"10.1137\/120880811"},{"issue":"1","key":"6875_CR51","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1007\/S10107-022-01822-7","volume":"199","author":"Y Arjevani","year":"2023","unstructured":"Arjevani Y, Carmon Y, Duchi JC et al (2023) Lower bounds for non-convex stochastic optimization. Math Program 199(1):165\u2013214. https:\/\/doi.org\/10.1007\/S10107-022-01822-7","journal-title":"Math Program"},{"key":"6875_CR52","doi-asserted-by":"crossref","unstructured":"He K, Zhang X, Ren S et\u00a0al (2015) Deep residual learning for image recognition. 2016 IEEE Conference on computer vision and pattern recognition (CVPR) pp 770\u2013778. https:\/\/api.semanticscholar.org\/CorpusID:206594692","DOI":"10.1109\/CVPR.2016.90"},{"key":"6875_CR53","doi-asserted-by":"crossref","unstructured":"Lin T, Doll\u00e1r P, Girshick RB et\u00a0al (2017) Feature pyramid networks for object detection. In: CVPR. IEEE Computer Society, pp 936\u2013944","DOI":"10.1109\/CVPR.2017.106"},{"key":"6875_CR54","unstructured":"Balduzzi D, Frean M, Leary L et\u00a0al (2017) The shattered gradients problem: If resnets are the answer, then what is the question? In: ICML, Proceedings of machine learning research, vol\u00a070. PMLR, pp 342\u2013350"},{"key":"6875_CR55","unstructured":"Li H, Xu Z, Taylor G et\u00a0al (2018) Visualizing the loss landscape of neural nets. In: NeurIPS, pp 6391\u20136401"},{"key":"6875_CR56","doi-asserted-by":"crossref","unstructured":"Yao Z, Gholami A, Keutzer K et\u00a0al (2020) Pyhessian: Neural networks through the lens of the hessian. In: IEEE BigData. IEEE, pp 581\u2013590","DOI":"10.1109\/BigData50022.2020.9378171"},{"key":"6875_CR57","doi-asserted-by":"crossref","unstructured":"LeCun Y, Bottou L, Bengio Y et\u00a0al (1998) Gradient-based learning applied to document recognition. Proc IEEE 86:2278\u20132324. https:\/\/api.semanticscholar.org\/CorpusID:14542261","DOI":"10.1109\/5.726791"},{"key":"6875_CR58","unstructured":"Xiao H, Rasul K, Vollgraf R (2017) Fashion-mnist: a novel image dataset for benchmarking machine learning algorithms. CoRR arXiv:1708.07747http:\/\/arxiv.org\/abs\/1708.07747"},{"key":"6875_CR59","unstructured":"Krizhevsky A, Hinton G (2009) Learning multiple layers of features from tiny images. Handbook Syst Autoimmune Diseases 1(4)"},{"key":"6875_CR60","doi-asserted-by":"publisher","unstructured":"Haykin S, Kosko B (2001) GradientBased Learning Applied to Document Recognition, pp 306\u201335.https:\/\/doi.org\/10.1109\/9780470544976.ch9","DOI":"10.1109\/9780470544976.ch9"},{"key":"6875_CR61","doi-asserted-by":"publisher","unstructured":"Szegedy C, Liu W, Jia Y et\u00a0al (2015) Going deeper with convolutions. In: IEEE Conference on computer vision and pattern recognition, CVPR 2015, Boston, MA, USA, June 7-12, 2015. IEEE Computer Society, pp 1\u20139.https:\/\/doi.org\/10.1109\/CVPR.2015.7298594","DOI":"10.1109\/CVPR.2015.7298594"},{"key":"6875_CR62","doi-asserted-by":"publisher","unstructured":"He K, Zhang X, Ren S et\u00a0al (2016) Identity mappings in deep residual networks. In: Leibe B, Matas J, Sebe N et\u00a0al (eds) Computer Vision - ECCV 2016 - 14th European Conference, Amsterdam, The Netherlands, October 11-14, 2016, Proceedings, Part IV, Lecture Notes in Computer Science, vol 9908. Springer, pp 630\u201364. https:\/\/doi.org\/10.1007\/978-3-319-46493-0_38","DOI":"10.1007\/978-3-319-46493-0_38"},{"key":"6875_CR63","doi-asserted-by":"publisher","unstructured":"Huang G, Liu Z, van\u00a0der Maaten L et\u00a0al (2017) Densely connected convolutional networks. In: 2017 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2017, Honolulu, HI, USA, July 21-26, 2017. IEEE Computer Society, pp 2261\u2013226. https:\/\/doi.org\/10.1109\/CVPR.2017.243","DOI":"10.1109\/CVPR.2017.243"},{"key":"6875_CR64","unstructured":"Howard AG, Zhu M, Chen B et\u00a0al (2017) Mobilenets: Efficient convolutional neural networks for mobile vision applications. CoRR arXiv:1704.04861http:\/\/arxiv.org\/abs\/1704.04861"},{"key":"6875_CR65","doi-asserted-by":"publisher","unstructured":"Ma N, Zhang X, Zheng H et\u00a0al (2018) Shufflenet V2: practical guidelines for efficient CNN architecture design. In: Ferrari V, Hebert M, Sminchisescu C et\u00a0al (eds) Computer Vision - ECCV 2018 - 15th European Conference, Munich, Germany, September 8-14, 2018, Proceedings, Part XIV, Lecture Notes in Computer Science, vol 11218. Springer, pp 122\u2013138. https:\/\/doi.org\/10.1007\/978-3-030-01264-9_8","DOI":"10.1007\/978-3-030-01264-9_8"},{"issue":"8","key":"6875_CR66","doi-asserted-by":"publisher","first-page":"2011","DOI":"10.1109\/TPAMI.2019.2913372","volume":"42","author":"J Hu","year":"2020","unstructured":"Hu J, Shen L, Albanie S et al (2020) Squeeze-and-excitation networks. IEEE Trans Pattern Anal Mach Intell 42(8):2011\u20132023. https:\/\/doi.org\/10.1109\/TPAMI.2019.2913372","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"key":"6875_CR67","unstructured":"Dosovitskiy A, Beyer L, Kolesnikov A et\u00a0al (2021) An image is worth 16x16 words: Transformers for image recognition at scale. In: International conference on learning representations. https:\/\/openreview.net\/forum?id=YicbFdNTTy"},{"key":"6875_CR68","doi-asserted-by":"crossref","unstructured":"Zhu J, Chen X, He K et\u00a0al (2025) Transformers without normalization. In: CVPR. Computer Vision Foundation \/ IEEE, pp 14901\u201314911","DOI":"10.1109\/CVPR52734.2025.01388"},{"key":"6875_CR69","doi-asserted-by":"crossref","unstructured":"Touvron H, Cord M, Sablayrolles A et\u00a0al (2021) Going deeper with image transformers. In: ICCV. IEEE, pp 32\u201342","DOI":"10.1109\/ICCV48922.2021.00010"},{"key":"6875_CR70","unstructured":"Yoshioka K (2024) vision-transformers-cifar10: Training vision transformers (vit) and related models on cifar-10. https:\/\/github.com\/kentaroy47\/vision-transformers-cifar10"}],"container-title":["Applied Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10489-025-06875-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10489-025-06875-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10489-025-06875-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T15:42:15Z","timestamp":1762530135000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10489-025-06875-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9,22]]},"references-count":70,"journal-issue":{"issue":"15","published-print":{"date-parts":[[2025,10]]}},"alternative-id":["6875"],"URL":"https:\/\/doi.org\/10.1007\/s10489-025-06875-7","relation":{},"ISSN":["0924-669X","1573-7497"],"issn-type":[{"type":"print","value":"0924-669X"},{"type":"electronic","value":"1573-7497"}],"subject":[],"published":{"date-parts":[[2025,9,22]]},"assertion":[{"value":"29 March 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 August 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 September 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing Interests"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics Approval and Consent to participate"}}],"article-number":"976"}}