{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,26]],"date-time":"2026-06-26T14:02:53Z","timestamp":1782482573136,"version":"3.54.5"},"reference-count":45,"publisher":"Springer Science and Business Media LLC","issue":"5-6","license":[{"start":{"date-parts":[[2024,9,3]],"date-time":"2024-09-03T00:00:00Z","timestamp":1725321600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,9,3]],"date-time":"2024-09-03T00:00:00Z","timestamp":1725321600000},"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":["Evol. Intel."],"published-print":{"date-parts":[[2024,10]]},"DOI":"10.1007\/s12065-024-00973-0","type":"journal-article","created":{"date-parts":[[2024,9,3]],"date-time":"2024-09-03T11:02:06Z","timestamp":1725361326000},"page":"4083-4093","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Optimizing performance of feedforward and convolutional neural networks through dynamic activation functions"],"prefix":"10.1007","volume":"17","author":[{"given":"Chinmay","family":"Rane","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kanishka","family":"Tyagi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Adrienne","family":"Kline","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tushar","family":"Chugh","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michael","family":"Manry","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,9,3]]},"reference":[{"key":"973_CR1","doi-asserted-by":"publisher","unstructured":"Cortez P, Cerdeira A, Almeida F, Matos T, Reis J (2009) Wine quality. UCI Machine Learning Repository. https:\/\/doi.org\/10.24432\/C56S3T","DOI":"10.24432\/C56S3T"},{"key":"973_CR2","doi-asserted-by":"publisher","unstructured":"Abdelouahab K, Pelcat M, Berry F (2017) Why tanh is a hardware friendly activation function for cnns. In: Proceedings of the 11th international conference on distributed smart cameras. Association for computing machinery, ICDSC, New York , p 199-201. https:\/\/doi.org\/10.1145\/3131885.3131937,","DOI":"10.1145\/3131885.3131937"},{"key":"973_CR3","unstructured":"Agostinelli F, Hoffman M, Sadowski P et\u00a0al (2015) Learning activation functions to improve deep neural networks. http:\/\/arxiv.org\/abs\/1412.6830"},{"key":"973_CR4","doi-asserted-by":"publisher","DOI":"10.1103\/physrevlett.114.111801","author":"P Baldi","year":"2015","unstructured":"Baldi P, Sadowski P, Whiteson D (2015) Enhanced higgs boson particle search with deep learning. Phys Rev Lett. https:\/\/doi.org\/10.1103\/physrevlett.114.111801","journal-title":"Phys Rev Lett"},{"issue":"2","key":"973_CR5","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1162\/neco.1992.4.2.141","volume":"4","author":"R Battiti","year":"1992","unstructured":"Battiti R (1992) First-and second-order methods for learning: between steepest descent and Newton\u2019s method. Neural Comput 4(2):141\u2013166","journal-title":"Neural Comput"},{"key":"973_CR6","volume-title":"Pattern recognition and machine learning (Information Science and Statistics)","author":"CM Bishop","year":"2006","unstructured":"Bishop CM (2006) Pattern recognition and machine learning (Information Science and Statistics). Springer-Verlag, Berlin"},{"key":"973_CR7","doi-asserted-by":"crossref","unstructured":"Campolucci P, Capperelli F, Guarnieri S, et\u00a0al (1996) Neural networks with adaptive spline activation function. In: Proceedings of 8th mediterranean electrotechnical conference on industrial applications in power systems, computer science and telecommunications (MELECON 96), vol 3, pp 1442\u20131445","DOI":"10.1109\/MELCON.1996.551220"},{"issue":"4","key":"973_CR8","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1007\/BF02551274","volume":"2","author":"G Cybenko","year":"1989","unstructured":"Cybenko G (1989) Approximation by superpositions of a sigmoidal function. Math Control Signals Syst 2(4):303\u2013314","journal-title":"Math Control Signals Syst"},{"key":"973_CR9","unstructured":"Data files C (2002) IPNN Lab, The University of Texas Arlington. https:\/\/ipnnl.uta.edu\/training-data-files\/classification\/"},{"issue":"Jul","key":"973_CR10","first-page":"2121","volume":"12","author":"J Duchi","year":"2011","unstructured":"Duchi J, Hazan E, Singer Y (2011) Adaptive subgradient methods for online learning and stochastic optimization. J Mach Learn Res 12(Jul):2121\u20132159","journal-title":"J Mach Learn Res"},{"key":"973_CR11","unstructured":"Eapi GR (2015) Comprehensive neural network forecasting system for ground level ozone in multiple regions. https:\/\/rc.library.uta.edu\/uta-ir\/handle\/10106\/25445"},{"issue":"8","key":"973_CR12","doi-asserted-by":"publisher","first-page":"895","DOI":"10.1016\/j.amjmed.2020.03.033","volume":"133","author":"S Ellahham","year":"2020","unstructured":"Ellahham S (2020) Artificial intelligence: the future for diabetes care. Am J Med 133(8):895\u2013900","journal-title":"Am J Med"},{"key":"973_CR13","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2024.127241","volume":"574","author":"Z Fang","year":"2024","unstructured":"Fang Z, Li H, Hu L et al (2024) A learnable population filter for dynamic multi-objective optimization. Neurocomputing 574:127241","journal-title":"Neurocomputing"},{"key":"973_CR14","unstructured":"Glorot X, Bordes A, Bengio Y (2011) Deep sparse rectifier neural networks. In: international conference on artificial intelligence and statistics, https:\/\/api.semanticscholar.org\/CorpusID:2239473"},{"key":"973_CR15","unstructured":"Goodfellow I, Bengio Y, Courville A (2016) Deep learning. MIT Press, http:\/\/www.deeplearningbook.org"},{"key":"973_CR16","doi-asserted-by":"publisher","first-page":"672","DOI":"10.1109\/72.761726","volume":"10","author":"S Guarnieri","year":"1999","unstructured":"Guarnieri S, Piazza F, Uncini A (1999) Multilayer feedforward networks with adaptive spline activation function. IEEE Trans Neural Netw 10:672\u201383. https:\/\/doi.org\/10.1109\/72.761726","journal-title":"IEEE Trans Neural Netw"},{"key":"973_CR17","doi-asserted-by":"publisher","first-page":"346","DOI":"10.1016\/j.commatsci.2018.07.052","volume":"154","author":"K Hamidieh","year":"2018","unstructured":"Hamidieh K (2018) A data-driven statistical model for predicting the critical temperature of a superconductor. Comput Mater Sci 154:346\u2013354. https:\/\/doi.org\/10.1016\/j.commatsci.2018.07.052","journal-title":"Comput Mater Sci"},{"issue":"2","key":"973_CR18","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1142\/S0218488598000094","volume":"6","author":"S Hochreiter","year":"1998","unstructured":"Hochreiter S (1998) The vanishing gradient problem during learning recurrent neural nets and problem solutions. Int J Uncertain Fuzziness Knowl-Based Syst 6(2):107\u2013116. https:\/\/doi.org\/10.1142\/S0218488598000094","journal-title":"Int J Uncertain Fuzziness Knowl-Based Syst"},{"issue":"2239","key":"973_CR19","doi-asserted-by":"publisher","first-page":"20200334","DOI":"10.1098\/rspa.2020.0334","volume":"476","author":"AD Jagtap","year":"2020","unstructured":"Jagtap AD, Kawaguchi K, Em Karniadakis G (2020) Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks. Proc R Soc A Math Phys Eng Sci 476(2239):20200334. https:\/\/doi.org\/10.1098\/rspa.2020.0334","journal-title":"Proc R Soc A Math Phys Eng Sci"},{"key":"973_CR20","unstructured":"Jock A.\u00a0Blackard DDJD, Anderson DCW (2000) UCI machine learning repository. https:\/\/archive.ics.uci.edu\/ml\/datasets\/covertype"},{"key":"973_CR21","doi-asserted-by":"publisher","DOI":"10.15598\/aeee.v15i4.2389","author":"P Kamencay","year":"2017","unstructured":"Kamencay P, Benco M, Mizdos T et al (2017) A new method for face recognition using convolutional neural network. Adv Electr Electr Eng. https:\/\/doi.org\/10.15598\/aeee.v15i4.2389","journal-title":"Adv Electr Electr Eng"},{"key":"973_CR22","unstructured":"Kingma DP, Ba J (2014) Adam: a method for stochastic optimization.https:\/\/api.semanticscholar.org\/CorpusID:6628106"},{"key":"973_CR23","unstructured":"Krizhevsky A (2009) Learning multiple layers of features from tiny images. https:\/\/api.semanticscholar.org\/CorpusID:18268744"},{"issue":"2","key":"973_CR24","doi-asserted-by":"publisher","first-page":"574","DOI":"10.1148\/radiol.2017162326","volume":"284","author":"P Lakhani","year":"2017","unstructured":"Lakhani P, Sundaram B (2017) Deep learning at chest radiography: Automated classification of pulmonary tuberculosis by using convolutional neural networks. Radiology 284(2):574\u2013582","journal-title":"Radiology"},{"key":"973_CR25","first-page":"9","volume-title":"Efficient BackProp","author":"YA LeCun","year":"2012","unstructured":"LeCun YA, Bottou L, Orr GB et al (2012) Efficient BackProp. Springer, Berlin, pp 9\u201348"},{"key":"973_CR26","unstructured":"Li H, Wang Z, Lan C, et\u00a0al (2023a) A novel dynamic multiobjective optimization algorithm with hierarchical response system. IEEE transactions on computational social systems"},{"key":"973_CR27","doi-asserted-by":"crossref","unstructured":"Li H, Wang Z, Lan C, et\u00a0al (2023b) A novel dynamic multiobjective optimization algorithm with non-inductive transfer learning based on multi-strategy adaptive selection. IEEE transactions on neural networks and learning systems","DOI":"10.1109\/TNNLS.2023.3295461"},{"issue":"5","key":"973_CR28","doi-asserted-by":"publisher","first-page":"1671","DOI":"10.4208\/cicp.oa-2020-0165","volume":"28","author":"L Lu","year":"2020","unstructured":"Lu L (2020) Dying ReLU and initialization: theory and numerical examples. Commun Comput Phys 28(5):1671\u20131706. https:\/\/doi.org\/10.4208\/cicp.oa-2020-0165","journal-title":"Commun Comput Phys"},{"key":"973_CR29","unstructured":"Maas AL (2013) Rectifier nonlinearities improve neural network acoustic models. https:\/\/api.semanticscholar.org\/CorpusID:16489696"},{"key":"973_CR30","doi-asserted-by":"crossref","unstructured":"Malalur SS, Manry MT (2010) Multiple optimal learning factors for feed-forward networks. In: Defense + Commercial Sensing, https:\/\/api.semanticscholar.org\/CorpusID:122383351","DOI":"10.1117\/12.850873"},{"key":"973_CR31","doi-asserted-by":"crossref","unstructured":"Manry MT, Hsieh CH, Chandrasekaran H (1999) Near-optimal flight load synthesis using neural nets. In: Neural networks for signal processing IX: proceedings of the 1999 IEEE signal processing society workshop (Cat. No. 98TH8468), IEEE, pp 535\u2013544","DOI":"10.1109\/NNSP.1999.788173"},{"key":"973_CR32","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1109\/TPAMI.2005.4","volume":"27","author":"S Marinai","year":"2005","unstructured":"Marinai S, Gori M, Soda G (2005) Artificial neural networks for document analysis and recognition. IEEE Trans Pattern Anal Mach Intell 27:23\u201335","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"key":"973_CR33","first-page":"159","volume-title":"Deep learning solutions for skin cancer detection and diagnosis","author":"H Nahata","year":"2020","unstructured":"Nahata H, Singh SP (2020) Deep learning solutions for skin cancer detection and diagnosis. Springer International Publishing, Cham, pp 159\u2013182"},{"key":"973_CR34","unstructured":"Nicolae A (2018) PLU: the piecewise linear unit activation function.arXiv:1809.09534"},{"issue":"2","key":"973_CR35","doi-asserted-by":"publisher","first-page":"370","DOI":"10.1109\/36.134086","volume":"30","author":"Y Oh","year":"1992","unstructured":"Oh Y, Sarabandi K, Ulaby F (1992) An empirical model and an inversion technique for radar scattering from bare soil surfaces. IEEE Trans Geosci Remote Sens 30(2):370\u2013381. https:\/\/doi.org\/10.1109\/36.134086","journal-title":"IEEE Trans Geosci Remote Sens"},{"key":"973_CR36","doi-asserted-by":"crossref","unstructured":"Parisi GI (2020) Human action recognition and assessment via deep neural network self-organization. arxiv:2001.05837","DOI":"10.1007\/978-3-030-46732-6_10"},{"key":"973_CR37","unstructured":"Rane CA (2016) Multilayer perceptron with adaptive activation function. Masters Thesis https:\/\/rc.library.uta.edu\/uta-ir\/bitstream\/handle\/10106\/25934\/RANE-THESIS-2016.pdf"},{"key":"973_CR38","unstructured":"Rane C, Tyagi K, Malalur S, et\u00a0al (2023) Optimal input gain: all you need to supercharge a feed-forward neural network. arxiv:2303.17732"},{"key":"973_CR39","doi-asserted-by":"crossref","unstructured":"Shepherd AJ (1997) Second-order methods for neural networks- fast and reliable training methods for multi-layer perceptrons. In: Perspectives in neural computing","DOI":"10.1007\/978-1-4471-0953-2"},{"key":"973_CR40","unstructured":"Simonyan K, Zisserman A (2014) Very deep convolutional networks for large-scale image recognition.arxiv:1409.1556"},{"key":"973_CR41","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1016\/B978-0-12-824054-0.00004-6","volume-title":"Artificial intelligence and machine learning for EDGE computing","author":"K Tyagi","year":"2022","unstructured":"Tyagi K, Rane C, Manry M (2022) Supervised learning. Artificial intelligence and machine learning for EDGE computing. Elsevier, Amsterdam, pp 3\u201322"},{"key":"973_CR42","doi-asserted-by":"publisher","unstructured":"Tyagi K, Kwak N, Manry M (2014) Optimal conjugate gradient algorithm for generalization of linear discriminant analysis based on L1 norm. In: Proceedings of the 3rd International Conference on Pattern Recognition Applications and Methods - ICPRAM. SciTePress,  pp 207\u2013212. https:\/\/doi.org\/10.5220\/0004825402070212","DOI":"10.5220\/0004825402070212"},{"key":"973_CR43","doi-asserted-by":"publisher","DOI":"10.1016\/0893-6080(91)90048-A","author":"Hc Yau","year":"2000","unstructured":"Yau Hc, Manry M (2000) Iterative improvement of a nearest neighbor classifier. Neural Netw. https:\/\/doi.org\/10.1016\/0893-6080(91)90048-A","journal-title":"Neural Netw"},{"issue":"12","key":"973_CR44","doi-asserted-by":"publisher","first-page":"1797","DOI":"10.1016\/S0008-8846(98)00165-3","volume":"28","author":"IC Yeh","year":"1998","unstructured":"Yeh IC (1998) Modeling of strength of high-performance concrete using artificial neural networks. Cem Concr Res 28(12):1797\u20131808","journal-title":"Cem Concr Res"},{"key":"973_CR45","unstructured":"Zeiler MD, Fergus R (2013) Visualizing and understanding convolutional networks. arxiv:1311.2901"}],"container-title":["Evolutionary Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12065-024-00973-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12065-024-00973-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12065-024-00973-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,19]],"date-time":"2024-10-19T06:22:01Z","timestamp":1729318921000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12065-024-00973-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,3]]},"references-count":45,"journal-issue":{"issue":"5-6","published-print":{"date-parts":[[2024,10]]}},"alternative-id":["973"],"URL":"https:\/\/doi.org\/10.1007\/s12065-024-00973-0","relation":{},"ISSN":["1864-5909","1864-5917"],"issn-type":[{"value":"1864-5909","type":"print"},{"value":"1864-5917","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,9,3]]},"assertion":[{"value":"17 December 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 July 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 August 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 September 2024","order":4,"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 no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}