{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,11,5]],"date-time":"2026-11-05T00:37:49Z","timestamp":1793839069227,"version":"4.6.1"},"reference-count":36,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"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":["Neural Networks"],"published-print":{"date-parts":[[2027,1]]},"DOI":"10.1016\/j.neunet.2026.109563","type":"journal-article","created":{"date-parts":[[2026,8,31]],"date-time":"2026-08-31T15:32:33Z","timestamp":1788190353000},"page":"109563","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":1,"special_numbering":"PC","title":["Orbit-based universal approximation via hypercyclicity on compact\u2013open topology"],"prefix":"10.1016","volume":"205","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7627-5308","authenticated-orcid":false,"given":"Farzona","family":"Mukhamedova","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7359-7966","authenticated-orcid":false,"given":"Ivan","family":"Tyukin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Farrukh","family":"Mukhamedov","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"issue":"1","key":"10.1016\/j.neunet.2026.109563_bib0001","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.jtbi.2011.04.022","article-title":"Quantum-like model of brain\u2019s functioning: Decision making from decoherence","volume":"281","author":"Asano","year":"2011","journal-title":"Journal of Theoretical Biology"},{"key":"10.1016\/j.neunet.2026.109563_bib0002","first-page":"930","article-title":"Universal approximation bounds for superposition of a sigmoidal function","volume":"19","author":"Barron","year":"1991","journal-title":"IEEE Transaction on Information Theory"},{"issue":"3","key":"10.1016\/j.neunet.2026.109563_bib0003","doi-asserted-by":"crossref","first-page":"930","DOI":"10.1109\/18.256500","article-title":"Universal approximation bounds for superpositions of a sigmoidal function","volume":"39","author":"Barron","year":"2002","journal-title":"IEEE Transactions on Information Theory"},{"key":"10.1016\/j.neunet.2026.109563_bib0004","series-title":"Number 179 in cambridge tracts in mathematics","article-title":"Dynamics of linear operators","author":"Bayart","year":"2009"},{"issue":"4","key":"10.1016\/j.neunet.2026.109563_bib0005","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1007\/BF02551274","article-title":"Approximation by superpositions of a sigmoidal function","volume":"2","author":"Cybenko","year":"1989","journal-title":"Mathematics of Control, Signals and Systems"},{"key":"10.1016\/j.neunet.2026.109563_bib0006","series-title":"Conference on learning theory","first-page":"907","article-title":"The power of depth for feedforward neural networks","author":"Eldan","year":"2016"},{"issue":"6","key":"10.1016\/j.neunet.2026.109563_bib0007","doi-asserted-by":"crossref","first-page":"801","DOI":"10.1016\/S0893-6080(05)80125-X","article-title":"Approximation of dynamical systems by continuous time recurrent neural networks","volume":"6","author":"Funahashi","year":"1993","journal-title":"Neural Networks"},{"key":"10.1016\/j.neunet.2026.109563_bib0008","doi-asserted-by":"crossref","first-page":"296","DOI":"10.1016\/j.neunet.2017.12.007","article-title":"On the approximation by single hidden layer feedforward neural networks with fixed weights","volume":"98","author":"Guliyev","year":"2018","journal-title":"Neural Networks"},{"key":"10.1016\/j.neunet.2026.109563_bib0009","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/j.ins.2015.09.021","article-title":"Approximation with random bases: Pro-et contra","volume":"364","author":"Gorban","year":"2016","journal-title":"Information Sciences"},{"key":"10.1016\/j.neunet.2026.109563_bib0010","series-title":"Linear chaos","author":"Grosse-Erdmann","year":"2011"},{"key":"10.1016\/j.neunet.2026.109563_bib0011","series-title":"International conference on machine learning","first-page":"2596","article-title":"Complexity of linear regions in deep networks","author":"Hanin","year":"2019"},{"key":"10.1016\/j.neunet.2026.109563_bib0012","unstructured":"Hanin, B., & Sellke, M. (2017). Approximating continuous functions by relu nets of minimal width. arxiv: 1710.11278."},{"issue":"2","key":"10.1016\/j.neunet.2026.109563_bib0013","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1016\/0893-6080(91)90009-T","article-title":"Approximation capabilities of multilayer feedforward networks","volume":"4","author":"Hornik","year":"1991","journal-title":"Neural Networks"},{"issue":"5","key":"10.1016\/j.neunet.2026.109563_bib0014","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1016\/0893-6080(89)90020-8","article-title":"Multilayer feedforward networks are universal approximators","volume":"2","author":"Hornik","year":"1989","journal-title":"Neural Networks"},{"issue":"1","key":"10.1016\/j.neunet.2026.109563_bib0015","doi-asserted-by":"crossref","DOI":"10.1038\/s41598-018-34531-3","article-title":"Quantum probability in decision making from quantum information representation of neuronal states","volume":"8","author":"Khrennikov","year":"2018","journal-title":"Scientific Reports"},{"key":"10.1016\/j.neunet.2026.109563_bib0016","doi-asserted-by":"crossref","DOI":"10.1016\/j.jmp.2025.102923","article-title":"Coupling quantum-like cognition with the neuronal networks within generalized probability theory","volume":"125","author":"Khrennikov","year":"2025","journal-title":"Journal of Mathematical Psychology"},{"issue":"5","key":"10.1016\/j.neunet.2026.109563_bib0017","first-page":"953","article-title":"On the representation of continuous functions of many variables by superposition of continuous functions of one variable and addition","volume":"114","author":"Kolmogorov","year":"1957","journal-title":"Doklady Akademii Nauk SSSR"},{"issue":"6","key":"10.1016\/j.neunet.2026.109563_bib0018","doi-asserted-by":"crossref","first-page":"861","DOI":"10.1016\/S0893-6080(05)80131-5","article-title":"Multilayer feedforward networks with a nonpolynomial activation function can approximate any function","volume":"6","author":"Leshno","year":"1993","journal-title":"Neural Networks"},{"key":"10.1016\/j.neunet.2026.109563_bib0019","unstructured":"Liang, S., & Srikant, R. (2016). Why deep neural networks for function approximation?arxiv: 1610.04161."},{"issue":"6","key":"10.1016\/j.neunet.2026.109563_bib0020","doi-asserted-by":"crossref","first-page":"1223","DOI":"10.1007\/s10955-017-1836-5","article-title":"Why does deep and cheap learning work so well","volume":"168","author":"Lin","year":"2017","journal-title":"Journal of Statistical Physics"},{"key":"10.1016\/j.neunet.2026.109563_bib0021","series-title":"International symposium on neural networks","first-page":"1110","article-title":"Uniform approximation capabilities of sum-of-product and sigma-pi-sigma neural networks","author":"Long","year":"2007"},{"key":"10.1016\/j.neunet.2026.109563_bib0022","article-title":"The expressive power of neural networks: A view from the width","volume":"30","author":"Lu","year":"2017","journal-title":"Advances in Neural Information Processing Systems"},{"issue":"1\u20133","key":"10.1016\/j.neunet.2026.109563_bib0023","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/S0925-2312(98)00111-8","article-title":"Lower bounds for approximation by mlp neural networks","volume":"25","author":"Maiorov","year":"1999","journal-title":"Neurocomputing"},{"key":"10.1016\/j.neunet.2026.109563_bib0024","doi-asserted-by":"crossref","first-page":"921","DOI":"10.1090\/S0002-9939-1961-0133108-4","article-title":"On a theorem of rudin and klee","volume":"12","author":"Michael","year":"1961","journal-title":"Proceedings of the AMS"},{"key":"10.1016\/j.neunet.2026.109563_bib0025","article-title":"On the number of linear regions of deep neural networks","volume":"27","author":"Mont\u00fafar","year":"2014","journal-title":"Advances in Neural Information Processing Systems"},{"issue":"1","key":"10.1016\/j.neunet.2026.109563_bib0026","first-page":"85","article-title":"Hypercyclic and supercyclic linear operators on non- archimedean vector spaces","volume":"25","author":"Mukhamedov","year":"2018","journal-title":"The Bulletin of the Belgian Mathematical Society"},{"issue":"22","key":"10.1016\/j.neunet.2026.109563_bib0027","first-page":"63","article-title":"A few remarks on supercyclicity of non- archimedean linear operators on c0(N)","volume":"14","author":"Mukhamedov","year":"2022","journal-title":"p-adic Numb Ultra. Analysis and Applications"},{"key":"10.1016\/j.neunet.2026.109563_bib0028","doi-asserted-by":"crossref","first-page":"296","DOI":"10.1016\/j.neunet.2018.08.019","article-title":"Optimal approximation of piecewise smooth functions using deep relu neural networks","volume":"108","author":"Petersen","year":"2018","journal-title":"Neural Networks"},{"key":"10.1016\/j.neunet.2026.109563_bib0029","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1017\/S0962492900002919","article-title":"Approximation theory of the mlp model in neural networks","volume":"8","author":"Pinkus","year":"1999","journal-title":"Acta Numerica"},{"key":"10.1016\/j.neunet.2026.109563_bib0030","series-title":"In international conference on machine learning","first-page":"2847","article-title":"On the expressive power of deep neural networks","author":"Raghu","year":"2017"},{"issue":"5","key":"10.1016\/j.neunet.2026.109563_bib0031","doi-asserted-by":"crossref","first-page":"237","DOI":"10.2307\/3029337","article-title":"The generalized weierstrass approximation theorem","volume":"21","author":"Stone","year":"1948","journal-title":"Mathematics Magazine"},{"key":"10.1016\/j.neunet.2026.109563_bib0032","series-title":"Conference on learning theory","first-page":"1517","article-title":"Benefits of depth in neural networks","author":"Telgarsky","year":"2016"},{"key":"10.1016\/j.neunet.2026.109563_bib0033","article-title":"Noncompact uniform universal approximation","volume":"173","author":"Teun","year":"2024","journal-title":"Neural Networks"},{"key":"10.1016\/j.neunet.2026.109563_bib0034","unstructured":"Tyukin, I. Y., Grechuk, B., Evgeny, E. M., & Gorban, A. N. (2025). When fractional quasi p-norms concentrate. arxiv: 2505.19635."},{"key":"10.1016\/j.neunet.2026.109563_bib0035","series-title":"Uber die analytische darstellbarkeit sogenannter willkurlicher funktionen reeller argumente","author":"Weierstrab","year":"1885"},{"key":"10.1016\/j.neunet.2026.109563_bib0036","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/j.neunet.2017.07.002","article-title":"Error bounds for approximations with deep relu networks","volume":"94","author":"Yarotsky","year":"2017","journal-title":"Neural Networks"}],"container-title":["Neural Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0893608026010208?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0893608026010208?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,10,20]],"date-time":"2026-10-20T17:39:02Z","timestamp":1792517942000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0893608026010208"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2027,1]]},"references-count":36,"alternative-id":["S0893608026010208"],"URL":"https:\/\/doi.org\/10.1016\/j.neunet.2026.109563","relation":{},"ISSN":["0893-6080"],"issn-type":[{"value":"0893-6080","type":"print"}],"subject":[],"published":{"date-parts":[[2027,1]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Orbit-based universal approximation via hypercyclicity on compact\u2013open topology","name":"articletitle","label":"Article Title"},{"value":"Neural Networks","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.neunet.2026.109563","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"109563"}}