{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,26]],"date-time":"2025-09-26T05:01:13Z","timestamp":1758862873700,"version":"3.37.3"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"24","license":[{"start":{"date-parts":[[2021,7,25]],"date-time":"2021-07-25T00:00:00Z","timestamp":1627171200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,7,25]],"date-time":"2021-07-25T00:00:00Z","timestamp":1627171200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100004271","name":"Sapienza Universit\u00e0 di Roma","doi-asserted-by":"publisher","award":["AR120172B7152382"],"award-info":[{"award-number":["AR120172B7152382"]}],"id":[{"id":"10.13039\/501100004271","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Universit\u00e0 degli Studi di Roma La Sapienza"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Neural Comput &amp; Applic"],"published-print":{"date-parts":[[2021,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The software implementations of neuronal systems have shown great effectiveness, even if the natural hardware separation between the processing and memory areas in computers slows down the analysis capacity. To overcome these limitations, new hardware configurations are moving towards neuromorphic models, capable of unifying the processing\/memory dichotomy. Recently, integrated photonic X-junctions formed by waveguides written by spatial solitons have shown the ability to perform supervised learning. The solitonic technology, compared to the traditional one, offers the advantage of realizing plastic circuitry, a typical characteristic of biological neural networks. This work extensively studies both supervised and unsupervised learning of photonic soliton X-junctions. By exploiting the plasticity of the nonlinear refractive index at the base of the soliton formation, X-junctions can readdress their behaviours forwarding data to different outputs. In this article, we will extend the state-of-the-art: starting from supervised learning, for which all possible cases are now investigated, a material sensitive to the transported signals will be introduced to allow the junction to carry out unsupervised learning. In this way, the junction autonomously recognises the transported signals without the external intervention of the operator. Learning and memory now physically coincide in fact, learning means that the junction slowly switches based on the information sent; any further unknown information sent will find the junction in the modified state which corresponds to the learned information and will be recognised as well (reasoning based on comparison with stored information).<\/jats:p>","DOI":"10.1007\/s00521-021-06299-7","type":"journal-article","created":{"date-parts":[[2021,7,25]],"date-time":"2021-07-25T15:02:49Z","timestamp":1627225369000},"page":"17071-17079","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Supervised and unsupervised learning using a fully-plastic all-optical unit of artificial intelligence based on solitonic waveguides"],"prefix":"10.1007","volume":"33","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4112-2544","authenticated-orcid":false,"given":"Alessandro","family":"Bile","sequence":"first","affiliation":[]},{"given":"Francesca","family":"Moratti","sequence":"additional","affiliation":[]},{"given":"Hamed","family":"Tari","sequence":"additional","affiliation":[]},{"given":"Eugenio","family":"Fazio","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,7,25]]},"reference":[{"key":"6299_CR1","doi-asserted-by":"publisher","first-page":"063002","DOI":"10.1088\/2040-8978\/18\/6\/063002","volume":"18","author":"E Agrell","year":"2016","unstructured":"Agrell E, Karlsson M, Chraplyvy AR, Richardson DJ, Krummrich PM, Winzer P, Roberts K, Fischer JK, Savory SJ, Eggleton BJ, Secondini M, Kschischang FR, Lord A, Prat J, Tomkos I, Bowers JE, Srinivasan S, Brandt-Pearce M, Gisin N (2016) Roadmap of optical communications. J Opt 18:063002","journal-title":"J Opt"},{"key":"6299_CR2","doi-asserted-by":"publisher","first-page":"88","DOI":"10.1038\/scientificamerican0387-88","volume":"256","author":"Y Abu-Mostafa","year":"1987","unstructured":"Abu-Mostafa Y, Psaltis D (1987) Optical neural computers. Sci Amer 256:88\u201395","journal-title":"Sci Amer"},{"doi-asserted-by":"crossref","unstructured":"Stoll HM and Lee LS (1988) A continuous-time optical neural network. In proc IEEE int conf neural netw. 373\u2013384","key":"6299_CR3","DOI":"10.1109\/ICNN.1988.23950"},{"key":"6299_CR4","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1016\/0030-3992(95)00070-4","volume":"28","author":"S Jutamulia","year":"1996","unstructured":"Jutamulia S, Yu F (1996) Overview of hybrid optical neural networks. Opt Laser Technol 28:59\u201372","journal-title":"Opt Laser Technol"},{"key":"6299_CR5","doi-asserted-by":"publisher","DOI":"10.1021\/acsphotonics.9b01673","author":"H Zhou","year":"2019","unstructured":"Zhou H, Zhao Y, Wang X, Gao D, Dong J, Zhang X (2019) Self-learning photonic signal processor with an optical neural network chip. arXiv Prepr arXiv:190207318. https:\/\/doi.org\/10.1021\/acsphotonics.9b01673","journal-title":"arXiv Prepr arXiv:1902.07318"},{"key":"6299_CR6","doi-asserted-by":"publisher","first-page":"208","DOI":"10.1038\/s41586-019-1157-8","volume":"569","author":"J Feldmann","year":"2019","unstructured":"Feldmann J, Youngblood N, Wright CD, Bhaskaran H, Pernice WHP (2019) All-optical spiking neurosynaptic networks with self-learning capabilities. Nature 569:208\u2013215","journal-title":"Nature"},{"key":"6299_CR7","doi-asserted-by":"publisher","first-page":"175827","DOI":"10.1109\/ACCESS.2019.2957245","volume":"7","author":"L De Marinis","year":"2019","unstructured":"De Marinis L, Cococcioni M, Castoldi P, Andriolli N (2019) Photonic neural networks: a survey. IEEE Access 7:175827\u2013175841","journal-title":"IEEE Access"},{"key":"6299_CR8","doi-asserted-by":"publisher","first-page":"3193","DOI":"10.1364\/JOSAB.31.003193","volume":"31","author":"SM Hendrickson","year":"2014","unstructured":"Hendrickson SM, Foster AC, Camacho RM, Clader BD (2014) Integrated nonlinear photonics: emerging applications and ongoing challenges\u2013a mini review. J Opt Soc Amer B Opt Phys 31:3193\u20133203","journal-title":"J Opt Soc Amer B Opt Phys"},{"key":"6299_CR9","doi-asserted-by":"publisher","first-page":"180","DOI":"10.1364\/OPTICA.5.000180","volume":"5","author":"L Yang","year":"2018","unstructured":"Yang L et al (2018) General architectures for on-chip optical space and mode switching. Optica 5:180\u2013187","journal-title":"Optica"},{"key":"6299_CR10","doi-asserted-by":"publisher","first-page":"1549","DOI":"10.1364\/OPTICA.5.001549","volume":"5","author":"L Yang","year":"2018","unstructured":"Yang L, Zhou T, Jia H, Yang S, Ding J, Xin F, Zhang L (2018) Universal multimode waveguide crossing based on transformation optics. Optica 5:1549\u20131556","journal-title":"Optica"},{"key":"6299_CR11","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1117\/12.943464","volume":"862","author":"A Barthelemy","year":"1988","unstructured":"Barthelemy A, Reynaud F, Colombeau B (1988) Single mode soliton beam waveguides, proc SPIE 0862. Opt Interconnect 862:27\u201331","journal-title":"Opt Interconnect"},{"key":"6299_CR12","doi-asserted-by":"publisher","first-page":"3211","DOI":"10.1103\/PhysRevLett.73.3211","volume":"73","author":"M Segev","year":"1994","unstructured":"Segev M, Valley GC, Crosignani B, DiPorto P, Yariv A (1994) Steady-state spatial screening solitons in photorefractive materials with external applied field. Phys Rev Lett 73:3211\u20133214","journal-title":"Phys Rev Lett"},{"key":"6299_CR13","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1016\/j.apsusc.2005.03.009","volume":"248","author":"E Fazio","year":"2005","unstructured":"Fazio E, Ramadan W, Petris A, Chauvet M, Bosco A, Vlad VI, Bertolotti M (2005) Writing single-mode waveguides in lithium niobate by ultralow intensity solitons. Appl Surf Sci 248:97\u2013102","journal-title":"Appl Surf Sci"},{"key":"6299_CR14","doi-asserted-by":"publisher","first-page":"1547","DOI":"10.1364\/OE.26.001547","volume":"26","author":"C Wang","year":"2018","unstructured":"Wang C, Zhang M, Stern B, Lipson M, Lon\u010dar M (2018) Nanophotonic lithium niobate electro-optic modulators. Opt Expr 26:1547\u20131555","journal-title":"Opt Expr"},{"issue":"26283","key":"6299_CR15","first-page":"1","volume":"6","author":"W Hu","year":"2016","unstructured":"Hu W, Wu K, Shum PP, Zheludev NI, Soci C (2016) All-optical implementation of the ant colony optimization algorithm. Sci Rep 6(26283):1\u20137","journal-title":"Sci Rep"},{"issue":"5716","key":"6299_CR16","first-page":"1","volume":"8","author":"M Alonzo","year":"2018","unstructured":"Alonzo M, Moscatelli D, Bastiani L, Belardini A, Soci C, Fazio E (2018) All-optical reinforcement learning in solitonic X-junction. Sci Rep 8(5716):1\u20137","journal-title":"Sci Rep"},{"key":"6299_CR17","doi-asserted-by":"publisher","first-page":"2193","DOI":"10.1063\/1.1794854","volume":"85","author":"E Fazio","year":"2004","unstructured":"Fazio E, Renzi F, Rinaldi R, Bertolotti M, Chauvet M, Ramadan W, Petris A, Vlad VI (2004) Screening-photovoltaic bright solitons in lithium niobate and associated single-mode waveguides. Appl Phys Lett 85:2193\u20132195","journal-title":"Appl Phys Lett"},{"key":"6299_CR18","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1364\/JOSAB.27.000001","volume":"27","author":"F Pettazzi","year":"2010","unstructured":"Pettazzi F, Coda V, Fanjoux G, Chauvet M, Fazio E (2010) Dynamic of second harmonic generation in photovoltaic photorefractive quadratic medium. J Opt Soc Am B 27:1\u20139","journal-title":"J Opt Soc Am B"},{"key":"6299_CR19","doi-asserted-by":"publisher","first-page":"7972","DOI":"10.1364\/OE.18.007972","volume":"18","author":"E Fazio","year":"2010","unstructured":"Fazio E, Belardini A, Alonzo M, Centini M, Chauvet M, Devaux F, Scalora M (2010) Observation of photorefractive simultons in lithium niobate. Opt Expr 18:7972\u20137981","journal-title":"Opt Expr"},{"key":"6299_CR20","doi-asserted-by":"publisher","first-page":"1397","DOI":"10.1109\/JQE.2012.2212000","volume":"48","author":"R Passier","year":"2012","unstructured":"Passier R, Alonzo M, Azio E (2012) Numerical analysis of waveguiding in luminescence-induced spatial soliton channels. IEEE J Quant Electr 48:1397\u20131402","journal-title":"IEEE J Quant Electr"},{"issue":"125501","key":"6299_CR21","first-page":"1","volume":"15","author":"T Fiumara","year":"2013","unstructured":"Fiumara T, Fazio E (2013) Design of a refractive index sensor based on surface soliton waveguides. J Opt 15(125501):1\u20136","journal-title":"J Opt"},{"key":"6299_CR22","doi-asserted-by":"publisher","first-page":"091107","DOI":"10.1063\/1.3313950","volume":"96","author":"E Fazio","year":"2010","unstructured":"Fazio E, Alonzo M, Devaux F, Toncelli A, Bazzan M, Sada C, Chauvet M (2010) Luminescence-induced photorefractive spatial solitons. Appl Phys Lett 96:091107","journal-title":"Appl Phys Lett"},{"issue":"9","key":"6299_CR23","doi-asserted-by":"publisher","first-page":"1132","DOI":"10.1364\/OPTICA.6.001132","volume":"6","author":"Y Zuo","year":"2019","unstructured":"Zuo Y, Li B, Devaux F, Zhao Y, Jiang Y, Chen Y, Chen P, Jo G, Liu J, Du S (2019) All-optical neural network with nonlinear activation function. Optica 6(9):1132","journal-title":"Optica"},{"issue":"10","key":"6299_CR24","first-page":"6098","volume":"96","author":"J Robertson","year":"2010","unstructured":"Robertson J, Hejda M, Bueno J, Hurtado A (2010) Ultrafast optical integration and pattern classification for neuromorphic photonics based on spiking VCSEL neurons. Scientific Rep 96(10):6098","journal-title":"Scientific Rep"},{"unstructured":"Kandel ER (2017) Alla ricerca della memoria. Codice Edizioni. ISBN 978\u201388\u20137578\u2013675\u20135","key":"6299_CR25"},{"key":"6299_CR26","doi-asserted-by":"publisher","DOI":"10.1063\/5.0040674","author":"A Bile","year":"2021","unstructured":"Bile A, Pepino R, Fazio E (2021) Study of magnetic switch for surface plasmon polariton circuits. AIP Adv. https:\/\/doi.org\/10.1063\/5.0040674","journal-title":"AIP Adv"}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-021-06299-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00521-021-06299-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-021-06299-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,11,5]],"date-time":"2021-11-05T16:16:38Z","timestamp":1636128998000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00521-021-06299-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,7,25]]},"references-count":26,"journal-issue":{"issue":"24","published-print":{"date-parts":[[2021,12]]}},"alternative-id":["6299"],"URL":"https:\/\/doi.org\/10.1007\/s00521-021-06299-7","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"type":"print","value":"0941-0643"},{"type":"electronic","value":"1433-3058"}],"subject":[],"published":{"date-parts":[[2021,7,25]]},"assertion":[{"value":"9 January 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 July 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 July 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declaration"}},{"value":"The authors declare that they have not conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}