{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,3]],"date-time":"2026-10-03T02:41:37Z","timestamp":1790995297583,"version":"4.1.0"},"publisher-location":"Cham","reference-count":27,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783032045577","type":"print"},{"value":"9783032045584","type":"electronic"}],"license":[{"start":{"date-parts":[[2025,9,12]],"date-time":"2025-09-12T00:00:00Z","timestamp":1757635200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,9,12]],"date-time":"2025-09-12T00:00:00Z","timestamp":1757635200000},"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":[],"published-print":{"date-parts":[[2026]]},"DOI":"10.1007\/978-3-032-04558-4_43","type":"book-chapter","created":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T11:17:22Z","timestamp":1757589442000},"page":"533-544","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Perpetual Generation: Online Learning of\u00a0Linear State-Space Models from\u00a0a\u00a0Single Stream"],"prefix":"10.1007","author":[{"given":"Michele","family":"Casoni","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tommaso","family":"Guidi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Stefano","family":"Melacci","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alessandro","family":"Betti","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marco","family":"Gori","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,9,12]]},"reference":[{"key":"43_CR1","unstructured":"Arjovsky, M., Shah, A., Bengio, Y.: Unitary evolution recurrent neural networks. In: International Conference on Machine Learning, pp. 1120\u20131128. PMLR (2016)"},{"key":"43_CR2","unstructured":"Bengio, Y., Frasconi, P.: Credit assignment through time: alternatives to backpropagation. In: Advances in Neural Information Processing Systems, vol. 6 (1993)"},{"issue":"2","key":"43_CR3","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1109\/72.279181","volume":"5","author":"Y Bengio","year":"1994","unstructured":"Bengio, Y., Simard, P., Frasconi, P.: Learning long-term dependencies with gradient descent is difficult. IEEE Trans. Neural Netw. 5(2), 157\u2013166 (1994)","journal-title":"IEEE Trans. Neural Netw."},{"key":"43_CR4","unstructured":"Bhatia, R.: Matrix analysis. In: Graduate Texts in Mathematics. Springer, New York (2013)"},{"key":"43_CR5","doi-asserted-by":"publisher","unstructured":"Casoni, M., Guidi, T., Tiezzi, M., Betti, A., Gori, M., Melacci, S.: Pitfalls in processing infinite-length sequences with popular approaches for sequential data. In: Suen, C.Y., Krzyzak, A., Ravanelli, M., Trentin, E., Subakan, C., Nobile, N. (eds.) ANNPR 2024. LNCS, vol. 15154, pp. 37\u201348, Springer, Cham (2024). https:\/\/doi.org\/10.1007\/978-3-031-71602-7_4","DOI":"10.1007\/978-3-031-71602-7_4"},{"key":"43_CR6","unstructured":"Chang, B., Chen, M., Haber, E., Chi, E.H.: AntisymmetricRNN: a dynamical system view on recurrent neural networks. In: International Conference on Learning Representations (2018)"},{"key":"43_CR7","unstructured":"Coddington, A., Levinson, N.: Theory of ordinary differential equations. In: International Series in Pure and Applied Mathematics. McGraw-Hill (1955)"},{"key":"43_CR8","doi-asserted-by":"crossref","unstructured":"Conway, J.B.: Functions of One Complex Variable I, 2nd edn. Springer, New York (1978)","DOI":"10.1007\/978-1-4612-6313-5"},{"key":"43_CR9","unstructured":"De, S., et\u00a0al.: Griffin: mixing gated linear recurrences with local attention for efficient language models. arXiv preprint arXiv:2402.19427 (2024)"},{"key":"43_CR10","unstructured":"Dubey, A., et\u00a0al.: The Llama 3 herd of models. arXiv preprint arXiv:2407.21783 (2024)"},{"key":"43_CR11","unstructured":"Elaydi, S.: An Introduction to Difference Equations. Undergraduate Texts in Mathematics. Springer, New York (2005)"},{"key":"43_CR12","unstructured":"Evans, L.C.: Partial Differential Equations. Graduate Studies in Mathematics. American Mathematical Society (1998)"},{"key":"43_CR13","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2024.127411","volume":"579","author":"C Gallicchio","year":"2024","unstructured":"Gallicchio, C.: Euler state networks: non-dissipative reservoir computing. Neurocomputing 579, 127411 (2024)","journal-title":"Neurocomputing"},{"key":"43_CR14","unstructured":"Gori, M., Melacci, S.: Collectionless artificial intelligence (2023)"},{"key":"43_CR15","unstructured":"Gu, A., Goel, K., Re, C.: Efficiently modeling long sequences with structured state spaces. In: International Conference on Learning Representations (2021)"},{"issue":"1","key":"43_CR16","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/aa9a90","volume":"34","author":"E Haber","year":"2017","unstructured":"Haber, E., Ruthotto, L.: Stable architectures for deep neural networks. Inverse Prob. 34(1), 014004 (2017)","journal-title":"Inverse Prob."},{"key":"43_CR17","doi-asserted-by":"crossref","unstructured":"Hespanha, J.P.: Linear Systems Theory: Second Edition. Princeton University Press (2018)","DOI":"10.23943\/9781400890088"},{"key":"43_CR18","doi-asserted-by":"crossref","unstructured":"Horn, R.A., Johnson, C.R.: Matrix Analysis. Cambridge University Press (2012)","DOI":"10.1017\/CBO9781139020411"},{"key":"43_CR19","unstructured":"Hurst, A., et\u00a0al.: GPT-4O system card. arXiv preprint arXiv:2410.21276 (2024)"},{"key":"43_CR20","unstructured":"Lax, P.D.: Linear Algebra and Its Applications. Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts. Wiley (2007)"},{"key":"43_CR21","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1016\/j.cosrev.2009.03.005","volume":"3","author":"M Luko\u0161evi\u010dius","year":"2009","unstructured":"Luko\u0161evi\u010dius, M., Jaeger, H.: Reservoir computing approaches to recurrent neural network training. Comput. Sci. Rev. 3, 127\u2013149 (2009)","journal-title":"Comput. Sci. Rev."},{"key":"43_CR22","unstructured":"Orvieto, A., De, S., Gulcehre, C., Pascanu, R., Smith, S.L.: Universality of linear recurrences followed by non-linear projections: finite-width guarantees and benefits of complex eigenvalues. In: ICML (2024)"},{"key":"43_CR23","unstructured":"Orvieto, A., et al.: Resurrecting recurrent neural networks for long sequences. In: International Conference on Machine Learning, pp. 26670\u201326698. PMLR (2023)"},{"key":"43_CR24","unstructured":"Smith, J.T.H., Warrington, A., Linderman, S.W.: Simplified state space layers for sequence modeling. arXiv preprint arXiv:2208.04933 (2022)"},{"key":"43_CR25","unstructured":"Team, G., et\u00a0al.: Gemini 1.5: unlocking multimodal understanding across millions of tokens of context. arXiv preprint arXiv:2403.05530 (2024)"},{"key":"43_CR26","unstructured":"Thompson, R., Walter, W.: Ordinary Differential Equations. Graduate Texts in Mathematics. Springer, New York (2013)"},{"key":"43_CR27","unstructured":"Tiezzi, M., Casoni, M., Betti, A., Gori, M., Melacci, S.: State-space modeling in long sequence processing: a survey on recurrence in the transformer era. arXiv preprint arXiv:2406.09062 (2024)"}],"container-title":["Lecture Notes in Computer Science","Artificial Neural Networks and Machine Learning \u2013 ICANN 2025"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-032-04558-4_43","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,7]],"date-time":"2026-08-07T14:25:17Z","timestamp":1786112717000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-04558-4_43"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9,12]]},"ISBN":["9783032045577","9783032045584"],"references-count":27,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-04558-4_43","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,9,12]]},"assertion":[{"value":"12 September 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"The authors have no competing interests to declare that are relevant to the content of this article.","order":1,"name":"Ethics","label":"Disclosure of Interests","group":{"name":"EthicsHeading","label":"Ethics"}},{"value":"ICANN","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Artificial Neural Networks","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Kaunas","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Lithuania","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2025","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"9 September 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"12 September 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"34","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"icann2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/e-nns.org\/icann2025\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}