{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T23:11:56Z","timestamp":1775689916136,"version":"3.50.1"},"publisher-location":"Cham","reference-count":40,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783032169549","type":"print"},{"value":"9783032169556","type":"electronic"}],"license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"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\/978-3-032-16955-6_8","type":"book-chapter","created":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T22:20:56Z","timestamp":1775686856000},"page":"137-150","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Deep Active Inference with\u00a0Neural Stochastic Differential Equations"],"prefix":"10.1007","author":[{"given":"Marc","family":"Pritsch","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Georgia","family":"Koppe","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,4,1]]},"reference":[{"key":"8_CR1","first-page":"47","volume":"4","author":"RA Adams","year":"2013","unstructured":"Adams, R.A., Stephan, K.E., Brown, H.R., Frith, C.D., Friston, K.J.: The computational anatomy of psychosis. Front. Psych. 4, 47 (2013)","journal-title":"Front. Psych."},{"key":"8_CR2","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1016\/j.jmp.2017.09.004","volume":"81","author":"CL Buckley","year":"2017","unstructured":"Buckley, C.L., Kim, C.S., McGregor, S., Seth, A.K.: The free energy principle for action and perception: a mathematical review. J. Math. Psychol. 81, 55\u201379 (2017)","journal-title":"J. Math. Psychol."},{"key":"8_CR3","doi-asserted-by":"publisher","DOI":"10.3389\/fncom.2020.574372","volume":"14","author":"O \u00c7atal","year":"2020","unstructured":"\u00c7atal, O., Wauthier, S., De Boom, C., Verbelen, T., Dhoedt, B.: Learning generative state space models for active inference. Front. Comput. Neurosci. 14, 574372 (2020)","journal-title":"Front. Comput. Neurosci."},{"key":"8_CR4","unstructured":"\u00c7atal, O., Wauthier, S., Verbelen, T., De\u00a0Boom, C., Dhoedt, B.: Deep active inference for autonomous robot navigation. In: Workshop on Bridging AI and Cognitive Science, International Conference on Learning Representations (ICLR) (2020)"},{"key":"8_CR5","unstructured":"Chen, R.T., Rubanova, Y., Bettencourt, J., Duvenaud, D.K.: Neural ordinary differential equations. Adv. Neural Inf. Process. Syst. 31 (2018)"},{"key":"8_CR6","doi-asserted-by":"crossref","unstructured":"Cho, K., et al.: Learning phrase representations using RNN encoder\u2013decoder for statistical machine translation. In: Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP), pp. 1724\u20131734 (2014)","DOI":"10.3115\/v1\/D14-1179"},{"key":"8_CR7","doi-asserted-by":"crossref","unstructured":"Collis, P., Singh, R., Kinghorn, P.F., Buckley, C.L.: Learning in hybrid active inference models. In: International Workshop on Active Inference, pp. 49\u201371. Springer (2024)","DOI":"10.1007\/978-3-031-77138-5_4"},{"key":"8_CR8","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmp.2020.102447","volume":"99","author":"L Da Costa","year":"2020","unstructured":"Da Costa, L., Parr, T., Sajid, N., Veselic, S., Neacsu, V., Friston, K.: Active inference on discrete state-spaces: a synthesis. J. Math. Psychol. 99, 102447 (2020)","journal-title":"J. Math. Psychol."},{"issue":"2","key":"8_CR9","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1207\/s15516709cog1402_1","volume":"14","author":"JL Elman","year":"1990","unstructured":"Elman, J.L.: Finding structure in time. Cogn. Sci. 14(2), 179\u2013211 (1990)","journal-title":"Cogn. Sci."},{"key":"8_CR10","first-page":"11662","volume":"33","author":"Z Fountas","year":"2020","unstructured":"Fountas, Z., Sajid, N., Mediano, P., Friston, K.: Deep active inference agents using monte-carlo methods. Adv. Neural. Inf. Process. Syst. 33, 11662\u201311675 (2020)","journal-title":"Adv. Neural. Inf. Process. Syst."},{"issue":"2","key":"8_CR11","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1038\/nrn2787","volume":"11","author":"K Friston","year":"2010","unstructured":"Friston, K.: The free-energy principle: a unified brain theory? Nat. Rev. Neurosci. 11(2), 127\u2013138 (2010)","journal-title":"Nat. Rev. Neurosci."},{"key":"8_CR12","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.physrep.2023.07.001","volume":"1024","author":"K Friston","year":"2023","unstructured":"Friston, K.: The free energy principle made simpler but not too simple. Phys. Rep. 1024, 1\u201329 (2023)","journal-title":"Phys. Rep."},{"issue":"1","key":"8_CR13","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1162\/NECO_a_00912","volume":"29","author":"K Friston","year":"2017","unstructured":"Friston, K., FitzGerald, T., Rigoli, F., Schwartenbeck, P., Pezzulo, G.: Active inference: a process theory. Neural Comput. 29(1), 1\u201349 (2017)","journal-title":"Neural Comput."},{"issue":"1\u20133","key":"8_CR14","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1016\/j.jphysparis.2006.10.001","volume":"100","author":"K Friston","year":"2006","unstructured":"Friston, K., Kilner, J., Harrison, L.: A free energy principle for the brain. J. Physiology-Paris 100(1\u20133), 70\u201387 (2006)","journal-title":"J. Physiology-Paris"},{"issue":"1","key":"8_CR15","doi-asserted-by":"publisher","first-page":"6606","DOI":"10.1038\/s41467-022-34326-1","volume":"13","author":"L Gwilliams","year":"2022","unstructured":"Gwilliams, L., King, J.R., Marantz, A., Poeppel, D.: Neural dynamics of phoneme sequences reveal position-invariant code for content and order. Nat. Commun. 13(1), 6606 (2022)","journal-title":"Nat. Commun."},{"key":"8_CR16","doi-asserted-by":"crossref","unstructured":"He, K., Zhang, X., Ren, S., Sun, J.: Deep residual learning for image recognition. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 770\u2013778 (2016)","DOI":"10.1109\/CVPR.2016.90"},{"key":"8_CR17","doi-asserted-by":"crossref","unstructured":"van\u00a0der Himst, O., Lanillos, P.: Deep active inference for partially observable MDPs. In: Active Inference: First International Workshop, IWAI 2020, Co-located with ECML\/PKDD 2020, Ghent, Belgium, September 14, 2020, Proceedings 1, pp. 61\u201371. Springer (2020)","DOI":"10.1007\/978-3-030-64919-7_8"},{"issue":"8","key":"8_CR18","doi-asserted-by":"publisher","first-page":"1735","DOI":"10.1162\/neco.1997.9.8.1735","volume":"9","author":"S Hochreiter","year":"1997","unstructured":"Hochreiter, S., Schmidhuber, J.: Long short-term memory. Neural Comput. 9(8), 1735\u20131780 (1997)","journal-title":"Neural Comput."},{"key":"8_CR19","unstructured":"Kidger, P.: On Neural Differential Equations. Ph.D. thesis, University of Oxford (2022)"},{"key":"8_CR20","unstructured":"Kidger, P., Foster, J., Li, X., Lyons, T.J.: Neural SDEs as infinite-dimensional GANs. In: International Conference on Machine Learning, pp. 5453\u20135463. PMLR (2021)"},{"key":"8_CR21","first-page":"18747","volume":"34","author":"P Kidger","year":"2021","unstructured":"Kidger, P., Foster, J., Li, X.C., Lyons, T.: Efficient and accurate gradients for neural SDEs. Adv. Neural. Inf. Process. Syst. 34, 18747\u201318761 (2021)","journal-title":"Adv. Neural. Inf. Process. Syst."},{"key":"8_CR22","unstructured":"Kingma, D.P., Ba, J.: Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980 (2014)"},{"key":"8_CR23","unstructured":"Kingma, D.P., Welling, M.: Auto-encoding variational bayes. International Conference on Learning Representations (ICLR) (2014)"},{"key":"8_CR24","doi-asserted-by":"crossref","unstructured":"Kingma, D.P., Welling, M., et\u00a0al.: An introduction to variational autoencoders. Found. Trends\u00ae Mach. Learn. 12(4), 307\u2013392 (2019)","DOI":"10.1561\/2200000056"},{"key":"8_CR25","doi-asserted-by":"crossref","unstructured":"Kloeden, P.E., Platen, E.: Stochastic differential equations. Springer (1992)","DOI":"10.1007\/978-3-662-12616-5"},{"key":"8_CR26","unstructured":"Kullback, S.: Information theory and statistics. Courier Corporation (1997)"},{"key":"8_CR27","unstructured":"Li, X., Kidger, P.: TorchSDE: Pytorch implementation of differentiable stochastic differential equation solvers (2020), version 0.2.6"},{"key":"8_CR28","unstructured":"Li, X., Wong, T.K.L., Chen, R.T., Duvenaud, D.: Scalable gradients for stochastic differential equations. In: International Conference on Artificial Intelligence and Statistics, pp. 3870\u20133882. PMLR (2020)"},{"key":"8_CR29","doi-asserted-by":"crossref","unstructured":"Liu, M., Gei\u00dfler, D., Bian, S., Zhou, B., Lukowicz, P.: Assessing the impact of sampling irregularity in time series data: human activity recognition as a case study. arXiv preprint arXiv:2501.15330 (2025)","DOI":"10.1109\/PerComWorkshops65533.2025.00083"},{"key":"8_CR30","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmp.2020.102348","volume":"96","author":"B Millidge","year":"2020","unstructured":"Millidge, B.: Deep active inference as variational policy gradients. J. Math. Psychol. 96, 102348 (2020)","journal-title":"J. Math. Psychol."},{"key":"8_CR31","doi-asserted-by":"crossref","unstructured":"\u00d8ksendal, B.: Stochastic differential equations. Springer (2003)","DOI":"10.1007\/978-3-642-14394-6"},{"issue":"3","key":"8_CR32","doi-asserted-by":"publisher","first-page":"1800233","DOI":"10.1002\/andp.201800233","volume":"531","author":"M Opper","year":"2019","unstructured":"Opper, M.: Variational inference for stochastic differential equations. Ann. Phys. 531(3), 1800233 (2019)","journal-title":"Ann. Phys."},{"key":"8_CR33","doi-asserted-by":"publisher","first-page":"334","DOI":"10.1016\/j.neuropsychologia.2018.01.041","volume":"111","author":"T Parr","year":"2018","unstructured":"Parr, T., Friston, K.J.: Active inference and the anatomy of oculomotion. Neuropsychologia 111, 334\u2013343 (2018)","journal-title":"Neuropsychologia"},{"key":"8_CR34","doi-asserted-by":"crossref","unstructured":"Parr, T., Pezzulo, G., Friston, K.J.: Active inference: the free energy principle in mind, brain, and behavior. MIT Press (2022)","DOI":"10.7551\/mitpress\/12441.001.0001"},{"issue":"20","key":"8_CR35","doi-asserted-by":"publisher","first-page":"2415","DOI":"10.1016\/j.visres.2009.08.010","volume":"49","author":"M Rolfs","year":"2009","unstructured":"Rolfs, M.: Microsaccades: small steps on a long way. Vision. Res. 49(20), 2415\u20132441 (2009)","journal-title":"Vision. Res."},{"issue":"6088","key":"8_CR36","doi-asserted-by":"publisher","first-page":"533","DOI":"10.1038\/323533a0","volume":"323","author":"DE Rumelhart","year":"1986","unstructured":"Rumelhart, D.E., Hinton, G.E., Williams, R.J.: Learning representations by back-propagating errors. Nature 323(6088), 533\u2013536 (1986)","journal-title":"Nature"},{"key":"8_CR37","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmp.2021.102632","volume":"107","author":"R Smith","year":"2022","unstructured":"Smith, R., Friston, K.J., Whyte, C.J.: A step-by-step tutorial on active inference and its application to empirical data. J. Math. Psychol. 107, 102632 (2022)","journal-title":"J. Math. Psychol."},{"key":"8_CR38","doi-asserted-by":"publisher","DOI":"10.1016\/j.drugalcdep.2020.108208","volume":"215","author":"R Smith","year":"2020","unstructured":"Smith, R., Schwartenbeck, P., Stewart, J.L., Kuplicki, R., Ekhtiari, H., Paulus, M.P., Investigators, T., et al.: Imprecise action selection in substance use disorder: Evidence for active learning impairments when solving the explore-exploit dilemma. Drug Alcohol Depend. 215, 108208 (2020)","journal-title":"Drug Alcohol Depend."},{"key":"8_CR39","doi-asserted-by":"crossref","unstructured":"Tschantz, A., Baltieri, M., Seth, A.K., Buckley, C.L.: Scaling active inference. In: 2020 International Joint Conference on Neural Networks (IJCNN), pp.\u00a01\u20138. IEEE (2020)","DOI":"10.1109\/IJCNN48605.2020.9207382"},{"key":"8_CR40","unstructured":"Tzen, B., Raginsky, M.: Neural stochastic differential equations: Deep latent gaussian models in the diffusion limit. arXiv preprint arXiv:1905.09883 (2019)"}],"container-title":["Communications in Computer and Information Science","Active Inference"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-032-16955-6_8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T22:20:58Z","timestamp":1775686858000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-16955-6_8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"ISBN":["9783032169549","9783032169556"],"references-count":40,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-16955-6_8","relation":{},"ISSN":["1865-0929","1865-0937"],"issn-type":[{"value":"1865-0929","type":"print"},{"value":"1865-0937","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026]]},"assertion":[{"value":"1 April 2026","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"IWAI","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Workshop on Active Inference","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Montreal, QC","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Canada","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":"15 October 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"17 October 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"6","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"iwai-ws2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/iwaiworkshop.github.io\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}