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In this study, we continue our effort to make the FEP a more physically principled formalism by implementing free energy minimization based on the principle of least action. We build a Bayesian mechanics (BM) by casting the formulation reported in the earlier publication (Kim in Neural Comput 30:2616\u20132659, 2018, <jats:ext-link xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" ext-link-type=\"doi\" xlink:href=\"https:\/\/doi.org\/10.1162\/neco_a_01115\">10.1162\/neco_a_01115<\/jats:ext-link>) to considering active inference beyond passive perception. The BM is a neural implementation of variational Bayes under the FEP in continuous time. The resulting BM is provided as an effective Hamilton\u2019s equation of motion and subject to the control signal arising from the brain\u2019s prediction errors at the proprioceptive level. To demonstrate the utility of our approach, we adopt a simple agent-based model and present a concrete numerical illustration of the brain performing recognition dynamics by integrating BM in neural phase space. Furthermore, we recapitulate the major theoretical architectures in the FEP by comparing our approach with the common state-space formulations.<\/jats:p>","DOI":"10.1007\/s00422-021-00859-9","type":"journal-article","created":{"date-parts":[[2021,1,20]],"date-time":"2021-01-20T10:03:26Z","timestamp":1611137006000},"page":"87-102","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Bayesian mechanics of perceptual inference and motor control in the brain"],"prefix":"10.1007","volume":"115","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1549-9305","authenticated-orcid":false,"given":"Chang Sub","family":"Kim","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,1,20]]},"reference":[{"key":"859_CR1","doi-asserted-by":"publisher","first-page":"611","DOI":"10.1007\/s00429-012-0475-5","volume":"218","author":"RA Adams","year":"2013","unstructured":"Adams RA, Shipp S, Friston KJ (2013) Predictions not commands: active inference in the motor system. 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