{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,11]],"date-time":"2026-08-11T07:28:23Z","timestamp":1786433303059,"version":"build-2736575974"},"reference-count":42,"publisher":"IOP Publishing","issue":"4","license":[{"start":{"date-parts":[[2026,8,11]],"date-time":"2026-08-11T00:00:00Z","timestamp":1786406400000},"content-version":"vor","delay-in-days":10,"URL":"https:\/\/publishingsupport.iopscience.iop.org\/iop-standard\/v1"},{"start":{"date-parts":[[2026,8,11]],"date-time":"2026-08-11T00:00:00Z","timestamp":1786406400000},"content-version":"tdm","delay-in-days":10,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["J. Neural Eng."],"published-print":{"date-parts":[[2026,8,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Neural encoding, decoding, and representation-learning approaches have substantially advanced our ability to predict sensory, behavioral, and cognitive variables from neural population activity. At the same time, dynamical systems approaches increasingly model neural computation as the evolution of latent population states governed by recurrent interactions and structured state transitions. Although these frameworks are often presented as competing paradigms, both can successfully reproduce neural observations while still failing to uniquely identify the computational mechanisms implemented by biological circuits. This perspective argues that this reflects a central unresolved challenge in systems neuroscience: observational recordings alone often provide insufficient constraints for distinguishing mechanistically valid neural dynamics from observationally equivalent alternatives. Accordingly, this perspective proposes a unifying framework integrating representational models, latent neural dynamics, identifiability analysis, and perturbation-based validation within a common mechanistic perspective. First, neural representations are discussed as potentially emerging from temporally localized projections of underlying latent dynamical processes evolving on low-dimensional manifolds. Second, recent advances in learning neural evolution operators using recurrent neural networks, latent state-space models, and dynamical system reconstruction methods are reviewed. Third, it is argued that latent trajectories and predictive performance alone do not guarantee mechanistic validity because multiple latent organizations and evolution operators may remain observationally equivalent despite implying distinct causal mechanisms. Finally, perturbation, intervention, and closed-loop neural interfaces are discussed as additional causal constraints capable of falsifying candidate dynamical explanations under targeted manipulation. Across these four principles, the central challenge in modern neuroscience is framed not simply as decoding neural activity or reconstructing latent trajectories, but as determining which inferred dynamical operators remain predictive under intervention and how perturbation can reduce the admissible class of observationally equivalent candidate mechanisms. From this perspective, evolution operators become experimentally testable hypotheses rather than purely descriptive latent models. Integrating latent dynamical modeling with perturbation-based validation may therefore support a transition from prediction-oriented neuroscience toward perturbation-constrained mechanistic dynamical neuroscience.<\/jats:p>","DOI":"10.1088\/1741-2552\/ae9345","type":"journal-article","created":{"date-parts":[[2026,7,31]],"date-time":"2026-07-31T22:52:02Z","timestamp":1785538322000},"page":"043002","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Learning neural evolution operators: from decoding to identifiable causal state-space models"],"prefix":"10.1088","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0905-8036","authenticated-orcid":true,"given":"Armin","family":"Hakkak Moghadam Torbati","sequence":"first","affiliation":[{"name":"Universite libre de Bruxelles (ULB)"},{"name":"ULB"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"266","published-online":{"date-parts":[[2026,8,11]]},"reference":[{"key":"jneae9345bib1","doi-asserted-by":"publisher","first-page":"5814","DOI":"10.1016\/j.cell.2024.08.051","type":"journal-article","article-title":"Decoding the brain: from neural representations to mechanistic models","volume":"187","author":"Mathis","year":"2024","journal-title":"Cell"},{"key":"jneae9345bib2","doi-asserted-by":"publisher","first-page":"947","DOI":"10.1038\/s41586-026-10150-1","type":"journal-article","article-title":"Compact deep neural network models of the visual cortex","volume":"652","author":"Cowley","year":"2026","journal-title":"Nature"},{"key":"jneae9345bib3","doi-asserted-by":"publisher","first-page":"1415","DOI":"10.1038\/s42256-023-00753-y","type":"journal-article","article-title":"Better models of human high-level visual cortex emerge from natural language supervision with a large and diverse dataset","volume":"5","author":"Wang","year":"2023","journal-title":"Nat. Mach. Intell."},{"key":"jneae9345bib4","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1016\/j.conb.2019.04.002","type":"journal-article","article-title":"Interpreting encoding and decoding models","volume":"55","author":"Kriegeskorte","year":"2019","journal-title":"Curr. Opin. Neurobiol."},{"key":"jneae9345bib5","doi-asserted-by":"publisher","first-page":"48","DOI":"10.1016\/j.neuroimage.2015.01.036","type":"journal-article","article-title":"Causal interpretation rules for encoding and decoding models in neuroimaging","volume":"110","author":"Weichwald","year":"2015","journal-title":"Neuroimage"},{"key":"jneae9345bib6","doi-asserted-by":"publisher","first-page":"2063","DOI":"10.1038\/s41593-023-01458-6","type":"journal-article","article-title":"Bayesian encoding and decoding as distinct perspectives on neural coding","volume":"26","author":"Lange","year":"2023","journal-title":"Nat. Neurosci."},{"key":"jneae9345bib7","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1005268","type":"journal-article","article-title":"Could a neuroscientist understand a microprocessor?","volume":"13","author":"Jonas","year":"2017","journal-title":"PLoS Comput. Biol."},{"key":"jneae9345bib8","doi-asserted-by":"publisher","DOI":"10.1088\/1741-2552\/ad3eb5","type":"journal-article","article-title":"A causal perspective on brainwave modeling for brain\u2013computer interfaces","volume":"21","author":"Barmpas","year":"2024","journal-title":"J. Neural Eng."},{"key":"jneae9345bib9","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1146\/annurev-neuro-092619-094115","type":"journal-article","article-title":"Computation through neural population dynamics","volume":"43","author":"Vyas","year":"2020","journal-title":"Annu. Rev. Neurosci."},{"key":"jneae9345bib10","doi-asserted-by":"publisher","first-page":"1582","DOI":"10.1038\/s41593-025-02031-z","type":"journal-article","article-title":"A neural manifold view of the brain","volume":"28","author":"Perich","year":"2025","journal-title":"Nat. Neurosci."},{"key":"jneae9345bib11","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1016\/j.conb.2021.10.014","type":"journal-article","article-title":"Dynamics on the manifold: identifying computational dynamical activity from neural population recordings","volume":"70","author":"Duncker","year":"2021","journal-title":"Curr. Opin. Neurobiol."},{"key":"jneae9345bib12","doi-asserted-by":"publisher","first-page":"1572","DOI":"10.1162\/neco_a_01381","type":"journal-article","article-title":"Shaping dynamics with multiple populations in low-rank recurrent networks","volume":"33","author":"Beiran","year":"2021","journal-title":"Neural Comput."},{"key":"jneae9345bib13","doi-asserted-by":"publisher","first-page":"739","DOI":"10.1016\/j.neuron.2022.12.016","type":"journal-article","article-title":"Parametric control of flexible timing through low-dimensional neural manifolds","volume":"111","author":"Beiran","year":"2023","journal-title":"Neuron"},{"key":"jneae9345bib14","doi-asserted-by":"publisher","first-page":"32","DOI":"10.1038\/s41540-025-00499-w","type":"journal-article","article-title":"A mechanism for the emergence of low-dimensional structures in brain dynamics","volume":"11","author":"Runfola","year":"2025","journal-title":"npj Syst. Biol. Appl."},{"key":"jneae9345bib15","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1038\/nature11129","type":"journal-article","article-title":"Neural population dynamics during reaching","volume":"487","author":"Churchland","year":"2012","journal-title":"Nature"},{"key":"jneae9345bib16","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1038\/nature12742","type":"journal-article","article-title":"Context-dependent computation by recurrent dynamics in prefrontal cortex","volume":"503","author":"Mante","year":"2013","journal-title":"Nature"},{"key":"jneae9345bib17","doi-asserted-by":"publisher","first-page":"978","DOI":"10.1016\/j.neuron.2017.05.025","type":"journal-article","article-title":"Neural manifolds for the control of movement","volume":"94","author":"Gallego","year":"2017","journal-title":"Neuron"},{"key":"jneae9345bib18","doi-asserted-by":"publisher","first-page":"1417","DOI":"10.1038\/s41467-021-21696-1","type":"journal-article","article-title":"Predictive learning as a network mechanism for extracting low-dimensional latent space representations","volume":"12","author":"Recanatesi","year":"2021","journal-title":"Nat. Commun."},{"key":"jneae9345bib19","doi-asserted-by":"publisher","first-page":"9670","DOI":"10.1038\/s41467-024-54032-4","type":"journal-article","article-title":"Predictive learning shapes the representational geometry of the human brain","volume":"15","author":"Greco","year":"2024","journal-title":"Nat. Commun."},{"key":"jneae9345bib20","doi-asserted-by":"publisher","first-page":"360","DOI":"10.1038\/s41586-023-06031-6","type":"journal-article","article-title":"Learnable latent embeddings for joint behavioural and neural analysis","volume":"617","author":"Schneider","year":"2023","journal-title":"Nature"},{"key":"jneae9345bib21","doi-asserted-by":"publisher","first-page":"693","DOI":"10.1038\/s41583-023-00740-7","type":"journal-article","article-title":"Reconstructing computational system dynamics from neural data with recurrent neural networks","volume":"24","author":"Durstewitz","year":"2023","journal-title":"Nat. Rev. Neurosci."},{"key":"jneae9345bib22","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1007\/s10827-009-0179-x","type":"journal-article","article-title":"A new look at state-space models for neural data","volume":"29","author":"Paninski","year":"2010","journal-title":"J. Comput. Neurosci."},{"key":"jneae9345bib23","doi-asserted-by":"publisher","first-page":"612","DOI":"10.1038\/s41592-024-02582-2","type":"journal-article","article-title":"MARBLE: interpretable representations of neural population dynamics using geometric deep learning","volume":"22","author":"Gosztolai","year":"2025","journal-title":"Nat. Methods"},{"key":"jneae9345bib24","doi-asserted-by":"publisher","DOI":"10.51628\/001c.73987","type":"journal-article","article-title":"Expressive architectures enhance interpretability of dynamics-based neural population models","volume":"2023","author":"Sedler","year":"2023","journal-title":"Neurons Behav. Data Anal. Theory"},{"key":"jneae9345bib25","doi-asserted-by":"publisher","first-page":"33805","DOI":"10.52202\/079017-1065","type":"conference-proceedings","article-title":"Modeling latent neural dynamics with gaussian process switching linear dynamical systems","volume":"vol 37","author":"Hu","year":"2024"},{"key":"jneae9345bib26","doi-asserted-by":"publisher","first-page":"1","DOI":"10.5555\/3722577.3722636","type":"journal-article","article-title":"Decomposed linear dynamical systems (dlds) for learning the latent components of neural dynamics","volume":"25","author":"Mudrik","year":"2024","journal-title":"J. Mach. Learn. Res."},{"key":"jneae9345bib27","article-title":"Generative modeling of neural dynamics via latent stochastic differential equations","author":"ElGazzar","year":"2024","type":"preprint"},{"key":"jneae9345bib28","article-title":"Inferring latent dynamics underlying neural population activity via neural differential equations","author":"Kim","year":"2021","type":"conference-proceedings"},{"key":"jneae9345bib29","article-title":"Lfads-latent factor analysis via dynamical systems","author":"Sussillo","year":"2016","type":"preprint"},{"key":"jneae9345bib30","doi-asserted-by":"publisher","first-page":"1572","DOI":"10.1038\/s41592-022-01675-0","type":"journal-article","article-title":"A large-scale neural network training framework for generalized estimation of single-trial population dynamics","volume":"19","author":"Keshtkaran","year":"2022","journal-title":"Nat. Methods"},{"key":"jneae9345bib31","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1038\/s41551-023-01106-1","type":"journal-article","article-title":"Dynamical flexible inference of nonlinear latent factors and structures in neural population activity","volume":"8","author":"Abbaspourazad","year":"2024","journal-title":"Nat. Biomed. Eng."},{"key":"jneae9345bib32","article-title":"Expressive dynamics models with nonlinear injective readouts enable reliable recovery of latent features from neural activity","author":"Versteeg","year":"2023","type":"preprint"},{"key":"jneae9345bib33","doi-asserted-by":"publisher","DOI":"10.1002\/advs.202504346","type":"journal-article","article-title":"A systematic computational framework for practical identifiability analysis in mathematical models arising from biology","volume":"12","author":"Wang","year":"2025","journal-title":"Adv. Sci."},{"key":"jneae9345bib34","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1007\/s10827-026-00927-8","type":"journal-article","article-title":"Resolving non-identifiability mitigates systematic errors in simultaneous models of neural tuning and functional coupling","volume":"54","author":"Sachdeva","year":"2026","journal-title":"J. Comput. Neurosci."},{"key":"jneae9345bib35","doi-asserted-by":"publisher","first-page":"1333","DOI":"10.1109\/TSP.2024.3371899","type":"journal-article","article-title":"Temporally causal discovery tests for discrete time series and neural spike trains","volume":"72","author":"Theocharous","year":"2024","journal-title":"IEEE Trans. Signal Process."},{"key":"jneae9345bib36","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1007074","type":"journal-article","article-title":"Perturbing low dimensional activity manifolds in spiking neuronal networks","volume":"15","author":"W\u00e4rnberg","year":"2019","journal-title":"PLoS Comput. Biol."},{"key":"jneae9345bib37","doi-asserted-by":"publisher","DOI":"10.1101\/2022.12.16.520768","type":"other","article-title":"Direct neural perturbations reveal a dynamical mechanism for robust computation","author":"O\u2019Shea","year":"2022"},{"key":"jneae9345bib38","doi-asserted-by":"publisher","first-page":"910","DOI":"10.1038\/s41586-024-07915-x","type":"journal-article","article-title":"Causal evidence of a line attractor encoding an affective state","volume":"634","author":"Vinograd","year":"2024","journal-title":"Nature"},{"key":"jneae9345bib39","doi-asserted-by":"publisher","DOI":"10.7554\/eLife.106827.3","type":"journal-article","article-title":"Biologically informed cortical models predict optogenetic perturbations","volume":"14","author":"Sourmpis","year":"2026","journal-title":"eLife"},{"key":"jneae9345bib40","doi-asserted-by":"publisher","DOI":"10.1016\/j.crmeth.2025.101180","type":"journal-article","article-title":"A real-time all-optical interface for dynamic perturbation of neural activity during behavior","volume":"5","author":"Zhang","year":"2025","journal-title":"Cell Rep. Methods"},{"key":"jneae9345bib41","doi-asserted-by":"publisher","DOI":"10.64898\/2026.02.01.703133","type":"other","article-title":"Closed-loop imitation learning reveals muscle-centric and latent-goal codes in primate sensorimotor cortex","author":"Vargas","year":"2026"},{"key":"jneae9345bib42","article-title":"Latent causal diffusions for single-cell perturbation modeling","author":"Lorch","year":"2026","type":"preprint"}],"container-title":["Journal of Neural Engineering"],"original-title":[],"link":[{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1741-2552\/ae9345","content-type":"text\/html","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1741-2552\/ae9345\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1741-2552\/ae9345","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1741-2552\/ae9345\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1741-2552\/ae9345\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1741-2552\/ae9345\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1741-2552\/ae9345\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"similarity-checking"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1741-2552\/ae9345\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,11]],"date-time":"2026-08-11T06:40:05Z","timestamp":1786430405000},"score":1,"resource":{"primary":{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1741-2552\/ae9345"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8,1]]},"references-count":42,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2026,8,11]]},"published-print":{"date-parts":[[2026,8,1]]}},"URL":"https:\/\/doi.org\/10.1088\/1741-2552\/ae9345","relation":{},"ISSN":["1741-2560","1741-2552"],"issn-type":[{"value":"1741-2560","type":"print"},{"value":"1741-2552","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,8,1]]},"assertion":[{"value":"Learning neural evolution operators: from decoding to identifiable causal state-space models","name":"article_title","label":"Article Title"},{"value":"Journal of Neural Engineering","name":"journal_title","label":"Journal Title"},{"value":"paper","name":"article_type","label":"Article Type"},{"value":"\u00a9 2026 IOP Publishing Ltd. All rights, including for text and data mining, AI training, and similar technologies, are reserved.","name":"copyright_information","label":"Copyright Information"},{"value":"2026-03-04","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2026-07-31","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2026-08-11","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}