Two different perspectives have informed efforts to explain the link between the brain and behaviour. One approach seeks to identify neural circuit elements that carry out specific functions, emphasizing connectivity between neurons as a substrate for neural computations. Another approach centres on neural manifolds — low-dimensional representations of behavioural signals in neural population activity — and suggests that neural computations are realized by emergent dynamics. Although manifolds reveal an interpretable structure in heterogeneous neuronal activity, finding the corresponding structure in connectivity remains a challenge. We highlight examples in which establishing the correspondence between low-dimensional activity and connectivity has been possible, unifying the neural manifold and circuit perspectives. This relationship is conspicuous in systems in which the geometry of neural responses mirrors their spatial layout in the brain, such as the fly navigational system. Furthermore, we describe evidence that, in systems in which neural responses are heterogeneous, the circuit comprises interactions between activity patterns on the manifold via low-rank connectivity. We suggest that unifying the manifold and circuit approaches is important if we are to be able to causally test theories about the neural computations that underlie behaviour.
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Steinmetz, N. A., Koch, C., Harris, K. D. & Carandini, M. Challenges and opportunities for large-scale electrophysiology with Neuropixels probes. Curr. Opin. Neurobiol. 50, 92–100 (2018).
Steinmetz, N. A. et al. Neuropixels 2.0: a miniaturized high-density probe for stable, long-term brain recordings. Science 372, eabf4588 (2021).
Ebrahimi, S. et al. Emergent reliability in sensory cortical coding and inter-area communication. Nature 605, 713–721 (2022).
Oh, S. W. et al. A mesoscale connectome of the mouse brain. Nature 508, 207–214 (2014).
Markov, N. T. et al. Cortical high-density counterstream architectures. Science 342, 1238406 (2013).
Harris, J. A. et al. Hierarchical organization of cortical and thalamic connectivity. Nature 508, 207–230 (2019).
Huang, L. et al. BRICseq bridges brain-wide interregional connectivity to neural activity and gene expression in single animals. Cell 182, 177–188.e27 (2020).
Skaggs, W. E., Knierim, J. J., Kudrimoti, H. S. & McNaughton, B. L. A model of the neural basis of the rat’s sense of direction. Adv. Neural Inf. Process. Syst. 7, 173–180 (1995).
Compte, A., Brunel, N., Goldman-Rakic, P. S. & Wang, X.-J. Synaptic mechanisms and network dynamics underlying spatial working memory in a cortical network model. Cereb. Cortex 10, 910–923 (2000).
Wang, X. J. Probabilistic decision making by slow reverberation in cortical circuits. Neuron 36, 955–968 (2002).
Machens, C. K., Romo, R. & Brody, C. D. Flexible control of mutual inhibition: a neural model of two-interval discrimination. Science 307, 1121–1124 (2005).
Lo, C.-C. & Wang, X.-J. Cortico-basal ganglia circuit mechanism for a decision threshold in reaction time tasks. Nat. Neurosci. 9, 956–963 (2006).
Engel, T. A. & Wang, X. J. Same or different? A neural circuit mechanism of similarity-based pattern match decision making. J. Neurosci. 31, 6982–6996 (2011).
Ardid, S. & Wang, X.-J. A tweaking principle for executive control: neuronal circuit mechanism for rule-based task switching and conflict resolution. J. Neurosci. 33, 19504–19517 (2013).
Roach, J. P., Churchland, A. K. & Engel, T. A. Choice selective inhibition drives stability and competition in decision circuits. Nat. Commun. 14, 147 (2023).
Martí, D., Deco, G., Mattia, M., Gigante, G. & Giudice, P. D. A fluctuation-driven mechanism for slow decision processes in reverberant networks. PLoS ONE 3, e2534 (2008).
Ksander, J., Katz, D. B. & Miller, P. A model of naturalistic decision making in preference tests. PLoS Comput. Biol. 17, e1009012 (2021).
Wong, K.-F. & Wang, X.-J. A recurrent network mechanism of time integration in perceptual decisions. J. Neurosci. 26, 1314–1328 (2006).
Wang, X.-J. in Principles of Frontal Lobe Function (eds Stuss, D. T. & Knight, R. T.) 226–248 (Oxford Academic, 2013).
McNaughton, B. L., Battaglia, F. P., Jensen, O., Moser, E. I. & Moser, M.-B. Path integration and the neural basis of the ’cognitive map’. Nat. Rev. Neurosci. 7, 663–678 (2006).
Murray, J. D. et al. Linking microcircuit dysfunction to cognitive impairment: effects of disinhibition associated with schizophrenia in a cortical working memory model. Cereb. Cortex 24, 859–872 (2014).
Lam, N. H. et al. Effects of altered excitation–inhibition balance on decision making in a cortical circuit model. J. Neurosci. 42, 1035–1053 (2021).
Inagaki, H. K., Fontolan, L., Romani, S. & Svoboda, K. Discrete attractor dynamics underlies persistent activity in the frontal cortex. Nature 566, 212–217 (2019).
Finkelstein, A. et al. Attractor dynamics gate cortical information flow during decision-making. Nat. Neurosci. 24, 843–850 (2021).
Duan, C. A. et al. Collicular circuits for flexible sensorimotor routing. Nat. Neurosci. 24, 1110–1120 (2021).
Urai, A. E., Doiron, B., Leifer, A. M. & Churchland, A. K. Large-scale neural recordings call for new insights to link brain and behavior. Nat. Neurosci. 25, 11–19 (2022).
Fusi, S., Miller, E. K. & Rigotti, M. Why neurons mix: high dimensionality for higher cognition. Curr. Opin. Neurobiol. 37, 66–74 (2016).
Cavanagh, S. E., Towers, J. P., Wallis, J. D., Hunt, L. T. & Kennerley, S. W. Reconciling persistent and dynamic hypotheses of working memory coding in prefrontal cortex. Nat. Commun. 9, 3498 (2018).
Murray, J. D. et al. Stable population coding for working memory coexists with heterogeneous neural dynamics in prefrontal cortex. Proc. Natl Acad. Sci. USA 114, 394–399 (2017).
Machens, C. K., Romo, R. & Brody, C. D. Functional, but not anatomical, separation of “what” and “when” in prefrontal cortex. J. Neurosci. 30, 350–360 (2010).
Cunningham, J. P. & Yu, B. M. Dimensionality reduction for large-scale neural recordings. Nat. Neurosci. 17, 1500–1509 (2014).
Gallego, J. A., Perich, M. G., Miller, L. E. & Solla, S. A. Neural manifolds for the control of movement. Neuron 94, 978–984 (2017).
Duncker, L. & Sahani, M. Dynamics on the manifold: identifying computational dynamical activity from neural population recordings. Curr. Opin. Neurobiol. 70, 163–170 (2021).
Kriegeskorte, N. & Wei, X.-X. Neural tuning and representational geometry. Nat. Rev. Neurosci. 22, 703–718 (2021).
Pandarinath, C. et al. Inferring single-trial neural population dynamics using sequential auto-encoders. Nat. Methods 15, 805–815 (2018).
Duncker, L., Bohner, G., Boussard, J. & Sahani, M. Learning interpretable continuous-time models of latent stochastic dynamical systems. Proc. 36th Intl Conf. Machine Learning 97, 1726–1734 (2019).
Genkin, M. & Engel, T. A. Moving beyond generalization to accurate interpretation of flexible models. Nat. Mach. Intell. 2, 674–683 (2020).
Zhao, Y. & Park, I. M. Variational online learning of neural dynamics. Front. Comput. Neurosci. 14, 71 (2020).
Genkin, M., Hughes, O. & Engel, T. A. Learning non-stationary Langevin dynamics from stochastic observations of latent trajectories. Nat. Commun. 12, 5986 (2021).
Vyas, S., Golub, M. D., Sussillo, D. & Shenoy, K. V. Computation through neural population dynamics. Annu. Rev. Neurosci. 43, 249–275 (2020).
Barack, D. L. & Krakauer, J. W. Two views on the cognitive brain. Nat. Rev. Neurosci. 22, 359–371 (2021).
Jazayeri, M. & Ostojic, S. Interpreting neural computations by examining intrinsic and embedding dimensionality of neural activity. Curr. Opin. Neurobiol. 70, 113–120 (2021).
Knierim, J. J. & Zhang, K. Attractor dynamics of spatially correlated neural activity in the limbic system. Annu. Rev. Neurosci. 35, 267–285 (2012).
Khona, M. & Fiete, I. R. Attractor and integrator networks in the brain. Nat. Rev. Neurosci. 23, 744–766 (2022).
Clark, B. J. & Taube, J. S. Vestibular and attractor network basis of the head direction cell signal in subcortical circuits. Front. Neural Circuits 6, 7 (2012).
Hulse, B. K. & Jayaraman, V. Mechanisms underlying the neural computation of head direction. Annu. Rev. Neurosci. 43, 1–24 (2016).
Turner-Evans, D. B. et al. The neuroanatomical ultrastructure and function of a biological ring attractor. Neuron 108, 145–163 (2020).
Chaudhuri, R., Gerçek, B., Pandey, B., Peyrache, A. & Fiete, I. The intrinsic attractor manifold and population dynamics of a canonical cognitive circuit across waking and sleep. Nat. Neurosci. 22, 1512–1520 (2019).
Seelig, J. D. & Jayaraman, V. Neural dynamics for landmark orientation and angular path integration. Nature 521, 186–191 (2015).
Turner-Evans, D. et al. Angular velocity integration in a fly heading circuit. eLife 6, e23496 (2017).
Kim, S. S., Rouault, H., Druckmann, S. & Jayaraman, V. Ring attractor dynamics in the Drosophila central brain. Science 356, 849–853 (2017).
Kim, S. S., Hermundstad, A. M., Romani, S., Abbott, L. F. & Jayaraman, V. Generation of stable heading representations in diverse visual scenes. Nature 576, 126–131 (2019).
Ajabi, Z., Keinath, A. T., Wei, X.-X. & Brandon, M. P. Population dynamics of head-direction neurons during drift and reorientation. Nature https://doi.org/10.1038/s41586-023-05813-2 (2023).
Duszkiewicz, A. J. et al. Reciprocal feature encoding by cortical excitatory and inhibitory neurons. Preprint at bioRxiv https://doi.org/10.1101/2022.03.14.484357 (2022).
Zhang, K. Representation of spatial orientation by the intrinsic dynamics of the head-direction cell ensemble: a theory. J. Neurosci. 16, 2112–2126 (1996).
Redish, A. D., Elga, A. N. & Touretzky, D. S. A coupled attractor model of the rodent head direction system. Netw. Comput. Neural Syst. 7, 671–685 (1996).
Cope, A. J., Sabo, C., Vasilaki, E., Barron, A. B. & Marshall, J. A. R. A computational model of the integration of landmarks and motion in the insect central complex. PLoS ONE 12, e0172325 (2017).
Song, P. & Wang, X.-J. Angular path integration by moving “hill of activity”: a spiking neuron model without recurrent excitation of the head-direction system. J. Neurosci. 25, 1002–1014 (2005).
Cueva, C. J., Wang, P. Y., Chin, M. & Wei, X.-X. Emergence of functional and structural properties of the head direction system by optimization of recurrent neural networks. Preprint at arXiv https://doi.org/10.48550/arXiv.1912.10189 (2019).
Green, J. et al. A neural circuit architecture for angular integration in Drosophila. Nature 546, 101–106 (2017).
Wolff, T., Iyer, N. A. & Rubin, G. M. Neuroarchitecture and neuroanatomy of the Drosophila central complex: a GAL4-based dissection of protocerebral bridge neurons and circuits. J. Comp. Neurol. 523, 997–1037 (2015).
Kutschireiter, A., Basnak, M. A., Wilson, R. I. & Drugowitsch, J. Bayesian inference in ring attractor networks. Proc. Natl Acad. Sci. USA 120, e2210622120 (2023).
Lyu, C., Abbott, L. F. & Maimon, G. Building an allocentric travelling direction signal via vector computation. Nature 601, 92–97 (2021).
Su, T.-S., Lee, W.-J., Huang, Y.-C., Wang, C.-T. & Lo, C.-C. Coupled symmetric and asymmetric circuits underlying spatial orientation in fruit flies. Nat. Commun. 8, 139 (2017).
Mittelstaedt, M. L. & Mittelstaedt, H. Homing by path integration in a mammal. Naturwissenschaften 67, 566–567 (1980).
Fyhn, M., Molden, S., Witter, M. P., Moser, E. I. & Moser, M.-B. Spatial representation in the entorhinal cortex. Science 305, 1258–1264 (2004).
Stensola, H. et al. The entorhinal grid map is discretized. Nature 492, 72–78 (2012).
Yoon, K. et al. Specific evidence of low-dimensional continuous attractor dynamics in grid cells. Nat. Neurosci. 16, 1077–1084 (2013).
Hafting, T., Fyhn, M., Molden, S., Moser, M.-B. & Moser, E. I. Microstructure of a spatial map in the entorhinal cortex. Nature 436, 801–806 (2005).
Gao, R., Xie, J., Wei, X.-X., Zhu, S.-C. & Wu, Y. N. On path integration of grid cells: group representation and isotropic scaling. Advances in Neural Information Systems 34 https://proceedings.neurips.cc/paper/2021/hash/f076073b2082f8741a9cd07b789c77a0-Abstract.html (2021).
Gardner, R. J. et al. Toroidal topology of population activity in grid cells. Nature 602, 123–128 (2022).
Fiete, I. R., Burak, Y. & Brookings, T. What grid cells convey about rat location. J. Neurosci. 28, 6858–6871 (2008).
Petrucco, L. et al. Neural dynamics and architecture of the heading direction circuit in a vertebrate brain. Preprint at bioRxiv https://doi.org/10.1101/2022.04.27.489672 (2022).
Nieh, E. H. et al. Geometry of abstract learned knowledge in the hippocampus. Nature 595, 80–84 (2021).
Low, R. J., Lewallen, S., Aronov, D., Nevers, R. & Tank, D. W. Probing variability in a cognitive map using manifold inference from neural dynamics. Preprint at bioRxiv https://doi.org/10.1101/418939 (2018).
Widloski, J., Marder, M. P. & Fiete, I. R. Inferring circuit mechanisms from sparse neural recording and global perturbation in grid cells. eLife 7, e33503 (2018).
Samsonovich, A. & McNaughton, B. L. Path integration and cognitive mapping in a continuous attractor neural network model. J. Neurosci. 17, 5900–5920 (1997).
Conklin, J. & Eliasmith, C. A controlled attractor network model of path integration in the rat. J. Comput. Neurosci. 18, 183–203 (2005).
Gu, Y. et al. A map-like micro-organization of grid cells in the medial entorhinal cortex. Cell 175, 737–750.e30 (2018).
Heys, J. G., Rangarajan, K. V. & Dombeck, D. A. The functional micro-organization of grid cells revealed by cellular-resolution imaging. Neuron 84, 1079–1090 (2014).
Obenhaus, H. A., Zong, W., Jacobsen, R. I. & Moser, E. I. Functional network topography of the medial entorhinal cortex. Proc. Natl Acad. Sci. USA 119, e2121655119 (2022).
Kropff, E. & Treves, A. The emergence of grid cells: intelligent design or just adaptation? Hippocampus 18, 1256–1269 (2008).
Dordek, Y., Soudry, D., Meir, R. & Derdikman, D. Extracting grid cell characteristics from place cell inputs using non-negative principal component analysis. eLife 5, e10094 (2016).
Monsalve-Mercado, M. M. & Leibold, C. Hippocampal spike-timing correlations lead to hexagonal grid fields. Phys. Rev. Lett. 119, 038101 (2017).
Burak, Y. & Fiete, I. R. Accurate path integration in continuous attractor network models of grid cells. PLoS Comput. Biol. 5, e1000291 (2009).
Banerjee, A., Egger, R. & Long, M. A. Using focal cooling to link neural dynamics and behavior. Neuron 109, 2508–2518 (2021).
Rudolph, U. & Möhler, H. Analysis of GABAA receptor function and dissection of the pharmacology of benzodiazepines and general anesthetics through mouse genetics. Annu. Rev. Pharmacol. Toxicol. 44, 475–498 (2004).
Cueva, C. J. & Wei, X.-X. Emergence of grid-like representations by training recurrent neural networks to perform spatial localization. Preprint at arXiv https://doi.org/10.48550/arXiv.1803.07770 (2018).
Sorscher, B., Mel, G. C., Ocko, S. A., Giocomo, L. M. & Ganguli, S. A unified theory for the computational and mechanistic origins of grid cells. Neuron 111, 121–137.e13 (2022).
Bock, D. D. et al. Network anatomy and in vivo physiology of visual cortical neurons. Nature 471, 177–182 (2011).
Wang, X.-J. 50 years of mnemonic persistent activity: quo vadis? Trends Neurosci. 44, 888–902 (2021).
Fuster, J. M. & Alexander, G. E. Neuron activity related to short-term memory. Science 173, 652–654 (1971).
Romo, R., Brody, C. D., Hernández, A. & Lemus, L. Neuronal correlates of parametric working memory in the prefrontal cortex. Nature 399, 470–473 (1999).
Kamiński, J. & Rutishauser, U. Between persistently active and activity-silent frameworks: novel vistas on the cellular basis of working memory. Ann. N. Y. Acad. Sci. 1464, 64–75 (2020).
Gold, J. I. & Shadlen, M. N. The neural basis of decision making. Annu. Rev. Neurosci. 30, 535–574 (2007).
O’Connell, R. G., Shadlen, M. N., Wong-Lin, K. & Kelly, S. P. Bridging neural and computational viewpoints on perceptual decision-making. Trends Neurosci. 41, 838–852 (2018).
Funahashi, S., Bruce, C. J. & Goldman-Rakic, P. S. Mnemonic coding of visual space in the monkey’s dorsolateral prefrontal cortex. J. Neurophysiol. 61, 331–349 (1989).
Constantinidis, C., Franowicz, M. N. & Goldman-Rakic, P. S. Coding specificity in cortical microcircuits: a multiple-electrode analysis of primate prefrontal cortex. J. Neurosci. 21, 3646–3655 (2001).
Shadlen, M. N. & Newsome, W. T. Neural basis of a perceptual decision in the parietal cortex (area LIP) of the rhesus monkey. J. Neurophysiol. 86, 1916–1936 (2001).
Roitman, J. D. & Shadlen, M. N. Response of neurons in the lateral intraparietal area during a combined visual discrimination reaction time task. J. Neurosci. 22, 9475–9489 (2002).
Hanks, T. D. et al. Distinct relationships of parietal and prefrontal cortices to evidence accumulation. Nature 520, 220–223 (2015).
Goard, M. J., Pho, G. N., Woodson, J. & Sur, M. Distinct roles of visual, parietal, and frontal motor cortices in memory-guided sensorimotor decisions. eLife 5, e13764 (2016).
Chandrasekaran, C., Peixoto, D., Newsome, W. T. & Shenoy, K. V. Laminar differences in decision-related neural activity in dorsal premotor cortex. Nat. Commun. 8, 996 (2017).
Peixoto, D. et al. Decoding and perturbing decision states in real time. Nature 591, 604–609 (2021).
Kilpatrick, Z. P., Ermentrout, B. & Doiron, B. Optimizing working memory with heterogeneity of recurrent cortical excitation. J. Neurosci. 33, 18999–19011 (2013).
Barbosa, J. et al. Interplay between persistent activity and activity-silent dynamics in the prefrontal cortex underlies serial biases in working memory. Nat. Neurosci. 23, 1016–1024 (2020).
Wimmer, K., Nykamp, D. Q., Constantinidis, C. & Compte, A. Bump attractor dynamics in prefrontal cortex explains behavioral precision in spatial working memory. Nat. Neurosci. 17, 431–439 (2014).
Stein, H. et al. Reduced serial dependence suggests deficits in synaptic potentiation in anti-NMDAR encephalitis and schizophrenia. Nat. Commun. 11, 4250 (2020).
Cano-Colino, M. & Compte, A. A computational model for spatial working memory deficits in schizophrenia. Pharmacopsychiatry 45, S49–S56 (2012).
Stein, H., Barbosa, J. & Compte, A. Towards biologically constrained attractor models of schizophrenia. Curr. Opin. Neurobiol. 70, 171–181 (2021).
Mante, V., Sussillo, D., Shenoy, K. V. & Newsome, W. T. Context-dependent computation by recurrent dynamics in prefrontal cortex. Nature 503, 78–84 (2013).
Chaisangmongkon, W., Swaminathan, S. K., Freedman, D. J. & Wang, X.-J. Computing by robust transience: how the fronto-parietal network performs sequential, category-based decisions. Neuron 93, 1504–1517.e4 (2017).
Kobak, D. et al. Demixed principal component analysis of neural population data. eLife 5, e10989 (2016).
Aoi, M. C., Mante, V. & Pillow, J. W. Prefrontal cortex exhibits multidimensional dynamic encoding during decision-making. Nat. Neurosci. 23, 1410–1420 (2020).
Koren, V., Andrei, A. R., Hu, M., Dragoi, V. & Obermayer, K. Reading-out task variables as a low-dimensional reconstruction of neural spike trains in single trials. PLoS ONE 14, e0222649 (2019).
Sussillo, D., Churchland, M. M., Kaufman, M. T. & Shenoy, K. V. A neural network that finds a naturalistic solution for the production of muscle activity. Nat. Neurosci. 18, 1025–1033 (2015).
Song, H. F., Yang, G. R. & Wang, X.-J. Training excitatory–inhibitory recurrent neural networks for cognitive tasks: a simple and flexible framework. PLoS Comput. Biol. 12, e1004792 (2016).
Yang, G. R., Joglekar, M. R., Song, H. F., Newsome, W. T. & Wang, X.-J. Task representations in neural networks trained to perform many cognitive tasks. Nat. Neurosci. 22, 297–306 (2019).
Feulner, B. & Clopath, C. Neural manifold under plasticity in a goal driven learning behaviour. PLoS Comput. Biol. 17, e1008621 (2021).
Mastrogiuseppe, F. & Ostojic, S. Linking connectivity, dynamics, and computations in low-rank recurrent neural networks. Neuron 99, 609–623.e29 (2018).
Eliasmith, C. & Anderson, C. H. Neural Engineering (Computational Neuroscience Series): Computational, Representation, and Dynamics in Neurobiological Systems (MIT Press, 2002).
Dubreuil, A., Valente, A., Beiran, M., Mastrogiuseppe, F. & Ostojic, S. The role of population structure in computations through neural dynamics. Nat. Neurosci. 25, 783–794 (2022).
Valente, A., Ostojic, S. & Pillow, J. Probing the relationship between latent linear dynamical systems and low-rank recurrent neural network models. Neural Comput. 34, 1871–1892 (2022).
Langdon, C. & Engel, T. A. Latent circuit inference from heterogeneous neural responses during cognitive tasks. Preprint at bioRxiv https://doi.org/10.1101/2022.01.23.477431 (2022).
Macke, J. H. et al. in Advances in Neural Information Processing Systems 24 https://papers.nips.cc/paper_files/paper/2011/hash/7143d7fbadfa4693b9eec507d9d37443-Abstract.html (2011).
Gao, Y., Busing, L., Shenoy, K. V. & Cunningham, J. P. in Advances in Neural Information Processing Systems 28 https://papers.nips.cc/paper_files/paper/2011/hash/7143d7fbadfa4693b9eec507d9d37443-Abstract.html (2015).
Rajan, K., Harvey, C. D. & Tank, D. W. Recurrent network models of sequence generation and memory. Neuron 90, 128–142 (2016).
Cohen, Z., DePasquale, B., Aoi, M. C. & Pillow, J. W. Recurrent dynamics of prefrontal cortex during context-dependent decision-making. Preprint at bioRxiv https://doi.org/10.1101/2020.11.27.401539 (2020).
Perich, M. G. & Rajan, K. Rethinking brain-wide interactions through multi-region ‘network of networks’ models. Curr. Opin. Neurobiol. 65, 146–151 (2020).
Bittner, S. R. et al. Interrogating theoretical models of neural computation with emergent property inference. eLife 10, e56265 (2021).
Friston, K. et al. Dynamic causal modelling revisited. NeuroImage 199, 730–744 (2019).
Friston, K. J., Harrison, L. & Penny, W. Dynamic causal modelling. NeuroImage 19, 1273–1302 (2003).
Chernov, M. M., Friedman, R. M., Chen, G., Stoner, G. R. & Roe, A. W. Functionally specific optogenetic modulation in primate visual cortex. Proc. Natl Acad. Sci. USA 115, 10505–10510 (2018).
Carrillo-Reid, L., Han, S., Yang, W., Akrouh, A. & Yuste, R. Controlling visually guided behavior by holographic recalling of cortical ensembles. Cell 178, 447–457.e5 (2019).
Marshel, J. H. et al. Cortical layer-specific critical dynamics triggering perception. Science 365, 6453 (2019).
Saxena, S. & Cunningham, J. P. Towards the neural population doctrine. Curr. Opin. Neurobiol. 55, 103–111 (2019).
Ebitz, R. B. & Hayden, B. Y. The population doctrine in cognitive neuroscience. Neuron 109, 3055–3068 (2021).
Cueva, C. J. et al. Low-dimensional dynamics for working memory and time encoding. Proc. Natl Acad. Sci. USA 117, 23021–23032 (2020).
Deneve, S., Alemi, A. & Bourdoukan, R. The brain as an efficient and robust adaptive learner. Neuron 94, 969–977 (2017).
Tenenbaum, J. B., Silva, VD & Langford, J. C. A global geometric framework for nonlinear dimensionality reduction. Science 290, 2319–2323 (2000).
Priebe, N. J. & Ferster, D. Mechanisms of neuronal computation in mammalian visual cortex. Neuron 75, 194–208 (2012).
Pollock, E. & Jazayeri, M. Engineering recurrent neural networks from task-relevant manifolds and dynamics. PLoS Comput. Biol. 16, e1008128 (2020).
Strang, G. Introduction to Linear Algebra (Wellesley-Cambridge, 1998).
Kuznetsov, Y. A. Topological Equivalence, Bifurcations, and Structural Stability of Dynamical Systems 39–76 (Springer, 2004).
This work was supported by the Swartz Foundation (C.L. and M.G.), National Institutes of Health (NIH) grant R01 EB026949 (T.A.E. and M.G.), NIH grant RF1DA055666 (T.A.E., C.L. and M.G.) and Alfred P. Sloan Foundation Research Fellowship (T.A.E.).
The authors declare no competing interests.
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Langdon, C., Genkin, M. & Engel, T.A. A unifying perspective on neural manifolds and circuits for cognition. Nat Rev Neurosci 24, 363–377 (2023). https://doi.org/10.1038/s41583-023-00693-x