Chaotic neural dynamics facilitate probabilistic computations through sampling

Terada, Yu; Toyoizumi, Taro

doi:10.1073/pnas.2312992121

Chaotic neural dynamics facilitate probabilistic computations through sampling

Journal Article · Mon Apr 22 00:00:00 EDT 2024 · Proceedings of the National Academy of Sciences of the United States of America

DOI:https://doi.org/10.1073/pnas.2312992121· OSTI ID:2339911

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Laboratory for Neural Computation and Adaptation, RIKEN Center for Brain Science, Saitama 351-0198, Japan, Department of Neurobiology, University of California, San Diego, La Jolla, CA 92093, The Institute for Physics of Intelligence, The University of Tokyo, Tokyo 113-0033, Japan
Laboratory for Neural Computation and Adaptation, RIKEN Center for Brain Science, Saitama 351-0198, Japan, Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan

Cortical neurons exhibit highly variable responses over trials and time. Theoretical works posit that this variability arises potentially from chaotic network dynamics of recurrently connected neurons. Here, we demonstrate that chaotic neural dynamics, formed through synaptic learning, allow networks to perform sensory cue integration in a sampling-based implementation. We show that the emergent chaotic dynamics provide neural substrates for generating samples not only of a static variable but also of a dynamical trajectory, where generic recurrent networks acquire these abilities with a biologically plausible learning rule through trial and error. Furthermore, the networks generalize their experience in the stimulus-evoked samples to the inference without partial or all sensory information, which suggests a computational role of spontaneous activity as a representation of the priors as well as a tractable biological computation for marginal distributions. These findings suggest that chaotic neural dynamics may serve for the brain function as a Bayesian generative model.

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Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0022042

OSTI ID:: 2339911

Alternate ID(s):: OSTI ID: 2472222

Journal Information:: Proceedings of the National Academy of Sciences of the United States of America, Journal Name: Proceedings of the National Academy of Sciences of the United States of America Journal Issue: 18 Vol. 121; ISSN 0027-8424

Publisher:: Proceedings of the National Academy of SciencesCopyright Statement

Country of Publication:: United States

Language:: English

References (84)

Dynamics of pattern formation in lateral-inhibition type neural fields Amari, Shun-ichi Biological Cybernetics, Vol. 27, Issue 2 https://doi.org/10.1007/BF00337259	journal	January 1977
Simple statistical gradient-following algorithms for connectionist reinforcement learning Williams, Ronald J. Machine Learning, Vol. 8, Issue 3-4 https://doi.org/10.1007/BF00992696	journal	May 1992
Neuronal variability: non-stationary responses to identical visual stimuli Tomko, George J.; Crapper, Donald R. Brain Research, Vol. 79, Issue 3 https://doi.org/10.1016/0006-8993(74)90438-7	journal	October 1974
Learning with three factors: modulating Hebbian plasticity with errors Kuśmierz, Łukasz; Isomura, Takuya; Toyoizumi, Taro Current Opinion in Neurobiology, Vol. 46 https://doi.org/10.1016/j.conb.2017.08.020	journal	October 2017
Edge of chaos and prediction of computational performance for neural circuit models Legenstein, Robert; Maass, Wolfgang Neural Networks, Vol. 20, Issue 3 https://doi.org/10.1016/j.neunet.2007.04.017	journal	April 2007
Adaptive balancing of exploration and exploitation around the edge of chaos in internal-chaos-based learning Matsuki, Toshitaka; Shibata, Katsunari Neural Networks, Vol. 132 https://doi.org/10.1016/j.neunet.2020.08.002	journal	December 2020
Generating Coherent Patterns of Activity from Chaotic Neural Networks Sussillo, David; Abbott, L. F. Neuron, Vol. 63, Issue 4 https://doi.org/10.1016/j.neuron.2009.07.018	journal	August 2009
Not Noisy, Just Wrong: The Role of Suboptimal Inference in Behavioral Variability Beck, Jeffrey M.; Ma, Wei Ji; Pitkow, Xaq Neuron, Vol. 74, Issue 1 https://doi.org/10.1016/j.neuron.2012.03.016	journal	April 2012
Recurrent Network Models of Sequence Generation and Memory Rajan, Kanaka; Harvey, Christopher D.; Tank, David W. Neuron, Vol. 90, Issue 1 https://doi.org/10.1016/j.neuron.2016.02.009	journal	April 2016
Decision Making and Sequential Sampling from Memory Shadlen, Michael N.; Shohamy, Daphna Neuron, Vol. 90, Issue 5 https://doi.org/10.1016/j.neuron.2016.04.036	journal	June 2016
Neural Variability and Sampling-Based Probabilistic Representations in the Visual Cortex Orbán, Gergő; Berkes, Pietro; Fiser, József Neuron, Vol. 92, Issue 2 https://doi.org/10.1016/j.neuron.2016.09.038	journal	October 2016
Imaging Cortical Dynamics in GCaMP Transgenic Rats with a Head-Mounted Widefield Macroscope Scott, Benjamin B.; Thiberge, Stephan Y.; Guo, Caiying Neuron, Vol. 100, Issue 5 https://doi.org/10.1016/j.neuron.2018.09.050	journal	December 2018
Bayesian Computation through Cortical Latent Dynamics Sohn, Hansem; Narain, Devika; Meirhaeghe, Nicolas Neuron, Vol. 103, Issue 5 https://doi.org/10.1016/j.neuron.2019.06.012	journal	September 2019
Fast, cell-resolution, contiguous-wide two-photon imaging to reveal functional network architectures across multi-modal cortical areas Ota, Keisuke; Oisi, Yasuhiro; Suzuki, Takayuki Neuron, Vol. 109, Issue 11 https://doi.org/10.1016/j.neuron.2021.03.032	journal	June 2021
Not so spontaneous: Multi-dimensional representations of behaviors and context in sensory areas Avitan, Lilach; Stringer, Carsen Neuron, Vol. 110, Issue 19 https://doi.org/10.1016/j.neuron.2022.06.019	journal	October 2022
From fixed points to chaos: Three models of delayed discrimination Barak, Omri; Sussillo, David; Romo, Ranulfo Progress in Neurobiology, Vol. 103 https://doi.org/10.1016/j.pneurobio.2013.02.002	journal	April 2013
The Bayesian brain: the role of uncertainty in neural coding and computation Knill, David C.; Pouget, Alexandre Trends in Neurosciences, Vol. 27, Issue 12 https://doi.org/10.1016/j.tins.2004.10.007	journal	December 2004
The organizing principles of neuronal avalanches: cell assemblies in the cortex? Plenz, Dietmar; Thiagarajan, Tara C. Trends in Neurosciences, Vol. 30, Issue 3 https://doi.org/10.1016/j.tins.2007.01.005	journal	March 2007
The low synaptic release probability in vivo Borst, J. Gerard G. Trends in Neurosciences, Vol. 33, Issue 6 https://doi.org/10.1016/j.tins.2010.03.003	journal	June 2010
Neuronal Dynamics Gerstner, Wulfram; Kistler, Werner M.; Naud, Richard https://doi.org/10.1017/CBO9781107447615	book	August 2014
Humans integrate visual and haptic information in a statistically optimal fashion Ernst, Marc O.; Banks, Martin S. Nature, Vol. 415, Issue 6870 https://doi.org/10.1038/415429a	journal	January 2002
Bayesian integration in sensorimotor learning Körding, Konrad P.; Wolpert, Daniel M. Nature, Vol. 427, Issue 6971 https://doi.org/10.1038/nature02169	journal	January 2004
Probabilistic reasoning by neurons Yang, Tianming; Shadlen, Michael N. Nature, Vol. 447, Issue 7148 https://doi.org/10.1038/nature05852	journal	June 2007
Sensitivity to perturbations in vivo implies high noise and suggests rate coding in cortex London, Michael; Roth, Arnd; Beeren, Lisa Nature, Vol. 466, Issue 7302 https://doi.org/10.1038/nature09086	journal	July 2010
Stimulus onset quenches neural variability: a widespread cortical phenomenon Churchland, Mark M.; Yu, Byron M.; Cunningham, John P. Nature Neuroscience, Vol. 13, Issue 3 https://doi.org/10.1038/nn.2501	journal	February 2010
Two layers of neural variability Churchland, Mark M.; Abbott, L. F. Nature Neuroscience, Vol. 15, Issue 11 https://doi.org/10.1038/nn.3247	journal	October 2012
Robust timing and motor patterns by taming chaos in recurrent neural networks Laje, Rodrigo; Buonomano, Dean V. Nature Neuroscience, Vol. 16, Issue 7 https://doi.org/10.1038/nn.3405	journal	May 2013
Targeting neurons and photons for optogenetics Packer, Adam M.; Roska, Botond; Häusser, Michael Nature Neuroscience, Vol. 16, Issue 7 https://doi.org/10.1038/nn.3427	journal	June 2013
Bayesian inference with probabilistic population codes Ma, Wei Ji; Beck, Jeffrey M.; Latham, Peter E. Nature Neuroscience, Vol. 9, Issue 11 https://doi.org/10.1038/nn1790	journal	October 2006
Neuronal variability: noise or part of the signal? Stein, Richard B.; Gossen, E. Roderich; Jones, Kelvin E. Nature Reviews Neuroscience, Vol. 6, Issue 5 https://doi.org/10.1038/nrn1668	journal	May 2005
Noise in the nervous system Faisal, A. Aldo; Selen, Luc P. J.; Wolpert, Daniel M. Nature Reviews Neuroscience, Vol. 9, Issue 4 https://doi.org/10.1038/nrn2258	journal	April 2008
Representation of visual uncertainty through neural gain variability Hénaff, Olivier J.; Boundy-Singer, Zoe M.; Meding, Kristof Nature Communications, Vol. 11, Issue 1 https://doi.org/10.1038/s41467-020-15533-0	journal	May 2020
Neuronal variability reflects probabilistic inference tuned to natural image statistics Festa, Dylan; Aschner, Amir; Davila, Aida Nature Communications, Vol. 12, Issue 1 https://doi.org/10.1038/s41467-021-23838-x	journal	June 2021
Fractional neural sampling as a theory of spatiotemporal probabilistic computations in neural circuits Qi, Yang; Gong, Pulin Nature Communications, Vol. 13, Issue 1 https://doi.org/10.1038/s41467-022-32279-z	journal	August 2022
Sampling-based Bayesian inference in recurrent circuits of stochastic spiking neurons Zhang, Wen-Hao; Wu, Si; Josić, Krešimir Nature Communications, Vol. 14, Issue 1 https://doi.org/10.1038/s41467-023-41743-3	journal	November 2023
The default mode network: where the idiosyncratic self meets the shared social world Yeshurun, Yaara; Nguyen, Mai; Hasson, Uri Nature Reviews Neuroscience, Vol. 22, Issue 3 https://doi.org/10.1038/s41583-020-00420-w	journal	January 2021
Backpropagation and the brain Lillicrap, Timothy P.; Santoro, Adam; Marris, Luke Nature Reviews Neuroscience, Vol. 21, Issue 6 https://doi.org/10.1038/s41583-020-0277-3	journal	April 2020
Task representations in neural networks trained to perform many cognitive tasks Yang, Guangyu Robert; Joglekar, Madhura R.; Song, H. Francis Nature Neuroscience, Vol. 22, Issue 2 https://doi.org/10.1038/s41593-018-0310-2	journal	January 2019
Cortical-like dynamics in recurrent circuits optimized for sampling-based probabilistic inference Echeveste, Rodrigo; Aitchison, Laurence; Hennequin, Guillaume Nature Neuroscience, Vol. 23, Issue 9 https://doi.org/10.1038/s41593-020-0671-1	journal	August 2020
The role of population structure in computations through neural dynamics Dubreuil, Alexis; Valente, Adrian; Beiran, Manuel Nature Neuroscience, Vol. 25, Issue 6 https://doi.org/10.1038/s41593-022-01088-4	journal	June 2022
Deterministic networks for probabilistic computing Jordan, Jakob; Petrovici, Mihai A.; Breitwieser, Oliver Scientific Reports, Vol. 9, Issue 1 https://doi.org/10.1038/s41598-019-54137-7	journal	December 2019
Gradient-based learning drives robust representations in recurrent neural networks by balancing compression and expansion Farrell, Matthew; Recanatesi, Stefano; Moore, Timothy Nature Machine Intelligence, Vol. 4, Issue 6 https://doi.org/10.1038/s42256-022-00498-0	journal	June 2022
Sequential structure of neocortical spontaneous activity in vivo Luczak, Artur; Barthó, Peter; Marguet, Stephan L. Proceedings of the National Academy of Sciences, Vol. 104, Issue 1 https://doi.org/10.1073/pnas.0605643104	journal	January 2007
Theory of orientation tuning in visual cortex. Ben-Yishai, R.; Bar-Or, R. L.; Sompolinsky, H. Proceedings of the National Academy of Sciences, Vol. 92, Issue 9 https://doi.org/10.1073/pnas.92.9.3844	journal	April 1995
A default mode of brain function Raichle, M. E.; MacLeod, A. M.; Snyder, A. Z. Proceedings of the National Academy of Sciences, Vol. 98, Issue 2 https://doi.org/10.1073/pnas.98.2.676	journal	January 2001
Sensory Cue Integration Trommershäuser, Julia; Kording, Konrad; Landy, Michael S. https://doi.org/10.1093/acprof:oso/9780195387247.001.0001	book	September 2011
The Noisy Brain: Stochastic Dynamics as a Principle of Brain Function Rolls, Edmund T.; Deco, Gustavo https://doi.org/10.1093/acprof:oso/9780199587865.001.0001	journal	January 2010
Emergence of Complex Computational Structures From Chaotic Neural Networks Through Reward-Modulated Hebbian Learning Hoerzer, Gregor M.; Legenstein, Robert; Maass, Wolfgang Cerebral Cortex, Vol. 24, Issue 3 https://doi.org/10.1093/cercor/bhs348	journal	November 2012
A reservoir of timescales in random neural network Stern, Merav; Istrate, Nicolae; Mazzucato, Luca https://doi.org/10.1101/2021.10.11.463861	preprint	August 2022
Baseline control of optimal performance in recurrent neural networks Ogawa, Shun; Fumarola, Francesco; Mazzucato, Luca https://doi.org/10.1101/2022.05.11.491436	preprint	May 2022
Optimal short-term memory before the edge of chaos in driven random recurrent networks Haruna, Taichi; Nakajima, Kohei Physical Review E, Vol. 100, Issue 6 https://doi.org/10.1103/PhysRevE.100.062312	journal	December 2019
Beyond the edge of chaos: Amplification and temporal integration by recurrent networks in the chaotic regime Toyoizumi, T.; Abbott, L. F. Physical Review E, Vol. 84, Issue 5 https://doi.org/10.1103/PhysRevE.84.051908	journal	November 2011
Transition to Chaos in Random Networks with Cell-Type-Specific Connectivity Aljadeff, Johnatan; Stern, Merav; Sharpee, Tatyana Physical Review Letters, Vol. 114, Issue 8 https://doi.org/10.1103/PhysRevLett.114.088101	journal	February 2015
Edge of Chaos and Avalanches in Neural Networks with Heavy-Tailed Synaptic Weight Distribution Kuśmierz, Łukasz; Ogawa, Shun; Toyoizumi, Taro Physical Review Letters, Vol. 125, Issue 2 https://doi.org/10.1103/PhysRevLett.125.028101	journal	July 2020
Chaos in Random Neural Networks Sompolinsky, H.; Crisanti, A.; Sommers, H. J. Physical Review Letters, Vol. 61, Issue 3 https://doi.org/10.1103/PhysRevLett.61.259	journal	July 1988
Suppressing chaos in neural networks by noise Molgedey, L.; Schuchhardt, J.; Schuster, H. G. Physical Review Letters, Vol. 69, Issue 26 https://doi.org/10.1103/PhysRevLett.69.3717	journal	December 1992
Gradient Learning in Spiking Neural Networks by Dynamic Perturbation of Conductances Fiete, Ila R.; Seung, H. Sebastian Physical Review Letters, Vol. 97, Issue 4 https://doi.org/10.1103/PhysRevLett.97.048104	journal	July 2006
Repeated sequential learning increases memory capacity via effective decorrelation in a recurrent neural network Kurikawa, Tomoki; Barak, Omri; Kaneko, Kunihiko Physical Review Research, Vol. 2, Issue 2 https://doi.org/10.1103/PhysRevResearch.2.023307	journal	June 2020
Lyapunov spectra of chaotic recurrent neural networks Engelken, Rainer; Wolf, Fred; Abbott, L. F. Physical Review Research, Vol. 5, Issue 4 https://doi.org/10.1103/PhysRevResearch.5.043044	journal	October 2023
Pattern-recognizing stochastic learning automata Barto, Andrew. G.; Anandan, P. IEEE Transactions on Systems, Man, and Cybernetics, Vol. SMC-15, Issue 3 https://doi.org/10.1109/TSMC.1985.6313371	journal	May 1985
Multi-Level Generative Chaotic Recurrent Network for Image Inpainting Chen, Cong; Abbott, Amos; Stilwell, Daniel 2021 IEEE Winter Conference on Applications of Computer Vision (WACV) https://doi.org/10.1109/WACV48630.2021.00367	conference	January 2021
The Asynchronous State in Cortical Circuits Renart, Alfonso; de la Rocha, Jaime; Bartho, Peter Science, Vol. 327, Issue 5965 https://doi.org/10.1126/science.1179850	journal	January 2010
Spontaneous Cortical Activity Reveals Hallmarks of an Optimal Internal Model of the Environment Berkes, Pietro; Orbán, Gergő; Lengyel, Máté Science, Vol. 331, Issue 6013 https://doi.org/10.1126/science.1195870	journal	January 2011
Chaos in Neuronal Networks with Balanced Excitatory and Inhibitory Activity van Vreeswijk, C.; Sompolinsky, H. Science, Vol. 274, Issue 5293 https://doi.org/10.1126/science.274.5293.1724	journal	December 1996
Neuropixels 2.0: A miniaturized high-density probe for stable, long-term brain recordings Steinmetz, Nicholas A.; Aydin, Cagatay; Lebedeva, Anna Science, Vol. 372, Issue 6539 https://doi.org/10.1126/science.abf4588	journal	April 2021
On the Computational Power of Winner-Take-All Maass, Wolfgang Neural Computation, Vol. 12, Issue 11 https://doi.org/10.1162/089976600300014827	journal	November 2000
Real-Time Computation at the Edge of Chaos in Recurrent Neural Networks Bertschinger, Nils; Natschläger, Thomas Neural Computation, Vol. 16, Issue 7 https://doi.org/10.1162/089976604323057443	journal	July 2004
Learning Curves for Stochastic Gradient Descent in Linear Feedforward Networks Werfel, Justin; Xie, Xiaohui; Seung, H. Sebastian Neural Computation, Vol. 17, Issue 12 https://doi.org/10.1162/089976605774320539	journal	December 2005
Neural Dynamics as Sampling: A Model for Stochastic Computation in Recurrent Networks of Spiking Neurons Buesing, Lars; Bill, Johannes; Nessler, Bernhard PLoS Computational Biology, Vol. 7, Issue 11 https://doi.org/10.1371/journal.pcbi.1002211	journal	November 2011
Probabilistic Inference in General Graphical Models through Sampling in Stochastic Networks of Spiking Neurons Pecevski, Dejan; Buesing, Lars; Maass, Wolfgang PLoS Computational Biology, Vol. 7, Issue 12 https://doi.org/10.1371/journal.pcbi.1002294	journal	December 2011
The Hamiltonian Brain: Efficient Probabilistic Inference with Excitatory-Inhibitory Neural Circuit Dynamics Aitchison, Laurence; Lengyel, Máté PLOS Computational Biology, Vol. 12, Issue 12 https://doi.org/10.1371/journal.pcbi.1005186	journal	December 2016
Encoding in Balanced Networks: Revisiting Spike Patterns and Chaos in Stimulus-Driven Systems Lajoie, Guillaume; Lin, Kevin K.; Thivierge, Jean-Philippe PLOS Computational Biology, Vol. 12, Issue 12 https://doi.org/10.1371/journal.pcbi.1005258	journal	December 2016
Neue Begründung der Theorie quadratischer Formen von unendlichvielen Veränderlichen. Hellinger, E. Journal für die reine und angewandte Mathematik (Crelles Journal), Vol. 1909, Issue 136 https://doi.org/10.1515/crll.1909.136.210	journal	July 1909
The Variable Discharge of Cortical Neurons: Implications for Connectivity, Computation, and Information Coding Shadlen, Michael N.; Newsome, William T. The Journal of Neuroscience, Vol. 18, Issue 10 https://doi.org/10.1523/JNEUROSCI.18-10-03870.1998	journal	May 1998
A Reward-Modulated Hebbian Learning Rule Can Explain Experimentally Observed Network Reorganization in a Brain Control Task Legenstein, R.; Chase, S. M.; Schwartz, A. B. Journal of Neuroscience, Vol. 30, Issue 25 https://doi.org/10.1523/JNEUROSCI.4284-09.2010	journal	June 2010
Encoding of Head Direction by Hippocampal Place Cells in Bats Rubin, Alon; Yartsev, Michael M.; Ulanovsky, Nachum The Journal of Neuroscience, Vol. 34, Issue 3 https://doi.org/10.1523/JNEUROSCI.5393-12.2014	journal	January 2014
Eligibility Traces and Plasticity on Behavioral Time Scales: Experimental Support of NeoHebbian Three-Factor Learning Rules Gerstner, Wulfram; Lehmann, Marco; Liakoni, Vasiliki Frontiers in Neural Circuits, Vol. 12 https://doi.org/10.3389/fncir.2018.00053	journal	July 2018
Multiple-Timescale Neural Networks: Generation of History-Dependent Sequences and Inference Through Autonomous Bifurcations Kurikawa, Tomoki; Kaneko, Kunihiko Frontiers in Computational Neuroscience, Vol. 15 https://doi.org/10.3389/fncom.2021.743537	journal	December 2021
Biologically plausible learning in recurrent neural networks reproduces neural dynamics observed during cognitive tasks Miconi, Thomas eLife, Vol. 6 https://doi.org/10.7554/eLife.20899	journal	February 2017
Reward-based training of recurrent neural networks for cognitive and value-based tasks Song, H. Francis; Yang, Guangyu R.; Wang, Xiao-Jing eLife, Vol. 6 https://doi.org/10.7554/eLife.21492	journal	January 2017
Local online learning in recurrent networks with random feedback Murray, James M. eLife, Vol. 8 https://doi.org/10.7554/eLife.43299	journal	May 2019
Motor cortex activity across movement speeds is predicted by network-level strategies for generating muscle activity Saxena, Shreya; Russo, Abigail A.; Cunningham, John eLife, Vol. 11 https://doi.org/10.7554/eLife.67620	journal	May 2022
Sampling motion trajectories during hippocampal theta sequences Ujfalussy, Balazs B.; Orbán, Gergő eLife, Vol. 11 https://doi.org/10.7554/eLife.74058	journal	November 2022
Signatures of Bayesian inference emerge from energy efficient synapses Malkin, James; O'Donnell, Cian; Houghton, Conor https://doi.org/10.7554/eLife.92595.1	preprint	December 2023

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