Computation Through Neural Population Dynamics.

Significant experimental, computational, and theoretical work has identified rich structure within the coordinated activity of interconnected neural populations. An emerging challenge now is to uncover the nature of the associated computations, how they are implemented, and what role they play in driving behavior. We term this computation through neural population dynamics. If successful, this framework will reveal general motifs of neural population activity and quantitatively describe how neural population dynamics implement computations necessary for driving goal-directed behavior. Here, we start with a mathematical primer on dynamical systems theory and analytical tools necessary to apply this perspective to experimental data. Next, we highlight some recent discoveries resulting from successful application of dynamical systems. We focus on studies spanning motor control, timing, decision-making, and working memory. Finally, we briefly discuss promising recent lines of investigation and future directions for the computation through neural population dynamics framework.

[1]  Eva L. Dyer,et al.  Latent Factors and Dynamics in Motor Cortex and Their Application to Brain–Machine Interfaces , 2018, The Journal of Neuroscience.

[2]  Henry Markram,et al.  Real-Time Computing Without Stable States: A New Framework for Neural Computation Based on Perturbations , 2002, Neural Computation.

[3]  Bingni W. Brunton,et al.  Extracting spatial–temporal coherent patterns in large-scale neural recordings using dynamic mode decomposition , 2014, Journal of Neuroscience Methods.

[4]  Francis R. Willett,et al.  Neural ensemble dynamics in dorsal motor cortex during speech in people with paralysis , 2018, bioRxiv.

[5]  Gamaleldin F. Elsayed,et al.  Structure in neural population recordings: an expected byproduct of simpler phenomena? , 2017, Nature Neuroscience.

[6]  Kristin Branson,et al.  Cortical pattern generation during dexterous movement is input-driven , 2019, Nature.

[7]  A. Schwartz,et al.  Behavioral and neural correlates of visuomotor adaptation observed through a brain-computer interface in primary motor cortex. , 2012, Journal of neurophysiology.

[8]  Rishidev Chaudhuri,et al.  Computational principles of memory , 2016, Nature Neuroscience.

[9]  Mehrdad Jazayeri,et al.  Navigating the Neural Space in Search of the Neural Code , 2017, Neuron.

[10]  R. Yuste,et al.  Controlling Visually Guided Behavior by Holographic Recalling of Cortical Ensembles , 2019, Cell.

[11]  Chethan Pandarinath,et al.  Inferring single-trial neural population dynamics using sequential auto-encoders , 2017, Nature Methods.

[12]  Mark M Churchland,et al.  Motor cortex signals for each arm are mixed across hemispheres and neurons yet partitioned within the population response , 2019, eLife.

[13]  R Shadmehr,et al.  Electromyographic Correlates of Learning an Internal Model of Reaching Movements , 1999, The Journal of Neuroscience.

[14]  Kevin L. Briggman,et al.  Optical Imaging of Neuronal Populations During Decision-Making , 2005, Science.

[15]  Lee E. Miller,et al.  Long-term stability of cortical population dynamics underlying consistent behavior , 2019, Nature Neuroscience.

[16]  Earl K. Miller,et al.  Working Memory 2.0 , 2018, Neuron.

[17]  Brent Doiron,et al.  Bridging large-scale neuronal recordings and large-scale network models using dimensionality reduction , 2018, Current Opinion in Neurobiology.

[18]  K. Shenoy,et al.  A Central Source of Movement Variability , 2006, Neuron.

[19]  Julie Messier,et al.  Differential effect of task conditions on errors of direction and extent of reaching movements , 1997, Experimental Brain Research.

[20]  Sergey L. Gratiy,et al.  Fully integrated silicon probes for high-density recording of neural activity , 2017, Nature.

[21]  Byron M. Yu,et al.  Dimensionality reduction for large-scale neural recordings , 2014, Nature Neuroscience.

[22]  R Huerta,et al.  Dynamical encoding by networks of competing neuron groups: winnerless competition. , 2001, Physical review letters.

[23]  Hansem Sohn,et al.  Bayesian Computation through Cortical Latent Dynamics , 2018, Neuron.

[24]  Xiao-Jing Wang,et al.  Task representations in neural networks trained to perform many cognitive tasks , 2019, Nature Neuroscience.

[25]  U. Karmarkar,et al.  Timing in the Absence of Clocks: Encoding Time in Neural Network States , 2007, Neuron.

[26]  Jose M. Carmena,et al.  Closed-Loop Decoder Adaptation Shapes Neural Plasticity for Skillful Neuroprosthetic Control , 2014, Neuron.

[27]  Byron M. Yu,et al.  Constraints on neural redundancy , 2018, eLife.

[28]  Mikhail A Lebedev,et al.  Analysis of neuronal ensemble activity reveals the pitfalls and shortcomings of rotation dynamics , 2019, Scientific Reports.

[29]  Stephen I. Ryu,et al.  Neural Dynamics of Reaching following Incorrect or Absent Motor Preparation , 2014, Neuron.

[30]  Krishna V. Shenoy,et al.  Combining Decoder Design and Neural Adaptation in Brain-Machine Interfaces , 2014, Neuron.

[31]  Rishidev Chaudhuri,et al.  The intrinsic attractor manifold and population dynamics of a canonical cognitive circuit across waking and sleep , 2019, Nature Neuroscience.

[32]  Surya Ganguli,et al.  Unsupervised Discovery of Demixed, Low-Dimensional Neural Dynamics across Multiple Timescales through Tensor Component Analysis , 2017, Neuron.

[33]  Dmitri B. Chklovskii,et al.  Neuronal Circuits Underlying Persistent Representations Despite Time Varying Activity , 2012, Current Biology.

[34]  Stephen I. Ryu,et al.  Motor Cortical Visuomotor Feedback Activity Is Initially Isolated from Downstream Targets in Output-Null Neural State Space Dimensions , 2017, Neuron.

[35]  P. Killeen,et al.  A behavioral theory of timing. , 1988, Psychological review.

[36]  Mark M. Churchland,et al.  Motor cortex signals corresponding to the two arms are shared across hemispheres, mixed among neurons, yet partitioned within the population response , 2019, bioRxiv.

[37]  Marc H. Schieber,et al.  Condition-Dependent Neural Dimensions Progressively Shift during Reach to Grasp , 2018, Cell reports.

[38]  D. Hubel,et al.  Receptive fields, binocular interaction and functional architecture in the cat's visual cortex , 1962, The Journal of physiology.

[39]  R. Yuste,et al.  Simultaneous two-photon imaging and two-photon optogenetics of cortical circuits in three dimensions , 2018, eLife.

[40]  Paul Cisek,et al.  Neural activity in primary motor and dorsal premotor cortex in reaching tasks with the contralateral versus ipsilateral arm. , 2003, Journal of neurophysiology.

[41]  E. Evarts,et al.  Relation of pyramidal tract activity to force exerted during voluntary movement. , 1968, Journal of neurophysiology.

[42]  John P. Cunningham,et al.  Dynamical segmentation of single trials from population neural data , 2011, NIPS.

[43]  Byron M. Yu,et al.  Factor-analysis methods for higher-performance neural prostheses. , 2009, Journal of neurophysiology.

[44]  Sandro Romani,et al.  Discrete attractor dynamics underlies persistent activity in the frontal cortex , 2019, Nature.

[45]  David Sussillo,et al.  Opening the Black Box: Low-Dimensional Dynamics in High-Dimensional Recurrent Neural Networks , 2013, Neural Computation.

[46]  Matthew T. Kaufman,et al.  A neural network that finds a naturalistic solution for the production of muscle activity , 2015, Nature Neuroscience.

[47]  Byron M. Yu,et al.  Cortical Areas Interact through a Communication Subspace , 2019, Neuron.

[48]  Robert E Kass,et al.  Functional network reorganization during learning in a brain-computer interface paradigm , 2008, Proceedings of the National Academy of Sciences.

[49]  Abigail A. Russo,et al.  Neural Trajectories in the Supplementary Motor Area and Motor Cortex Exhibit Distinct Geometries, Compatible with Different Classes of Computation , 2019, Neuron.

[50]  John P. Cunningham,et al.  Single-Neuron Stability during Repeated Reaching in Macaque Premotor Cortex , 2007, The Journal of Neuroscience.

[51]  John F. Kalaska,et al.  Emerging ideas and tools to study the emergent properties of the cortical neural circuits for voluntary motor control in non-human primates , 2019, F1000Research.

[52]  Richard A. Andersen,et al.  Intrinsic Variable Learning for Brain-Machine Interface Control by Human Anterior Intraparietal Cortex , 2019, Neuron.

[53]  Zachary F Mainen,et al.  Preparing and selecting actions with neural populations: toward cortical circuit mechanisms , 2015, Current Opinion in Neurobiology.

[54]  David J. Freedman,et al.  Computing by Robust Transience: How the Fronto-Parietal Network Performs Sequential, Category-Based Decisions , 2017, Neuron.

[55]  Shreya Saxena,et al.  Towards the neural population doctrine , 2019, Current Opinion in Neurobiology.

[56]  Michael N. Shadlen,et al.  A Neural Mechanism for Sensing and Reproducing a Time Interval , 2015, Current Biology.

[57]  D V Buonomano,et al.  Decoding Temporal Information: A Model Based on Short-Term Synaptic Plasticity , 2000, The Journal of Neuroscience.

[58]  Byron M. Yu,et al.  Neural constraints on learning , 2014, Nature.

[59]  Xiao-Jing Wang,et al.  Reward-based training of recurrent neural networks for cognitive and value-based tasks , 2016, bioRxiv.

[60]  Krishna V. Shenoy,et al.  The need for calcium imaging in nonhuman primates: New motor neuroscience and brain-machine interfaces , 2017, Experimental Neurology.

[61]  Christian Ethier,et al.  Cortical population activity within a preserved neural manifold underlies multiple motor behaviors , 2018, Nature Communications.

[62]  Omri Barak,et al.  Recurrent neural networks as versatile tools of neuroscience research , 2017, Current Opinion in Neurobiology.

[63]  Matthew T. Kaufman,et al.  Supplementary materials for : Cortical activity in the null space : permitting preparation without movement , 2014 .

[64]  W. Meck.  Neuropharmacology of timing and time perception. , 1996, Brain research. Cognitive brain research.

[65]  Krishna V Shenoy,et al.  Structure and variability of delay activity in premotor cortex , 2019, PLoS Comput. Biol..

[66]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1952, The Journal of physiology.

[67]  Matthew T. Kaufman,et al.  The Largest Response Component in the Motor Cortex Reflects Movement Timing but Not Movement Type , 2016, eNeuro.

[68]  Abigail A. Russo,et al.  Motor Cortex Embeds Muscle-like Commands in an Untangled Population Response , 2018, Neuron.

[69]  A. Riehle,et al.  Monkey primary motor and premotor cortex: single-cell activity related to prior information about direction and extent of an intended movement. , 1989, Journal of neurophysiology.

[70]  Kevin L. Briggman,et al.  From crawling to cognition: analyzing the dynamical interactions among populations of neurons , 2006, Current Opinion in Neurobiology.

[71]  Marc Levoy,et al.  Neuronal Dynamics Regulating Brain and Behavioral State Transitions , 2019, Cell.

[72]  M. Sahani,et al.  Cortical control of arm movements: a dynamical systems perspective. , 2013, Annual review of neuroscience.

[73]  Annika L A Nichols,et al.  A global brain state underlies C. elegans sleep behavior , 2017, Science.

[74]  D. Buonomano,et al.  The neural basis of temporal processing. , 2004, Annual review of neuroscience.

[75]  S. Wise.  The primate premotor cortex: past, present, and preparatory. , 1985, Annual review of neuroscience.

[76]  Hugo L. Fernandes,et al.  Primary motor cortical discharge during force field adaptation reflects muscle-like dynamics. , 2013, Journal of neurophysiology.

[77]  Stephen I. Ryu,et al.  Causal Role of Motor Preparation during Error-Driven Learning , 2020, Neuron.

[78]  Byron M. Yu,et al.  Extracting Dynamical Structure Embedded in Neural Activity , 2005, NIPS.

[79]  Jude F. Mitchell,et al.  Spatial Attention Decorrelates Intrinsic Activity Fluctuations in Macaque Area V4 , 2009, Neuron.

[80]  G. Schöner,et al.  Preshaping and continuous evolution of motor cortical representations during movement preparation , 2003, The European journal of neuroscience.

[81]  Abigail A. Russo,et al.  Neural Trajectories in the Supplementary Motor Area and Motor Cortex Exhibit Distinct Geometries, Compatible with Different Classes of Computation , 2020, Neuron.

[82]  V. Jayaraman,et al.  Ring attractor dynamics in the Drosophila central brain , 2017, Science.

[83]  P. Killeen,et al.  A behavioral theory of timing , 1988 .

[84]  Jose M. Carmena,et al.  Emergence of Coordinated Neural Dynamics Underlies Neuroprosthetic Learning and Skillful Control , 2017, Neuron.

[85]  Juliana Y. Rhee,et al.  Acute off-target effects of neural circuit manipulations , 2015, Nature.

[86]  Gopal Santhanam,et al.  Preparatory activity in premotor and motor cortex reflects the speed of the upcoming reach. , 2006, Journal of neurophysiology.

[87]  L .Paninski,et al.  Neural data science: accelerating the experiment-analysis-theory cycle in large-scale neuroscience , 2017, Current Opinion in Neurobiology.

[88]  A P Georgopoulos,et al.  On the relations between the direction of two-dimensional arm movements and cell discharge in primate motor cortex , 1982, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[89]  Devika Narain,et al.  A Dynamical Systems Perspective on Flexible Motor Timing , 2018, Trends in Cognitive Sciences.

[90]  Guangyu R. Yang,et al.  Training Excitatory-Inhibitory Recurrent Neural Networks for Cognitive Tasks: A Simple and Flexible Framework , 2016, PLoS Comput. Biol..

[91]  John P. Cunningham,et al.  Tensor Analysis Reveals Distinct Population Structure that Parallels the Different Computational Roles of Areas M1 and V1 , 2016, PLoS Comput. Biol..

[92]  Mark M. Churchland,et al.  The roles of monkey M1 neuron classes in movement preparation and execution , 2013, Journal of neurophysiology.

[93]  Robert D Flint,et al.  Long-Term Stability of Motor Cortical Activity: Implications for Brain Machine Interfaces and Optimal Feedback Control , 2016, The Journal of Neuroscience.

[94]  Matthew T. Kaufman,et al.  Neural population dynamics during reaching , 2012, Nature.

[95]  Byron M. Yu,et al.  Neural Variability in Premotor Cortex Provides a Signature of Motor Preparation , 2006, The Journal of Neuroscience.

[96]  Devika Narain,et al.  Flexible timing by temporal scaling of cortical responses , 2017, Nature Neuroscience.

[97]  David J. Freedman,et al.  Preferential Encoding of Visual Categories in Parietal Cortex Compared to Prefrontal Cortex , 2011, Nature Neuroscience.

[98]  Chethan Pandarinath,et al.  Neural population dynamics in human motor cortex during movements in people with ALS , 2015, eLife.

[99]  Naoshige Uchida,et al.  Demixed principal component analysis of neural population data , 2014, eLife.

[100]  Tadashi Isa,et al.  Reflexive limb selection and control of reach direction to moving targets in cats, monkeys, and humans. , 2010, Journal of neurophysiology.

[101]  William E. Allen,et al.  Thirst regulates motivated behavior through modulation of brainwide neural population dynamics , 2019, Science.

[102]  Hansjörg Scherberger,et al.  Predicting Reaction Time from the Neural State Space of the Premotor and Parietal Grasping Network , 2015, The Journal of Neuroscience.

[103]  D. Rosenbaum.  Human movement initiation: specification of arm, direction, and extent. , 1980, Journal of experimental psychology. General.

[104]  Nicholas A. Steinmetz,et al.  Spontaneous behaviors drive multidimensional, brainwide activity , 2019, Science.

[105]  V. Jayaraman,et al.  Encoding and Decoding of Overlapping Odor Sequences , 2006, Neuron.

[106]  Francis R. Willett,et al.  Neural ensemble dynamics in dorsal motor cortex during speech in people with paralysis , 2019, eLife.

[107]  D. Wolpert,et al.  Motor learning , 2010, Current Biology.

[108]  W. Newsome,et al.  Context-dependent computation by recurrent dynamics in prefrontal cortex , 2013, Nature.

[109]  Hansjörg Scherberger,et al.  Neural Population Dynamics during Reaching Are Better Explained by a Dynamical System than Representational Tuning , 2016, PLoS Comput. Biol..

[110]  Matthew T. Kaufman,et al.  A category-free neural population supports evolving demands during decision-making , 2014, Nature Neuroscience.

[111]  David J. Freedman,et al.  Experience-dependent representation of visual categories in parietal cortex , 2006, Nature.

[112]  Christof Koch,et al.  Optogenetics: 10 years after ChR2 in neurons—views from the community , 2015, Nature Neuroscience.

[113]  Gilles Laurent,et al.  Transient Dynamics for Neural Processing , 2008, Science.

[114]  Konrad Paul Kording,et al.  Relevance of error: what drives motor adaptation? , 2009, Journal of neurophysiology.

[115]  M. Orger,et al.  Whole-Brain Activity Maps Reveal Stereotyped, Distributed Networks for Visuomotor Behavior , 2014, Neuron.

[116]  Surya Ganguli,et al.  Accurate Estimation of Neural Population Dynamics without Spike Sorting , 2017, Neuron.

[117]  Byron M. Yu,et al.  Single-Trial Neural Correlates of Arm Movement Preparation , 2011, Neuron.

[118]  L. F. Abbott,et al.  Generating Coherent Patterns of Activity from Chaotic Neural Networks , 2009, Neuron.

[119]  Haim Sompolinsky,et al.  From Whole-Brain Data to Functional Circuit Models: The Zebrafish Optomotor Response , 2016, Cell.

[120]  Lee E. Miller,et al.  Neural Manifolds for the Control of Movement , 2017, Neuron.

[121]  Surya Ganguli,et al.  Cortical layer–specific critical dynamics triggering perception , 2019, Science.

[122]  Stephen I. Ryu,et al.  Trial-by-Trial Motor Cortical Correlates of a Rapidly Adapting Visuomotor Internal Model , 2017, The Journal of Neuroscience.

[123]  A Bastian,et al.  Prior information preshapes the population representation of movement direction in motor cortex , 1998, Neuroreport.

[124]  Nuo Li,et al.  Robust neuronal dynamics in premotor cortex during motor planning , 2016, Nature.

[125]  Byron M. Yu,et al.  Learning by neural reassociation , 2018, Nature Neuroscience.

[126]  J. Cunningham,et al.  Different population dynamics in the supplementary motor area and motor cortex during reaching , 2018, Nature Communications.

[127]  Thomas M. Hall,et al.  A Common Structure Underlies Low-Frequency Cortical Dynamics in Movement, Sleep, and Sedation , 2014, Neuron.

[128]  Steven M Chase,et al.  Distinct types of neural reorganization during long-term learning. , 2019, Journal of neurophysiology.

[129]  Seth W. Egger,et al.  Internal models of sensorimotor integration regulate cortical dynamics , 2019, Nature Neuroscience.

[130]  Emil Wärnberg,et al.  Perturbing low dimensional activity manifolds in spiking neuronal networks , 2019, PLoS Comput. Biol..

[131]  E. Evarts.  TEMPORAL PATTERNS OF DISCHARGE OF PYRAMIDAL TRACT NEURONS DURING SLEEP AND WAKING IN THE MONKEY. , 1964, Journal of neurophysiology.

[132]  James J DiCarlo,et al.  Neural population control via deep image synthesis , 2018, Science.

[133]  V. Jayaraman,et al.  Intensity versus Identity Coding in an Olfactory System , 2003, Neuron.

[134]  Scott W. Linderman,et al.  Bayesian Learning and Inference in Recurrent Switching Linear Dynamical Systems , 2017, AISTATS.

[135]  Drew N. Robson,et al.  Brain-wide neuronal dynamics during motor adaptation in zebrafish , 2012, Nature.

[136]  W. Maass,et al.  State-dependent computations: spatiotemporal processing in cortical networks , 2009, Nature Reviews Neuroscience.

[137]  J. Kalaska,et al.  Comparison of variability of initial kinematics and endpoints of reaching movements , 1999, Experimental Brain Research.

[138]  D. Wolpert,et al.  Motor Planning, Not Execution, Separates Motor Memories , 2016, Neuron.

[139]  Krishna V Shenoy,et al.  Simultaneous motor preparation and execution in a last-moment reach correction task , 2019, Nature Communications.

[140]  M. Treisman.  Temporal discrimination and the indifference interval. Implications for a model of the "internal clock". , 1963, Psychological monographs.

[141]  Byron M. Yu,et al.  Brain–computer interfaces for dissecting cognitive processes underlying sensorimotor control , 2016, Current Opinion in Neurobiology.

[142]  J. Tanji,et al.  Anticipatory activity of motor cortex neurons in relation to direction of an intended movement. , 1976, Journal of neurophysiology.

[143]  John P. Cunningham,et al.  Gaussian-process factor analysis for low-dimensional single-trial analysis of neural population activity , 2008, NIPS.

[144]  K. Shenoy,et al.  Neural Population Dynamics Underlying Motor Learning Transfer , 2018, Neuron.

[145]  Devika Narain,et al.  Flexible sensorimotor computations through rapid reconfiguration of cortical dynamics , 2018 .

[146]  A. P. Georgopoulos,et al.  Neuronal population coding of movement direction. , 1986, Science.

[147]  Matthew T. Kaufman,et al.  Cortical Preparatory Activity: Representation of Movement or First Cog in a Dynamical Machine? , 2010, Neuron.

[148]  Byron M. Yu,et al.  Roles of monkey premotor neuron classes in movement preparation and execution. , 2010, Journal of neurophysiology.

[149]  W. Gerstner,et al.  Optimal Control of Transient Dynamics in Balanced Networks Supports Generation of Complex Movements , 2014, Neuron.

[150]  John W. Krakauer,et al.  Motor Planning , 2015, The Neuroscientist : a review journal bringing neurobiology, neurology and psychiatry.

[151]  J. Maunsell,et al.  Attention improves performance primarily by reducing interneuronal correlations , 2009, Nature Neuroscience.

[152]  Theodore H. Lindsay,et al.  Global Brain Dynamics Embed the Motor Command Sequence of Caenorhabditis elegans , 2015, Cell.

[153]  K. Shenoy,et al.  Temporal complexity and heterogeneity of single-neuron activity in premotor and motor cortex. , 2007, Journal of neurophysiology.

[154]  David Sussillo,et al.  FixedPointFinder: A Tensorflow toolbox for identifying and characterizing fixed points in recurrent neural networks , 2018, J. Open Source Softw..

[155]  Mark M Churchland,et al.  Conservation of preparatory neural events in monkey motor cortex regardless of how movement is initiated , 2018, eLife.

[156]  G. Laurent,et al.  Transient Dynamics versus Fixed Points in Odor Representations by Locust Antennal Lobe Projection Neurons , 2005, Neuron.

[157]  Byron M. Yu,et al.  New neural activity patterns emerge with long-term learning , 2019, Proceedings of the National Academy of Sciences.

[158]  Lee E. Miller,et al.  A neural population mechanism for rapid learning , 2017 .

[159]  John P. Cunningham,et al.  Reorganization between preparatory and movement population responses in motor cortex , 2016, Nature Communications.

[160]  W. Schultz,et al.  Role of primate basal ganglia and frontal cortex in the internal generation of movements , 1992, Experimental Brain Research.

[161]  P. Cisek.  Integrated Neural Processes for Defining Potential Actions and Deciding between Them: A Computational Model , 2006, The Journal of Neuroscience.

[162]  K. Shenoy,et al.  Delay of movement caused by disruption of cortical preparatory activity. , 2007, Journal of neurophysiology.

[163]  Selmaan N. Chettih,et al.  Single-neuron perturbations reveal feature-specific competition in V1 , 2019, Nature.