Neural circuits as computational dynamical systems

Many recent studies of neurons recorded from cortex reveal complex temporal dynamics. How such dynamics embody the computations that ultimately lead to behavior remains a mystery. Approaching this issue requires developing plausible hypotheses couched in terms of neural dynamics. A tool ideally suited to aid in this question is the recurrent neural network (RNN). RNNs straddle the fields of nonlinear dynamical systems and machine learning and have recently seen great advances in both theory and application. I summarize recent theoretical and technological advances and highlight an example of how RNNs helped to explain perplexing high-dimensional neurophysiological data in the prefrontal cortex.

[1]  James Martens,et al.  Deep learning via Hessian-free optimization , 2010, ICML.

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

[3]  Xiao-Jing Wang,et al.  The importance of mixed selectivity in complex cognitive tasks , 2013, Nature.

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

[5]  R. Romo,et al.  Dynamics of Cortical Neuronal Ensembles Transit from Decision Making to Storage for Later Report , 2012, The Journal of Neuroscience.

[6]  Ilya Sutskever,et al.  Training Deep and Recurrent Networks with Hessian-Free Optimization , 2012, Neural Networks: Tricks of the Trade.

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

[8]  Geoffrey E. Hinton,et al.  Training Recurrent Neural Networks , 2013 .

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

[10]  Eberhard E. Fetz,et al.  Cortical mechanisms controlling limb movement , 1993, Current Opinion in Neurobiology.

[11]  Ranulfo Romo,et al.  Flexible Control of Mutual Inhibition: A Neural Model of Two-Interval Discrimination , 2005, Science.

[12]  Paul J. Werbos,et al.  Backpropagation Through Time: What It Does and How to Do It , 1990, Proc. IEEE.

[13]  Timothy D. Hanks,et al.  Bounded Integration in Parietal Cortex Underlies Decisions Even When Viewing Duration Is Dictated by the Environment , 2008, The Journal of Neuroscience.

[14]  Mohamed Chtourou,et al.  On the training of recurrent neural networks , 2011, Eighth International Multi-Conference on Systems, Signals & Devices.

[15]  Jürgen Schmidhuber,et al.  Long Short-Term Memory , 1997, Neural Computation.

[16]  Herbert Jaeger,et al.  Echo State Property Linked to an Input: Exploring a Fundamental Characteristic of Recurrent Neural Networks , 2013, Neural Computation.

[17]  R. Desimone,et al.  Neural mechanisms of selective visual attention. , 1995, Annual review of neuroscience.

[18]  Bruno B Averbeck,et al.  Rapid Sequences of Population Activity Patterns Dynamically Encode Task-Critical Spatial Information in Parietal Cortex , 2010, The Journal of Neuroscience.

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

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

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

[22]  Dean V. Buonomano,et al.  ROBUST TIMING AND MOTOR PATTERNS BY TAMING CHAOS IN RECURRENT NEURAL NETWORKS , 2012, Nature Neuroscience.

[23]  Jefferson E. Roy,et al.  Prefrontal Cortex Activity during Flexible Categorization , 2010, The Journal of Neuroscience.

[24]  J. Cowan,et al.  Excitatory and inhibitory interactions in localized populations of model neurons. , 1972, Biophysical journal.

[25]  Yoshua Bengio,et al.  Learning long-term dependencies with gradient descent is difficult , 1994, IEEE Trans. Neural Networks.

[26]  Herbert Jaeger,et al.  The''echo state''approach to analysing and training recurrent neural networks , 2001 .

[27]  L. Abbott,et al.  Stimulus-dependent suppression of chaos in recurrent neural networks. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  R. Desimone,et al.  Selective attention gates visual processing in the extrastriate cortex. , 1985, Science.

[29]  Xiao-Jing Wang Neural dynamics and circuit mechanisms of decision-making , 2012, Current Opinion in Neurobiology.

[30]  Ilya Sutskever,et al.  Learning Recurrent Neural Networks with Hessian-Free Optimization , 2011, ICML.

[31]  A. Selverston,et al.  Dynamical principles in neuroscience , 2006 .

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

[33]  L. Abbott,et al.  Transferring Learning from External to Internal Weights in Echo-State Networks with Sparse Connectivity , 2012, PloS one.

[34]  Richard A. Andersen,et al.  A back-propagation programmed network that simulates response properties of a subset of posterior parietal neurons , 1988, Nature.

[35]  Christopher D. Harvey,et al.  Choice-specific sequences in parietal cortex during a virtual-navigation decision task , 2012, Nature.

[36]  Paul Miller,et al.  Heterogenous Population Coding of a Short-Term Memory and Decision Task , 2010, The Journal of Neuroscience.

[37]  K. Doya,et al.  Bifurcations in the learning of recurrent neural networks , 1992, [Proceedings] 1992 IEEE International Symposium on Circuits and Systems.

[38]  Sommers,et al.  Chaos in random neural networks. , 1988, Physical review letters.

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

[40]  J. Gold,et al.  The neural basis of decision making. , 2007, Annual review of neuroscience.

[41]  Sukbin Lim,et al.  Noise Tolerance of Attractor and Feedforward Memory Models , 2012, Neural Computation.

[42]  Trevor Bekolay,et al.  Supplementary Materials for A Large-Scale Model of the Functioning Brain , 2012 .

[43]  Xiao-Jing Wang,et al.  Angular Path Integration by Moving “Hill of Activity”: A Spiking Neuron Model without Recurrent Excitation of the Head-Direction System , 2005, The Journal of Neuroscience.

[44]  John J. Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities , 1999 .

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

[46]  Ramón Huerta,et al.  Transient Cognitive Dynamics, Metastability, and Decision Making , 2008, PLoS Comput. Biol..

[47]  J. Rinn,et al.  DeCoN: Genome-wide Analysis of In Vivo Transcriptional Dynamics during Pyramidal Neuron Fate Selection in Neocortex , 2015, Neuron.

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

[49]  E. Miller,et al.  An integrative theory of prefrontal cortex function. , 2001, Annual review of neuroscience.

[50]  W. Newsome,et al.  Neural basis of a perceptual decision in the parietal cortex (area LIP) of the rhesus monkey. , 2001, Journal of neurophysiology.

[51]  H S Seung,et al.  How the brain keeps the eyes still. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[52]  Harald Haas,et al.  Harnessing Nonlinearity: Predicting Chaotic Systems and Saving Energy in Wireless Communication , 2004, Science.

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

[54]  Chris Eliasmith,et al.  A Unified Approach to Building and Controlling Spiking Attractor Networks , 2005, Neural Computation.

[55]  Paul Miller,et al.  Natural stimuli evoke dynamic sequences of states in sensory cortical ensembles , 2007, Proceedings of the National Academy of Sciences.

[56]  L. Abbott,et al.  From fixed points to chaos: Three models of delayed discrimination , 2013, Progress in Neurobiology.

[57]  M. Shadlen,et al.  Response of Neurons in the Lateral Intraparietal Area during a Combined Visual Discrimination Reaction Time Task , 2002, The Journal of Neuroscience.

[58]  J. Reynolds,et al.  Attentional modulation of visual processing. , 2004, Annual review of neuroscience.

[59]  Razvan Pascanu,et al.  Advances in optimizing recurrent networks , 2012, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing.

[60]  Nicholas A. Steinmetz,et al.  Top-down control of visual attention , 2010, Current Opinion in Neurobiology.

[61]  M N Shadlen,et al.  Motion perception: seeing and deciding. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[62]  Surya Ganguli,et al.  Memory traces in dynamical systems , 2008, Proceedings of the National Academy of Sciences.