ROBUST TIMING AND MOTOR PATTERNS BY TAMING CHAOS IN RECURRENT NEURAL NETWORKS

The brain's ability to tell time and produce complex spatiotemporal motor patterns is critical for anticipating the next ring of a telephone or playing a musical instrument. One class of models proposes that these abilities emerge from dynamically changing patterns of neural activity generated in recurrent neural networks. However, the relevant dynamic regimes of recurrent networks are highly sensitive to noise; that is, chaotic. We developed a firing rate model that tells time on the order of seconds and generates complex spatiotemporal patterns in the presence of high levels of noise. This is achieved through the tuning of the recurrent connections. The network operates in a dynamic regime that exhibits coexisting chaotic and locally stable trajectories. These stable patterns function as 'dynamic attractors' and provide a feature that is characteristic of biological systems: the ability to 'return' to the pattern being generated in the face of perturbations.

[1]  Dean V. Buonomano,et al.  Neural Network Model of the Cerebellum: Temporal Discrimination and the Timing of Motor Responses , 1999, Neural Computation.

[2]  D. Hansel,et al.  Very long transients, irregular firing, and chaotic dynamics in networks of randomly connected inhibitory integrate-and-fire neurons. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  P. J. Sjöström,et al.  Correction: Highly Nonrandom Features of Synaptic Connectivity in Local Cortical Circuits , 2005, PLoS Biology.

[4]  Xiao-Jing Wang.  Synaptic reverberation underlying mnemonic persistent activity , 2001, Trends in Neurosciences.

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

[6]  José Carlos Príncipe,et al.  Special issue on echo state networks and liquid state machines , 2007, Neural Networks.

[7]  Javier F. Medina,et al.  Computer simulation of cerebellar information processing , 2000, Nature Neuroscience.

[8]  Javier F. Medina,et al.  Timing Mechanisms in the Cerebellum: Testing Predictions of a Large-Scale Computer Simulation , 2000, The Journal of Neuroscience.

[9]  M. London,et al.  Sensitivity to perturbations in vivo implies high noise and suggests rate coding in cortex , 2010, Nature.

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

[11]  Daniel Durstewitz,et al.  Self-Organizing Neural Integrator Predicts Interval Times through Climbing Activity , 2003, The Journal of Neuroscience.

[12]  Guido Boffetta,et al.  Detecting barriers to transport: a review of different techniques , 2001, nlin/0102022.

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

[14]  D. Munson.  Circuits and systems , 1982, Proceedings of the IEEE.

[15]  Andrea Milani,et al.  Stable Chaos in the Asteroid Belt , 1997 .

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

[17]  Gustavo Deco,et al.  Computational significance of transient dynamics in cortical networks , 2007, The European journal of neuroscience.

[18]  A. Litwin-Kumar,et al.  Slow dynamics and high variability in balanced cortical networks with clustered connections , 2012, Nature Neuroscience.

[19]  Asohan Amarasingham,et al.  Internally Generated Cell Assembly Sequences in the Rat Hippocampus , 2008, Science.

[20]  G. Fagiolo.  Clustering in complex directed networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  F. Wolf,et al.  Dynamic Flux Tubes Form Reservoirs of Stability in Neuronal Circuits , 2012 .

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

[23]  Jonathan D. Cohen,et al.  A Model of Interval Timing by Neural Integration , 2011, The Journal of Neuroscience.

[24]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[25]  Hugo Merchant,et al.  Measuring time with different neural chronometers during a synchronization-continuation task , 2011, Proceedings of the National Academy of Sciences.

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

[27]  S. Keele,et al.  Dissociation of the lateral and medial cerebellum in movement timing and movement execution , 2004, Experimental Brain Research.

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

[29]  H. Kantz.  A robust method to estimate the maximal Lyapunov exponent of a time series , 1994 .

[30]  G. Edelman,et al.  Large-scale model of mammalian thalamocortical systems , 2008, Proceedings of the National Academy of Sciences.

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

[32]  M. Nicolelis,et al.  Interval timing and the encoding of signal duration by ensembles of cortical and striatal neurons. , 2003, Behavioral neuroscience.

[33]  Alexandre Pouget,et al.  Dynamical Constraints on Using Precise Spike Timing to Compute in Recurrent Cortical Networks , 2008, Neural Computation.

[34]  Dean V Buonomano,et al.  Embedding Multiple Trajectories in Simulated Recurrent Neural Networks in a Self-Organizing Manner , 2009, The Journal of Neuroscience.

[35]  M. Shadlen,et al.  A representation of the hazard rate of elapsed time in macaque area LIP , 2005, Nature Neuroscience.

[36]  J. Yorke,et al.  Strange attractors that are not chaotic , 1984 .

[37]  Catalin V. Buhusi,et al.  What makes us tick? Functional and neural mechanisms of interval timing , 2005, Nature Reviews Neuroscience.

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

[39]  A. Wolf,et al.  Determining Lyapunov exponents from a time series , 1985 .

[40]  Andrea Milani,et al.  An example of stable chaos in the Solar System , 1992, Nature.

[41]  Sen Song,et al.  Highly Nonrandom Features of Synaptic Connectivity in Local Cortical Circuits , 2005, PLoS biology.

[42]  D. Buonomano,et al.  Population clocks: motor timing with neural dynamics , 2010, Trends in Cognitive Sciences.

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

[44]  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.

[45]  Dezhe Z. Jin,et al.  Support for a synaptic chain model of neuronal sequence generation , 2010, Nature.

[46]  A. Nobre,et al.  Dissociating explicit timing from temporal expectation with fMRI , 2008, Current Opinion in Neurobiology.

[47]  S. Haykin,et al.  Adaptive Filter Theory , 1986 .

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

[49]  K. D. Punta,et al.  An ultra-sparse code underlies the generation of neural sequences in a songbird , 2002 .

[50]  Stephen G. Lisberger,et al.  Learned Timing of Motor Behavior in the Smooth Eye Movement Region of the Frontal Eye Fields , 2011, Neuron.

[51]  R. Church,et al.  Application of scalar timing theory to individual trials. , 1994, Journal of experimental psychology. Animal behavior processes.

[52]  J. Yorke,et al.  Crises, sudden changes in chaotic attractors, and transient chaos , 1983 .

[53]  M M Merzenich,et al.  Temporal information transformed into a spatial code by a neural network with realistic properties , 1995, Science.

[54]  Nicolas Brunel,et al.  Dynamics of networks of randomly connected excitatory and inhibitory spiking neurons , 2000, Journal of Physiology-Paris.

[55]  M. Sahani,et al.  Observers Exploit Stochastic Models of Sensory Change to Help Judge the Passage of Time , 2011, Current Biology.

[56]  Andrew M. Clark,et al.  Stimulus onset quenches neural variability: a widespread cortical phenomenon , 2010, Nature Neuroscience.

[57]  Emiliano Macaluso,et al.  Learning about Time: Plastic Changes and Interindividual Brain Differences , 2012, Neuron.

[58]  Ian G Woods,et al.  The you Gene Encodes an EGF-CUB Protein Essential for Hedgehog Signaling in Zebrafish , 2005, PLoS biology.

[59]  Christopher Miall,et al.  The Storage of Time Intervals Using Oscillating Neurons , 1989, Neural Computation.

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

[61]  W. Freeman,et al.  How brains make chaos in order to make sense of the world , 1987, Behavioral and Brain Sciences.

[62]  H. Sompolinsky,et al.  Chaos in Neuronal Networks with Balanced Excitatory and Inhibitory Activity , 1996, Science.

[63]  John E. Schlerf,et al.  Dedicated and intrinsic models of time perception , 2008, Trends in Cognitive Sciences.

[64]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[65]  Richard Hans Robert Hahnloser,et al.  An ultra-sparse code underliesthe generation of neural sequences in a songbird , 2002, Nature.