Training Spiking Neuronal Networks With Applications in Engineering Tasks

In this paper, spiking neuronal models employing means, variances, and correlations for computation are introduced. We present two approaches in the design of spiking neuronal networks, both of which are applied to engineering tasks. In exploring the input-output relationship of integrate-and-fire (IF) neurons with Poisson inputs, we are able to define mathematically robust learning rules, which can be applied to multilayer and time-series networks. We show through experimental applications that it is possible to train spike-rate networks on function approximation problems and on the dynamic task of robot arm control.

[1]  P. Werbos,et al.  Beyond Regression : "New Tools for Prediction and Analysis in the Behavioral Sciences , 1974 .

[2]  Jianfeng Feng,et al.  Is the integrate-and-fire model good enough?--a review , 2001, Neural Networks.

[3]  J. Knott The organization of behavior: A neuropsychological theory , 1951 .

[4]  Wulfram Gerstner,et al.  SPIKING NEURON MODELS Single Neurons , Populations , Plasticity , 2002 .

[5]  T. Flash,et al.  The coordination of arm movements: an experimentally confirmed mathematical model , 1985, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[6]  Geoffrey E. Hinton,et al.  Learning internal representations by error propagation , 1986 .

[7]  B Tirozzi,et al.  Stochastic resonance tuned by correlations in neural models. , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[8]  Jing Peng,et al.  An Efficient Gradient-Based Algorithm for On-Line Training of Recurrent Network Trajectories , 1990, Neural Computation.

[9]  R. Stein Some models of neuronal variability. , 1967, Biophysical journal.

[10]  A. Hodgkin,et al.  The frequency of nerve action potentials generated by applied currents , 1967, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[11]  R. C. Tees Review of The organization of behavior: A neuropsychological theory. , 2003 .

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

[13]  C. Micchelli Interpolation of scattered data: Distance matrices and conditionally positive definite functions , 1986 .

[14]  E. Bizzi,et al.  Human arm trajectory formation. , 1982, Brain : a journal of neurology.

[15]  Henry C. Tuckwell,et al.  Introduction to theoretical neurobiology , 1988 .

[16]  M. Kawato,et al.  Formation and control of optimal trajectory in human multijoint arm movement , 1989, Biological Cybernetics.

[17]  Phill Rowcliffe,et al.  Spiking perceptrons , 2006, IEEE Transactions on Neural Networks.

[18]  Richard O. Duda,et al.  Pattern classification and scene analysis , 1974, A Wiley-Interscience publication.

[19]  Jianfeng Feng,et al.  Training the integrate-and-fire model with the informax principle: I , 2002 .

[20]  Wolfgang Maass,et al.  Movement Generation with Circuits of Spiking Neurons , 2005, Neural Computation.

[21]  Jianfeng Feng,et al.  Optimal control of neuronal activity. , 2003, Physical review letters.

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

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

[24]  T. Sejnowski,et al.  Correlated neuronal activity and the flow of neural information , 2001, Nature Reviews Neuroscience.

[25]  Jianfeng Feng,et al.  Dynamics of moment neuronal networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  Wulfram Gerstner,et al.  Reduction of the Hodgkin-Huxley Equations to a Single-Variable Threshold Model , 1997, Neural Computation.

[27]  Guido Bugmann,et al.  A Spiking Neuron Model: Applications and Learning , 2002, Neural Networks.

[28]  Wulfram Gerstner,et al.  Spiking Neuron Models , 2002 .

[29]  P J Webros BACKPROPAGATION THROUGH TIME: WHAT IT DOES AND HOW TO DO IT , 1990 .

[30]  Lokendra Shastri,et al.  Learning Phonetic Features Using Connectionist Networks , 1987, IJCAI.

[31]  C. Atkeson,et al.  Kinematic features of unrestrained vertical arm movements , 1985, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[32]  R. L. Hardy Multiquadric equations of topography and other irregular surfaces , 1971 .

[33]  B. Schrauwen,et al.  Isolated word recognition with the Liquid State Machine: a case study , 2005, Inf. Process. Lett..

[34]  C. Nicholson Electric current flow in excitable cells J. J. B. Jack, D. Noble &R. W. Tsien Clarendon Press, Oxford (1975). 502 pp., £18.00 , 1976, Neuroscience.

[35]  Jianfeng Feng,et al.  Training integrate-and-fire neurons with the Informax principle II , 2003, IEEE Trans. Neural Networks.

[36]  Sander M. Bohte,et al.  Error-backpropagation in temporally encoded networks of spiking neurons , 2000, Neurocomputing.

[37]  Frank Rosenblatt,et al.  PRINCIPLES OF NEURODYNAMICS. PERCEPTRONS AND THE THEORY OF BRAIN MECHANISMS , 1963 .

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

[39]  O. L. Z. Book Review: The Organization of Behaviour: A Neuropsychological Theory , 1950 .

[40]  Bruce W. Knight,et al.  Dynamics of Encoding in a Population of Neurons , 1972, The Journal of general physiology.