Approximation of Spike-trains by Digital Spiking Neuron

A digital spiking neuron (DSN) consists of shift registers and can generate spike-trains with various patterns of inter-spike intervals. In this paper we present a learning algorithm for the DSN in order to approximate given spike-trains. We study a case where a student DSN accepts a spike-train from a teacher DSN. It is shown that the student can reproduce a spike-train of the teacher based on the learning algorithm. We also study a case where a chaotic analog spiking neuron is used as a teacher. It is shown that the DSN can approximate a sampled chaotic spike-train with a small error.

[1]  Toshimichi Saito,et al.  Reconfigurable Digital Spiking Neuron and Its Pulse-Coupled Network: Basic Characteristics and Potential Applications , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[2]  Toshimichi Saito,et al.  Various spike-trains from a digital spiking neuron: analysis of inter-spike intervals and their modulation , 2006, The 2006 IEEE International Joint Conference on Neural Network Proceedings.

[3]  Leon Glass,et al.  Bistability, period doubling bifurcations and chaos in a periodically forced oscillator , 1982 .

[4]  Shigetoshi Nara,et al.  Errorless reproduction of given pattern dynamics by means of cellular automata. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Eugene M. Izhikevich,et al.  Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting , 2006 .

[6]  Leon O. Chua,et al.  A Nonlinear Dynamics Perspective of Wolfram's New Kind of Science Part I: Threshold of Complexity , 2002, Int. J. Bifurc. Chaos.

[7]  Reinhard Eckhorn,et al.  Neural mechanisms of scene segmentation: recordings from the visual cortex suggest basic circuits for linking field models , 1999, IEEE Trans. Neural Networks.

[8]  Byeong Gi Lee,et al.  A theory on sequence spaces and shift register generators , 1996, IEEE Trans. Commun..

[9]  Hiroyuki Torikai Basic Characteristics and Learning Potential of a Digital Spiking Neuron , 2007, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[10]  Toshimichi Saito,et al.  Grouping synchronization in a pulse-coupled network of chaotic spiking oscillators , 2004, IEEE Transactions on Neural Networks.

[11]  DeLiang Wang,et al.  Synchrony and Desynchrony in Integrate-and-Fire Oscillators , 1998, Neural Computation.

[12]  J J Hopfield,et al.  Rapid local synchronization of action potentials: toward computation with coupled integrate-and-fire neurons. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[13]  Nabil H. Farhat,et al.  The Bifurcating Neuron Network 2: an analog associative memory , 2002, Neural Networks.

[14]  장태인,et al.  발전소 시뮬레이터 I/O 인터페이스 시스템 통신 프로토콜 설계·구현 , 1999 .

[15]  Toshimichi Saito,et al.  Synchronization phenomena in pulse-coupled networks driven by spike-train inputs , 2004, IEEE Transactions on Neural Networks.

[16]  Ian Oppermann,et al.  UWB wireless sensor networks: UWEN - a practical example , 2004, IEEE Communications Magazine.

[17]  Serdar Iplikci,et al.  Dynamic reconstruction of chaotic systems from inter-spike intervals using least squares support vector machines , 2006 .

[18]  Nikolai F. Rulkov,et al.  Pseudo-chaotic time hopping for UWB impulse radio , 2001 .