Asynchronous Cellular Automaton-Based Neuron: Theoretical Analysis and On-FPGA Learning

A generalized asynchronous cellular automaton-based neuron model is a special kind of cellular automaton that is designed to mimic the nonlinear dynamics of neurons. The model can be implemented as an asynchronous sequential logic circuit and its control parameter is the pattern of wires among the circuit elements that is adjustable after implementation in a field-programmable gate array (FPGA) device. In this paper, a novel theoretical analysis method for the model is presented. Using this method, stabilities of neuron-like orbits and occurrence mechanisms of neuron-like bifurcations of the model are clarified theoretically. Also, a novel learning algorithm for the model is presented. An equivalent experiment shows that an FPGA-implemented learning algorithm enables an FPGA-implemented model to automatically reproduce typical nonlinear responses and occurrence mechanisms observed in biological and model neurons.

[1]  Eugene M. Izhikevich,et al.  Which model to use for cortical spiking neurons? , 2004, IEEE Transactions on Neural Networks.

[2]  Eduardo Ros,et al.  Real-time computing platform for spiking neurons (RT-spike) , 2006, IEEE Trans. Neural Networks.

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

[4]  Takashi Matsubara,et al.  Neuron-Like Responses and Bifurcations of a Generalized Asynchronous Sequential Logic Spiking Neuron Model , 2012, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[5]  Tetsuya Hishiki,et al.  A Generalized Rotate-and-Fire Digital Spiking Neuron Model and Its On-FPGA Learning , 2011, IEEE Transactions on Circuits and Systems II: Express Briefs.

[6]  Nikil D. Dutt,et al.  A configurable simulation environment for the efficient simulation of large-scale spiking neural networks on graphics processors , 2009, Neural Networks.

[7]  K.V. Shenoy,et al.  Power feasibility of implantable digital spike sorting circuits for neural prosthetic systems , 2005, IEEE Transactions on Neural Systems and Rehabilitation Engineering.

[8]  Gert Cauwenberghs,et al.  Dynamically Reconfigurable Silicon Array of Spiking Neurons With Conductance-Based Synapses , 2007, IEEE Transactions on Neural Networks.

[9]  Sylvie Renaud,et al.  Real-Time Simulation of Biologically Realistic Stochastic Neurons in VLSI , 2010, IEEE Transactions on Neural Networks.

[10]  C. Budd,et al.  Review of ”Piecewise-Smooth Dynamical Systems: Theory and Applications by M. di Bernardo, C. Budd, A. Champneys and P. 2008” , 2020 .

[11]  Kea-Tiong Tang,et al.  VLSI Implementation of a Bio-Inspired Olfactory Spiking Neural Network , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[12]  Takashi Matsubara,et al.  A Novel Bifurcation-Based Synthesis of Asynchronous Cellular Automaton Based Neuron , 2012, ICANN.

[13]  Anthony G. Pipe,et al.  Implementing Spiking Neural Networks for Real-Time Signal-Processing and Control Applications: A Model-Validated FPGA Approach , 2007, IEEE Transactions on Neural Networks.

[14]  Narayan Srinivasa,et al.  Programming Time-Multiplexed Reconfigurable Hardware Using a Scalable Neuromorphic Compiler , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[15]  Sylvie Renaud,et al.  A $Q$ -Modification Neuroadaptive Control Architecture for Discrete-Time Systems , 2010 .

[16]  G. Edelman,et al.  Spike-timing dynamics of neuronal groups. , 2004, Cerebral cortex.

[17]  Michael J. Watts,et al.  IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS Publication Information , 2020, IEEE Transactions on Neural Networks and Learning Systems.

[18]  Sho Hashimoto,et al.  A Novel Hybrid Spiking Neuron: Bifurcations, Responses, and On-Chip Learning , 2010, IEEE Transactions on Circuits and Systems I: Regular Papers.

[19]  Eugene M. Izhikevich,et al.  Simple model of spiking neurons , 2003, IEEE Trans. Neural Networks.

[20]  Liam McDaid,et al.  Silicon-Based Dynamic Synapse With Depressing Response , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[21]  Arindam Basu,et al.  Neural Dynamics in Reconfigurable Silicon , 2010, IEEE Transactions on Biomedical Circuits and Systems.

[22]  Takashi Matsubara,et al.  A generalized asynchronous digital spiking neuron: Theoretical analysis and compartmental model , 2012, The 2012 International Joint Conference on Neural Networks (IJCNN).

[23]  R.H. Lee,et al.  Methodology and Design Flow for Assisted Neural-Model Implementations in FPGAs , 2007, IEEE Transactions on Neural Systems and Rehabilitation Engineering.

[24]  J. A. Kuznecov Elements of applied bifurcation theory , 1998 .

[25]  G. Bi,et al.  Synaptic Modifications in Cultured Hippocampal Neurons: Dependence on Spike Timing, Synaptic Strength, and Postsynaptic Cell Type , 1998, The Journal of Neuroscience.

[26]  Tetsuya Hishiki,et al.  A Novel Rotate-and-Fire Digital Spiking Neuron and its Neuron-Like Bifurcations and Responses , 2011, IEEE Transactions on Neural Networks.

[27]  A. Hodgkin The local electric changes associated with repetitive action in a non‐medullated axon , 1948, The Journal of physiology.

[28]  Don M. Long Toward replacement parts of the brain, implantable biomimetic electronics as neural prostheses , 2006 .

[29]  Kwabena Boahen,et al.  Silicon-Neuron Design: A Dynamical Systems Approach , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[30]  Takashi Matsubara,et al.  A novel asynchronous digital spiking neuron model and its various neuron-like bifurcations and responses , 2011, The 2011 International Joint Conference on Neural Networks.

[31]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[32]  Takashi Matsubara,et al.  Dynamic Response Behaviors of a Generalized Asynchronous Digital Spiking Neuron Model , 2011, ICONIP.