Towards Deterministic and Stochastic Computations with the Izhikevich Spiking-Neuron Model

In this paper we analyze simple computations with spiking neural networks (SNN), laying the foundation for more sophisticated calculations. We consider both a deterministic and a stochastic computation framework with SNNs, by utilizing the Izhikevich neuron model in various simulated experiments. Within the deterministic-computation framework, we design and implement fundamental mathematical operators such as addition, subtraction, multiplexing and multiplication. We show that cross-inhibition of groups of neurons in a winner-takes-all (WTA) network-configuration produces considerable computation power and results in the generation of selective behavior that can be exploited in various robotic control tasks. In the stochastic-computation framework, we discuss an alternative computation paradigm to the classic von Neumann architecture, which supports information storage and decision making. This paradigm uses the experimentally-verified property of networks of randomly connected spiking neurons, of storing information as a stationary probability distribution in each of the sub-network of the SNNs. We reproduce this property by simulating the behavior of a toy-network of randomly-connected stochastic Izhikevich neurons.

[1]  Tim Gollisch,et al.  Modeling Single-Neuron Dynamics and Computations: A Balance of Detail and Abstraction , 2006, Science.

[2]  F. Gabbiani,et al.  Logarithmic Compression of Sensory Signals within the Dendritic Tree of a Collision-Sensitive Neuron , 2012, The Journal of Neuroscience.

[3]  Wolfgang Maass,et al.  On the Computational Power of Winner-Take-All , 2000, Neural Computation.

[4]  C. Koch,et al.  Methods in Neuronal Modeling: From Ions to Networks , 1998 .

[5]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1990 .

[6]  H. Pashler,et al.  Measuring the Crowd Within , 2008, Psychological science.

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

[8]  Stefan Habenschuss,et al.  Stochastic Computations in Cortical Microcircuit Models , 2013, PLoS Comput. Biol..

[9]  Erik De Schutter,et al.  Computational Modeling Methods for Neuroscientists , 2009 .

[10]  Johannes Schemmel,et al.  Six Networks on a Universal Neuromorphic Computing Substrate , 2012, Front. Neurosci..

[11]  Giacomo Indiveri,et al.  Spiking analog VLSI neuron assemblies as constraint satisfaction problem solvers , 2015, 2016 IEEE International Symposium on Circuits and Systems (ISCAS).

[12]  Stefan Habenschuss,et al.  Solving Constraint Satisfaction Problems with Networks of Spiking Neurons , 2016, Front. Neurosci..

[13]  Wolfgang Maass,et al.  Noise as a Resource for Computation and Learning in Networks of Spiking Neurons , 2014, Proceedings of the IEEE.

[14]  Koji Ishihara,et al.  Control of the Correlation of Spontaneous Neuron Activity in Biological and Noise-activated CMOS Artificial Neural Microcircuits , 2017, ArXiv.

[15]  Charles Kemp,et al.  How to Grow a Mind: Statistics, Structure, and Abstraction , 2011, Science.

[16]  L. Abbott,et al.  Model neurons: From Hodgkin-Huxley to hopfield , 1990 .

[17]  Rodrigo Alvarez-Icaza,et al.  Neurogrid: A Mixed-Analog-Digital Multichip System for Large-Scale Neural Simulations , 2014, Proceedings of the IEEE.

[18]  Terrence J. Sejnowski,et al.  Engineering intelligent electronic systems based on computational neuroscience [scanning the issue] , 2014, Proc. IEEE.

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