A CORDIC Based Digital Hardware For Adaptive Exponential Integrate and Fire Neuron

This paper presents a COordinate Rotation DIgital Computer (CORDIC) based Adaptive Exponential Integrate and Fire (AdEx) neuron for efficient large scale biological neural network implementation. The accuracy of the modified model is investigated by both calculating various errors and bifurcation analysis; both show that the proposed model follows the same signaling, dynamical behavior, and bifurcation pattern as the original model. Network behavior of the original and proposed models are also observed to be very much alike in following the same activity patterns. The model is hardware synthesized and implemented on FPGA as a proof of concept. Measurement results show that the proposed model can reproduce neuronal behaviors similar to the original model. Hardware device utilization and speed also confirm the efficiency of the realized hardware compared with previous works.

[1]  Yingxue Wang,et al.  A Two-Dimensional Configurable Active Silicon Dendritic Neuron Array , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[2]  Bernabé Linares-Barranco,et al.  On algorithmic rate-coded AER generation , 2006, IEEE Transactions on Neural Networks.

[3]  R. FitzHugh.  Impulses and Physiological States in Theoretical Models of Nerve Membrane. , 1961, Biophysical journal.

[4]  Jilles Vreeken,et al.  Spiking neural networks, an introduction , 2003 .

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

[6]  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.

[7]  Joachim Haß,et al.  An Approximation to the Adaptive Exponential Integrate-and-Fire Neuron Model Allows Fast and Predictive Fitting to Physiological Data , 2012, Front. Comput. Neurosci..

[8]  Bryan Tripp,et al.  A digital hardware design for real-time simulation of large neural-system models in physical settings , 2014, BMC Neuroscience.

[9]  Georg Schnitger,et al.  On the computational power of sigmoid versus Boolean threshold circuits , 1991, [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science.

[10]  Arindam Basu,et al.  A Learning-Enabled Neuron Array IC Based Upon Transistor Channel Models of Biological Phenomena , 2013, IEEE Transactions on Biomedical Circuits and Systems.

[11]  Sergio Davies,et al.  Learning in spiking neural networks , 2013 .

[12]  R. Andersen,et al.  Frontiers in cognitive neuroscience , 1992 .

[13]  Hiroyuki Torikai,et al.  A Novel PWC Spiking Neuron Model: Neuron-Like Bifurcation Scenarios and Responses , 2012, IEEE Transactions on Circuits and Systems I: Regular Papers.

[14]  John Stephen Walther,et al.  The Story of Unified Cordic , 2000, J. VLSI Signal Process..

[15]  Huxley Af,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve. 1952. , 1990 .

[16]  W. Gerstner,et al.  Dynamic I-V curves are reliable predictors of naturalistic pyramidal-neuron voltage traces. , 2008, Journal of neurophysiology.

[17]  Olivier Temam,et al.  Hardware spiking neurons design: Analog or digital? , 2012, The 2012 International Joint Conference on Neural Networks (IJCNN).

[18]  F. Grassia,et al.  Silicon neuron: digital hardware implementation of the quartic model , 2014, Artificial Life and Robotics.

[19]  Filip Ponulak,et al.  Introduction to spiking neural networks: Information processing, learning and applications. , 2011, Acta neurobiologiae experimentalis.

[20]  Arash Ahmadi,et al.  An analog implementation of biologically plausible neurons using CCII building blocks , 2012, Neural Networks.

[21]  Wulfram Gerstner,et al.  A neuronal learning rule for sub-millisecond temporal coding , 1996, Nature.

[22]  Johannes Schemmel,et al.  A VLSI Implementation of the Adaptive Exponential Integrate-and-Fire Neuron Model , 2010, NIPS.

[23]  J. Hindmarsh,et al.  The assembly of ionic currents in a thalamic neuron I. The three-dimensional model , 1989, Proceedings of the Royal Society of London. B. Biological Sciences.

[24]  Arash Ahmadi,et al.  Biologically Inspired Spiking Neurons: Piecewise Linear Models and Digital Implementation , 2012, IEEE Transactions on Circuits and Systems I: Regular Papers.

[25]  R. Eckhorn,et al.  Coherent oscillations: A mechanism of feature linking in the visual cortex? , 1988, Biological Cybernetics.

[26]  Wulfram Gerstner,et al.  Phenomenological models of synaptic plasticity based on spike timing , 2008, Biological Cybernetics.

[27]  A. Cassidy,et al.  Dynamical digital silicon neurons , 2008, 2008 IEEE Biomedical Circuits and Systems Conference.

[28]  Vedat Tavsanoglu,et al.  Architecture of a Fully Pipelined Real-Time Cellular Neural Network Emulator , 2015, IEEE Transactions on Circuits and Systems I: Regular Papers.

[29]  Arash Ahmadi,et al.  Digital Multiplierless Implementation of Biological Adaptive-Exponential Neuron Model , 2014, IEEE Transactions on Circuits and Systems I: Regular Papers.

[30]  Jack E. Volder.  The CORDIC Trigonometric Computing Technique , 1959, IRE Trans. Electron. Comput..

[31]  Shih-Chii Liu,et al.  Minitaur, an Event-Driven FPGA-Based Spiking Network Accelerator , 2014, IEEE Transactions on Very Large Scale Integration (VLSI) Systems.

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

[33]  Gert Cauwenberghs,et al.  Neuromorphic Silicon Neuron Circuits , 2011, Front. Neurosci.

[34]  C. Morris,et al.  Voltage oscillations in the barnacle giant muscle fiber. , 1981, Biophysical journal.

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

[36]  Wulfram Gerstner,et al.  Adaptive exponential integrate-and-fire model , 2009, Scholarpedia.

[37]  Rob J Hyndman,et al.  Another look at measures of forecast accuracy , 2006 .

[38]  Wulfram Gerstner,et al.  Firing patterns in the adaptive exponential integrate-and-fire model , 2008, Biological Cybernetics.

[39]  Jonathan Touboul,et al.  Dynamics and bifurcations of the adaptive exponential integrate-and-fire model , 2008, Biological Cybernetics.

[40]  H. Wilson.  Simplified dynamics of human and mammalian neocortical neurons. , 1999, Journal of theoretical biology.

[41]  Johannes J. Letzkus,et al.  Dendritic mechanisms controlling spike-timing-dependent synaptic plasticity , 2007, Trends in Neurosciences.

[42]  Ch. von der Malsburg,et al.  A neural cocktail-party processor , 1986, Biological Cybernetics.

[43]  Indranil Saha,et al.  journal homepage: www.elsevier.com/locate/neucom , 2022 .

[44]  D. Hansel,et al.  How Spike Generation Mechanisms Determine the Neuronal Response to Fluctuating Inputs , 2003, The Journal of Neuroscience.

[45]  Sander M. Bohte,et al.  Spiking Neural Networks: Principles and Challenges , 2014, ESANN.

[46]  Janusz A. Starzyk,et al.  Memristor Crossbar Architecture for Synchronous Neural Networks , 2014, IEEE Transactions on Circuits and Systems I: Regular Papers.

[47]  Wulfram Gerstner,et al.  Adaptive exponential integrate-and-fire model as an effective description of neuronal activity. , 2005, Journal of neurophysiology.

[48]  Derek Abbott,et al.  Digital Multiplierless Realization of Two Coupled Biological Morris-Lecar Neuron Model , 2015, IEEE Transactions on Circuits and Systems I: Regular Papers.

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

[50]  Andrew S. Cassidy,et al.  Design of silicon brains in the nano-CMOS era: Spiking neurons, learning synapses and neural architecture optimization , 2013, Neural Networks.