How the Accuracy and Computational Cost of Spiking Neuron Simulation are Affected by the Time Span and Firing Rate

It is known that, depending on the numerical method, the simulation accuracy of a spiking neuron increases monotonically and that the computational cost increases in a power-law complexity as the time step reduces. Moreover, the accuracy and computational cost also are substantially affected by the mechanism responsible for generating the action potentials. However, little attention has been paid to how the time span and firing rate influence the simulation. The purpose of this study was to describe how the accuracy, computational cost, and efficiency are affected by the time span and firing rate. We found that the simulation is importantly affected by these two variables

[1]  Ernst Hairer,et al.  Solving Ordinary Differential Equations I: Nonstiff Problems , 2009 .

[2]  Mark D. Humphries,et al.  Solution Methods for a New Class of Simple Model Neurons , 2007, Neural Computation.

[3]  R. K. Ursem.  Multi-objective Optimization using Evolutionary Algorithms , 2009 .

[4]  Örjan Ekeberg,et al.  A computer based model for realistic simulations of neural networks , 1991, Biological Cybernetics.

[5]  R. Yuste.  Dendritic Spines , 2010 .

[6]  J. Lambert.  Numerical Methods for Ordinary Differential Equations , 1991 .

[7]  Humberto Sossa,et al.  The step size impact on the computational cost of spiking neuron simulation , 2017, 2017 Computing Conference.

[8]  Romain Brette,et al.  The Brian Simulator , 2009, Front. Neurosci..

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

[10]  Steven C. Chapra,et al.  Numerical Methods for Engineers , 1986 .

[11]  T. Chai,et al.  Root mean square error (RMSE) or mean absolute error (MAE)? – Arguments against avoiding RMSE in the literature , 2014 .

[12]  Szabolcs Káli,et al.  A flexible, interactive software tool for fitting the parameters of neuronal models , 2014, Front. Neuroinform..

[13]  Wulfram Gerstner,et al.  Neuronal Dynamics: From Single Neurons To Networks And Models Of Cognition , 2014 .

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

[15]  M. Hines,et al.  Efficient computation of branched nerve equations. , 1984, International journal of bio-medical computing.

[16]  Sander M. Bohte,et al.  Computing with Spiking Neuron Networks , 2012, Handbook of Natural Computing.

[17]  Cyrille Rossant,et al.  Automatic Fitting of Spiking Neuron Models to Electrophysiological Recordings , 2010, Front. Neuroinform..

[18]  C. Kambhampati,et al.  Spiking Neurons: Is coincidence-factor enough for comparing responses with fluctuating membrane voltage? , 2008 .

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

[20]  Louis Tao,et al.  Efficient and Accurate Time-Stepping Schemes for Integrate-and-Fire Neuronal Networks , 2001, Journal of Computational Neuroscience.

[21]  James M. Bower,et al.  The Book of GENESIS , 1994, Springer New York.

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

[23]  Alexander R. Nectow,et al.  Exponential Time Differencing for Hodgkin-Huxley-like ODEs , 2013, SIAM J. Sci. Comput..

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

[25]  Steve B. Furber,et al.  Accuracy and Efficiency in Fixed-Point Neural ODE Solvers , 2015, Neural Computation.

[26]  Jonathan Touboul,et al.  On the Simulation of Nonlinear Bidimensional Spiking Neuron Models , 2010, Neural Computation.

[27]  Ankur Gupta,et al.  Biologically-inspired spiking neural networks with Hebbian learning for vision processing , 2008 .

[28]  Eduardo Ros,et al.  Event- and Time-Driven Techniques Using Parallel CPU-GPU Co-processing for Spiking Neural Networks , 2017, Front. Neuroinform..

[29]  Germán Mato,et al.  On Numerical Simulations of Integrate-and-Fire Neural Networks , 1998, Neural Computation.

[30]  Johannes Partzsch,et al.  Rate and Pulse Based Plasticity Governed by Local Synaptic State Variables , 2010, Front. Syn. Neurosci..

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

[32]  Markus Diesmann,et al.  Exact Subthreshold Integration with Continuous Spike Times in Discrete-Time Neural Network Simulations , 2007, Neural Computation.

[33]  Christopher J. Bishop,et al.  Pulsed Neural Networks , 1998 .

[34]  M. London,et al.  Dendritic computation. , 2005, Annual review of neuroscience.

[35]  H. A. Antosiewicz,et al.  Automatic Computation of Nerve Excitation , 1955 .

[36]  Ronald J. MacGregor,et al.  Neural and brain modeling , 1987 .

[37]  D. Debanne,et al.  Axon physiology. , 2011, Physiological reviews.

[38]  Lyle N. Long.  Toward Human-Level Massively-Parallel Neural Networks with Hodgkin-Huxley Neurons , 2016, AGI.

[39]  Wulfram Gerstner,et al.  A benchmark test for a quantitative assessment of simple neuron models , 2008, Journal of Neuroscience Methods.

[40]  Wofgang Maas,et al.  Networks of spiking neurons: the third generation of neural network models , 1997 .

[41]  Wolfgang Hackbusch,et al.  The Concept of Stability in Numerical Mathematics , 2014 .

[42]  Aaditya V. Rangan,et al.  Fast numerical methods for simulating large-scale integrate-and-fire neuronal networks , 2007, Journal of Computational Neuroscience.

[43]  F. Ponulak.  ReSuMe-New Supervised Learning Method for Spiking Neural Networks , 2005 .

[44]  L. F Abbott,et al.  Lapicque’s introduction of the integrate-and-fire model neuron (1907) , 1999, Brain Research Bulletin.

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

[46]  Robert Plonsey,et al.  Bioelectricity: A Quantitative Approach Duke University’s First MOOC , 2013 .

[47]  Stephan Henker,et al.  Accuracy evaluation of numerical methods used in state-of-the-art simulators for spiking neural networks , 2011, Journal of Computational Neuroscience.

[48]  J. Rubin,et al.  The selection of mixed-mode oscillations in a Hodgkin-Huxley model with multiple timescales. , 2008, Chaos.

[49]  C. Willmott,et al.  Advantages of the mean absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance , 2005 .

[50]  Michael L. Hines,et al.  Independent Variable Time-Step Integration of Individual Neurons for Network Simulations , 2005, Neural Computation.

[51]  Wyeth Bair,et al.  Spiking neural network simulation: numerical integration with the Parker-Sochacki method , 2009, Journal of Computational Neuroscience.

[52]  Nicolas Brunel,et al.  Lapicque’s 1907 paper: from frogs to integrate-and-fire , 2007, Biological Cybernetics.

[53]  Jonathan Touboul,et al.  Importance of the Cutoff Value in the Quadratic Adaptive Integrate-and-Fire Model , 2008, Neural Computation.

[54]  Nicholas T. Carnevale,et al.  Simulation of networks of spiking neurons: A review of tools and strategies , 2006, Journal of Computational Neuroscience.

[55]  Alois Knoll,et al.  Neuromorphic implementations of neurobiological learning algorithms for spiking neural networks , 2015, Neural Networks.

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

[57]  Nabil H. Farhat,et al.  The double queue method: a numerical method for integrate-and-fire neuron networks , 2001, Neural Networks.

[58]  Stefan Rotter,et al.  Exact digital simulation of time-invariant linear systems with applications to neuronal modeling , 1999, Biological Cybernetics.

[59]  Lyle N. Long,et al.  On the Capabilities and Computational Costs of Neuron Models , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[60]  Lyle N. Long,et al.  A Review of Biologically Plausible Neuron Models for Spiking Neural Networks , 2010 .

[61]  Jonathan Touboul,et al.  Spiking Dynamics of Bidimensional Integrate-and-Fire Neurons , 2009, SIAM J. Appl. Dyn. Syst..

[62]  J. Touboul.  Nonlinear and Stochastic Methods in Neurosciences , 2008 .

[63]  J. Jack,et al.  Electric current flow in excitable cells , 1975 .

[64]  Romain Brette,et al.  Exact Simulation of Integrate-and-Fire Models with Synaptic Conductances , 2006, Neural Computation.

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

[66]  H. Hasegawa,et al.  Responses of a Hodgkin-Huxley neuron to various types of spike-train inputs. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[67]  Ammar Belatreche,et al.  DL-ReSuMe: A Delay Learning-Based Remote Supervised Method for Spiking Neurons , 2015, IEEE Transactions on Neural Networks and Learning Systems.

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

[69]  James M. Bower,et al.  Rallpacks: a set of benchmarks for neuronal simulators , 1992, Trends in Neurosciences.

[70]  Raul C. Mureşan,et al.  The "Neocortex" Neural Simulator. A Modern Design. , 2004 .

[71]  C. Eliasmith,et al.  The use and abuse of large-scale brain models , 2014, Current Opinion in Neurobiology.

[72]  M. Mascagni,et al.  Numerical Methods for Neuronal Modeling 14.1 Introduction , 1989 .

[73]  R. Stein.  A THEORETICAL ANALYSIS OF NEURONAL VARIABILITY. , 1965, Biophysical journal.

[74]  James G. King,et al.  Reconstruction and Simulation of Neocortical Microcircuitry , 2015, Cell.

[75]  Desmond J. Higham,et al.  Numerical Methods for Ordinary Differential Equations - Initial Value Problems , 2010, Springer undergraduate mathematics series.

[76]  Wulfram Gerstner,et al.  The quantitative single-neuron modeling competition , 2008, Biological Cybernetics.

[77]  David A. Pope.  An exponential method of numerical integration of ordinary differential equations , 1963, CACM.

[78]  M. Hochbruck,et al.  Exponential integrators , 2010, Acta Numerica.