Dynamical System Guided Mapping of Quantitative Neuronal Models Onto Neuromorphic Hardware

We present an approach to map neuronal models onto neuromorphic hardware using mathematical insights from dynamical system theory. Quantitatively accurate mappings are important for neuromorphic systems to both leverage and extend existing theoretical and numerical cortical modeling results. In the present study, we first calibrate the on-chip bias generators on our custom hardware. Then, taking advantage of the hardware's high-throughput spike communication, we rapidly estimate key mapping parameters with a set of linear relationships for static inputs derived from dynamical system theory. We apply this mapping procedure to three different chips, and show close matching to the neuronal model and between chips-the Jenson-Shannon divergence was reduced to at least one tenth that of the shuffled control. We confirm that our mapping procedure generalizes to dynamic inputs: Silicon neurons match spike timings of a simulated neuron with a standard deviation of 3.4% of the average inter-spike interval.

[1]  S. Renaud,et al.  Automated tuning of analog neuromimetic integrated circuits , 2009, 2009 IEEE Biomedical Circuits and Systems Conference.

[2]  E. Vittoz,et al.  An analytical MOS transistor model valid in all regions of operation and dedicated to low-voltage and low-current applications , 1995 .

[3]  Johannes Schemmel,et al.  A wafer-scale neuromorphic hardware system for large-scale neural modeling , 2010, Proceedings of 2010 IEEE International Symposium on Circuits and Systems.

[4]  Nicolas Brunel,et al.  Dynamics of Sparsely Connected Networks of Excitatory and Inhibitory Spiking Neurons , 2000, Journal of Computational Neuroscience.

[5]  Giacomo Indiveri,et al.  A Systematic Method for Configuring VLSI Networks of Spiking Neurons , 2011, Neural Computation.

[6]  P. Hasler,et al.  A bio-physically inspired silicon neuron , 2004 .

[7]  Tobi Delbrück,et al.  Bias Current Generators with Wide Dynamic Range , 2004, 2004 IEEE International Symposium on Circuits and Systems (IEEE Cat. No.04CH37512).

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

[9]  Carver Mead,et al.  Analog VLSI and neural systems , 1989 .

[10]  E. Culurciello,et al.  A biomorphic digital image sensor , 2003, IEEE J. Solid State Circuits.

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

[12]  Kwabena Boahen,et al.  Point-to-point connectivity between neuromorphic chips using address events , 2000 .

[13]  Nicolas Brunel,et al.  Firing Rate of the Noisy Quadratic Integrate-and-Fire Neuron , 2003, Neural Computation.

[14]  Richard F. Lyon,et al.  An analog electronic cochlea , 1988, IEEE Trans. Acoust. Speech Signal Process..

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

[16]  Kwabena Boahen,et al.  A burst-mode word-serial address-event link-I: transmitter design , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[17]  G. Edelman,et al.  Large-scale model of mammalian thalamocortical systems , 2008, Proceedings of the National Academy of Sciences.

[18]  Kwabena Boahen,et al.  Synchrony in Silicon: The Gamma Rhythm , 2007, IEEE Transactions on Neural Networks.

[19]  Jianhua Lin,et al.  Divergence measures based on the Shannon entropy , 1991, IEEE Trans. Inf. Theory.

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

[21]  Ralph Etienne-Cummings,et al.  Configuring of Spiking Central Pattern Generator Networks for Bipedal Walking Using Genetic Algorthms , 2007, 2007 IEEE International Symposium on Circuits and Systems.

[22]  Yannick Bornat,et al.  A Library of Analog Operators Based on the Hodgkin-Huxley Formalism for the Design of Tunable, Real-Time, Silicon Neurons , 2011, IEEE Transactions on Biomedical Circuits and Systems.

[23]  Kwabena Boahen,et al.  Optic nerve signals in a neuromorphic chip I: Outer and inner retina models , 2004, IEEE Transactions on Biomedical Engineering.

[24]  Craig T. Jin,et al.  A log-domain implementation of the Izhikevich neuron model , 2010, Proceedings of 2010 IEEE International Symposium on Circuits and Systems.

[25]  Andreas G. Andreou,et al.  Current-mode subthreshold MOS circuits for analog VLSI neural systems , 1991, IEEE Trans. Neural Networks.

[26]  Gert Cauwenberghs,et al.  A Multichip Neuromorphic System for Spike-Based Visual Information Processing , 2007, Neural Computation.

[27]  Kathie L. Olsen,et al.  Neurotech for Neuroscience: Unifying Concepts, Organizing Principles, and Emerging Tools , 2007, The Journal of Neuroscience.

[28]  Anthony N. Burkitt,et al.  A Review of the Integrate-and-fire Neuron Model: I. Homogeneous Synaptic Input , 2006, Biological Cybernetics.

[29]  Gert Cauwenberghs,et al.  A subthreshold aVLSI implementation of the Izhikevich simple neuron model , 2010, 2010 Annual International Conference of the IEEE Engineering in Medicine and Biology.

[30]  Kwabena Boahen,et al.  Thermodynamically Equivalent Silicon Models of Voltage-Dependent Ion Channels , 2007, Neural Computation.

[31]  Bo Wen,et al.  A Silicon Cochlea With Active Coupling , 2009, IEEE Transactions on Biomedical Circuits and Systems.

[32]  Bertram E. Shi,et al.  Neuromorphic implementation of orientation hypercolumns , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[33]  G. Ermentrout,et al.  Parabolic bursting in an excitable system coupled with a slow oscillation , 1986 .

[34]  G. Geelen,et al.  An inherently linear and compact MOST-only current division technique , 1992 .

[35]  C. Mead,et al.  Neuromorphic Robot Vision with Mixed Analog- Digital Architecture , 2005 .

[36]  Sylvie Renaud,et al.  Automated Parameter Estimation of the Hodgkin-Huxley Model Using the Differential Evolution Algorithm: Application to Neuromimetic Analog Integrated Circuits , 2011, Neural Computation.