Arithmetic computing via rate coding in neural circuits with spike-triggered adaptive synapses

We present spiking neural circuits with spike-time dependent adaptive synapses capable of performing a variety of basic mathematical computations. These circuits encode and process information in the spike rates that lie between 40-140 Hz. The synapses in our circuit obey simple, local and spike-time dependent adaptation rules. We demonstrate that our circuits can perform the fundamental operations - addition, subtraction, multiplication and division, as well as other non-linear transformations such as exponentiation and logarithm for time dependent signals in real-time. We show that our spiking neural circuits are tolerant to a high degree of noise in the input variables, and illustrate its computational capability in an exemplary signal estimation problem. Our circuits can thus be used in a wide variety of hardware and software implementations for navigation, control and computation.

[1]  Shigeru Shinomoto,et al.  Kernel bandwidth optimization in spike rate estimation , 2009, Journal of Computational Neuroscience.

[2]  Wolfgang Maass,et al.  Networks of Spiking Neurons: The Third Generation of Neural Network Models , 1996, Electron. Colloquium Comput. Complex..

[3]  N. Ulanovsky,et al.  What the bat's voice tells the bat's brain , 2008, Proceedings of the National Academy of Sciences.

[4]  Gary D. Bernard,et al.  A proposed mechanism for multiplication of neural signals , 1976, Biological Cybernetics.

[5]  Steven W. Smith,et al.  The Scientist and Engineer's Guide to Digital Signal Processing , 1997 .

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

[7]  Mark C. W. van Rossum,et al.  Accurate multiplication with noisy spiking neurons , 2011, Journal of neural engineering.

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

[9]  B. Batlogg,et al.  Auditory Spatial Receptive Fields Created by Multiplication , 2022 .

[10]  Wulfram Gerstner,et al.  Predicting neuronal activity with simple models of the threshold type: Adaptive Exponential Integrate-and-Fire model with two compartments , 2007, Neurocomputing.

[11]  Christof Koch,et al.  The role of single neurons in information processing , 2000, Nature Neuroscience.

[12]  Eric L. Schwartz,et al.  Computing with the Leaky Integrate-and-Fire Neuron: Logarithmic Computation and Multiplication , 1997, Neural Computation.

[13]  Haza Nuzly Abdul Hamed,et al.  Computing with Spiking Neuron Networks A Review , 2014, SOCO 2014.

[14]  Holger G. Krapp,et al.  Multiplication and stimulus invariance in a looming-sensitive neuron , 2004, Journal of Physiology-Paris.