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Front. Neurosci. | doi: 10.3389/fnins.2018.00115

Computing Generalized Matrix Inverse On Spiking Neural Substrate

 Rohit Shukla1*, Soroosh Khoram1, Erik Jorgensen2, Jing Li1, Mikko Lipasti1 and Stephen Wright3
  • 1Electrical and Computer Engineering, University of Wisconsin-Madison, United States
  • 2Electrical and Computer Engineering, Georgia Institute of Technology, United States
  • 3Computer Sciences, University of Wisconsin-Madison, United States

Emerging neural hardware substrates, such as IBM’s TrueNorth Neurosynaptic System, can
provide an appealing platform for deploying numerical algorithms. For example, a recurrent
Hopfield neural network can be used to find the Moore-Penrose generalized inverse of a matrix,
thus enabling a broad class of linear optimizations to be solved efficiently, at low energy cost.
However, deploying numerical algorithms on hardware platforms that severely limit the range and
precision of representation for numeric quantities can be quite challenging. This paper discusses
these challenges and proposes a rigorous mathematical framework for reasoning about range and
precision on such substrates. The paper derives techniques for normalizing inputs and properly
quantizing synaptic weights originating from arbitrary systems of linear equations, so that solvers
for those systems can be implemented in a provably correct manner on hardware-constrained
neural substrates. The analytical model is empirically validated on the IBM TrueNorth platform,
and results show that the guarantees provided by the framework for range and precision hold
under experimental conditions. Experiments with optical flow demonstrate the energy benefits of
deploying a reduced-precision and energy-efficient generalized matrix inverse engine on the IBM
TrueNorth platform, reflecting 10□ to 100□ improvement over FPGA and ARM core baselines.

Keywords: spiking neural networks, TrueNorth, Matrix inversion, Hopfield Neural Network, neuromorphic computing, stochastic computing

Received: 02 Dec 2017; Accepted: 13 Feb 2018.

Edited by:

Arindam Basu, Nanyang Technological University, Singapore

Reviewed by:

Guillaume Garreau, IBM Research Almaden, United States
Subhrajit Roy, IBM Research, Australia  

Copyright: © 2018 Shukla, Khoram, Jorgensen, Li, Lipasti and Wright. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

* Correspondence: Mr. Rohit Shukla, University of Wisconsin-Madison, Electrical and Computer Engineering, Madison, 53706, Wisconsin, United States, rshukla3@wisc.edu