Small Neuron Number Analog of Restricted Boltzmann Machine


Borisenok S.

1st International Conference on Engineering and Applied Natural Sciences (ICEANS 2022), Konya, Turkey, 10 - 13 May 2022, pp.752

  • Publication Type: Conference Paper / Summary Text
  • City: Konya
  • Country: Turkey
  • Page Numbers: pp.752

Abstract

To reduce the exponential complexity of the representation for many-body wave function, a two layer artificial neural network (ANN) called a Restricted Boltzmann Machine (RBM) has been invented by Carleo and Troyer in 2017. It can work very efficiently for modeling quantum systems and quantum computations. However, a ‘black box’ representation of an RBM network to the system of N qubits contains a relatively large number of neurons in both layers (visible and hidden). Here we discuss the possibility to decrease the number of such elements by using a certain type of non-linear neurons with the developed set of the threshold outcomes, particularly, Hodgkin-Huxley (HH) elements. The HH neuron input does not stimulate the active output if it stays below a certain level. If the input overcomes a minimum threshold level, the HH neuron produces a single spike; for the current stimulus above a certain greater level acting during a longer time interval, the outcome forms a spike train, bursting, and similar varieties of behavior. This property is sufficient to replace the hidden layer of linear mathematical neurons with a smaller number of HH elements. The greater is the variety of thresholds, the smaller is the number of neurons in the hidden layer. The computational costs to model the system of N qubits can be much less than the computational costs for the exponents in the standard RBM approach.