New optimization algorithms for neural network training using operator splitting techniques.

Journal: Neural networks : the official journal of the International Neural Network Society
Published Date:

Abstract

In the following paper we present a new type of optimization algorithms adapted for neural network training. These algorithms are based upon sequential operator splitting technique for some associated dynamical systems. Furthermore, we investigate through numerical simulations the empirical rate of convergence of these iterative schemes toward a local minimum of the loss function, with some suitable choices of the underlying hyper-parameters. We validate the convergence of these optimizers using the results of the accuracy and of the loss function on the MNIST, MNIST-Fashion and CIFAR 10 classification datasets.

Authors

  • Cristian Daniel Alecsa
    Tiberiu Popoviciu Institute of Numerical Analysis Romanian Academy, Cluj-Napoca, RO-400320, Romania; Romanian Institute of Science and Technology, Cluj-Napoca, RO-400022, Romania. Electronic address: alecsa@rist.ro.
  • Titus Pinţa
    Mathematical Institute University of Oxford, Oxford, England, OX2 6GG, United Kingdom of Great Britain and Northern Ireland. Electronic address: Titus.Pinta@maths.ox.ac.uk.
  • Imre Boros
    Tiberiu Popoviciu Institute of Numerical Analysis Romanian Academy, Cluj-Napoca, RO-400320, Romania; Department of Mathematics Babeş-Bolyai University, Cluj-Napoca, RO-400084, Romania. Electronic address: imre.boros@math.ubbcluj.ro.