LTI ODE-valued neural networks adaptation of the back propagation algorithm

Abstract

In [Velasco et al., 2014], a new approach of the classical artificial neural network archi-tecture is introduced, named ’LTI ODE-valued neural networks’, whereLTI ODEstandsfor Linear Time Invariant Ordinal Differential Equation. In this novel system, nodes inthe artificial neural network are characterized by: inputs in the form of differentiablecontinuous-time signals; linear time-invariant ordinary differential equations (LTI ODE)as connection weights; and activation functions evaluated in the frequency domain.It was shown that this new configuration allows solving multiple problems at the sametime using a common neural structure. However, the article concludes with the need fordeveloping learning algorithms for the new model of neural network.Taking as starting point the drawback pointed out in [Velasco et al., 2014], the mainobjective of this master thesis is to develop a training algorithm for a LTI ODE-valuedneural network. As a first and natural approach, modifications of the BackPropagationalgorithm is considered as a general framework. Moreover, since the nature of the inputsare differentiable continuous-time signals, it is analyzed how to obtain a model that canbe physically implemented in the form of an analogical circuit