Discrete-time backpropagation for training synaptic delay-based artificial neural networks

The aim of the paper is to endow a well-known structure for processing time-dependent information, synaptic delay-based ANNs, with a reliable and easy to implement algorithm suitable for training temporal decision processes. In fact, we extend the backpropagation algorithm to discrete-time feedforward networks that include adaptable internal time delays in the synapses. The structure of the network is similar to the one presented by Day and Davenport (1993), that is, in addition to the weights modeling the transmission capabilities of the synaptic connections, we model their length by means of a parameter that indicates the delay a discrete-event suffers when going from the origin neuron to the target neuron through a synaptic connection. Like the weights, these delays are also trainable, and a training algorithm can be derived that is almost as simple as the backpropagation algorithm, and which is really an extension of it. We present examples of the application of these networks and algorithm to the prediction of time series and to the recognition of patterns in electrocardiographic signals. In the first case, we employ the temporal reasoning characteristics of these networks for the prediction of future values in a benchmark example of a time series: the one governed by the Mackey-Glass chaotic equation. In the second case, we provide a real life example. The problem consists in identifying different types of beats through two levels of temporal processing, one relating the morphological features which make up the beat in time and another one that relates the positions of beats in time, that is, considers rhythm characteristics of the ECG signal. In order to do this, the network receives the signal sequentially, no windowing, segmentation, or thresholding are applied