Coupled nonlinear delay systems as deep convolutional neural networks

Abstract

Neural networks are currently transforming the feld of computer algorithms. With increasingly demanding applications it becomes clear that their execution on current computing substrates is severely limited. Addressing this bottleneck, reservoir computing was successfully implemented on a large variety of physical substrates. However, demonstration of hierarchical multilayer systems such as deep neural networks are lagging behind. Here, we implement cascaded time-delay reservoirs via coupled nonlinear oscillators. By cascading temporal response-features of consecutive layers we show that such architectures conceptually correspond to deep convolutional neural networks. A system featuring unidirectionally cascaded layers reduces the long-term prediction error of a chaotic sequence by more than one order of magnitude compared to a single layer system of the same size.