Deep Learning with a Single Neuron: Folding a Deep Neural Network in Time using Feedback-Modulated Delay Loops

Deep neural networks are among the most widely applied machine learning tools showing outstanding performance in a broad range of tasks. We present a method for folding a deep neural network of arbitrary size into a single neuron with multiple time-delayed feedback loops. This single-neuron deep neural network comprises only a single nonlinearity and appropriately adjusted modulations of the feedback signals. The network states emerge in time as a temporal unfolding of the neuron's dynamics. By adjusting the feedback-modulation within the loops, we adapt the network's connection weights. These connection weights are determined via a modified back-propagation algorithm that we designed for such types of networks. Our approach fully recovers standard Deep Neural Networks (DNN), encompasses sparse DNNs, and extends the DNN concept toward dynamical systems implementations. The new method, which we call Folded-in-time DNN (Fit-DNN), exhibits promising performance in a set of benchmark tasks.