Deep neural networks using a single neuron: folded-in-time architecture using feedback-modulated delay loops

Florian Stelzer,Serhiy Yanchuk,Raul Vicente,Ingo Fischer,André Röhm

doi:10.1038/s41467-021-25427-4

Abstract

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 back-propagation algorithm, where both the delay-induced and local network connections must be taken into account. Our approach can fully represent 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.

Highlights

Deep neural networks are among the most widely applied machine learning tools showing outstanding performance in a broad range of tasks
We are able to show that our foldingin-time approach is fully equivalent to a feed-forward deep neural network under certain constraints—and that it, in addition, encompasses dynamical systems specific architectures
The traditional Deep Neural Networks consist of multiple layers of neurons coupled in a feed-forward architecture

Summary

Introduction

Deep neural networks are among the most widely applied machine learning tools showing outstanding performance in a broad range of tasks. The data-driven representations learned by DNNs empower state-of-the-art solutions to a range of tasks in computer vision, reinforcement learning, robotics, healthcare, and natural language processing[1,2,3,4,5,6,7,8,9] Their success has motivated the implementation of DNNs using alternative hardware platforms, such as photonic or electronic concepts, see, e.g., refs. Temporal modulation of the signals within the individual delay loops allows realizing adjustable connection weights among the hidden layers This approach can reduce the required hardware drastically and offers a new perspective on how to construct trainable complex systems: The large network of many interacting elements is replaced by a single element, representing different elements in time by interacting with its own delayed states. The delay-based reservoir computing concept inspired successful implementations in terms of hardware efficiency[13], processing speed[16,20,21], task performance[22,23], and last, but not least, energy consumption[16,22]

Methods

Results

Conclusion