Institute of Mathematics, Technische Universität Berlin, Berlin, Germany.
Department of Mathematics, Humboldt-Universität zu Berlin, Berlin, Germany.
Nat Commun. 2021 Aug 27;12(1):5164. doi: 10.1038/s41467-021-25427-4.
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.
深度神经网络是应用最广泛的机器学习工具之一，在广泛的任务中表现出了出色的性能。我们提出了一种将任意大小的深度神经网络折叠成具有多个时滞反馈回路的单个神经元的方法。这个单神经元深度神经网络仅包含单个非线性和适当调整的反馈信号调制。网络状态随着神经元动力学的时间展开而出现。通过调整环路中的反馈调制，我们调整网络的连接权重。这些连接权重是通过反向传播算法确定的，其中必须考虑延迟引起的和本地网络连接。我们的方法可以完全表示标准深度神经网络（DNN），包含稀疏 DNN，并将 DNN 概念扩展到动态系统实现。我们称之为“时间折叠深度神经网络（Fit-DNN）”的新方法在一组基准任务中表现出了有希望的性能。
