Infinite-dimensional Folded-in-time Deep Neural Networks

• URL: http://arxiv.org/abs/2101.02966v1
• Date: Fri, 8 Jan 2021 11:30:50 GMT
• Title: Infinite-dimensional Folded-in-time Deep Neural Networks
• Authors: Florian Stelzer (1 and 2), Serhiy Yanchuk (1) ((1) Institute of Mathematics, Technische Universit\"at Berlin, Germany, (2) Department of Mathematics, Humboldt-Universit\"at zu Berlin, Germany)
• Abstract summary: In this work, we present an infinite-dimensional generalization, which allows for a more rigorous mathematical analysis. We also provide a functional backpropagation algorithm, which enables descent training of the weights.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The method recently introduced in arXiv:2011.10115 realizes a deep neural network with just a single nonlinear element and delayed feedback. It is applicable for the description of physically implemented neural networks. In this work, we present an infinite-dimensional generalization, which allows for a more rigorous mathematical analysis and a higher flexibility in choosing the weight functions. Precisely speaking, the weights are described by Lebesgue integrable functions instead of step functions. We also provide a functional backpropagation algorithm, which enables gradient descent training of the weights. In addition, with a slight modification, our concept realizes recurrent neural networks.

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