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Infinite-dimensional Folded-in-time Deep Neural Networks

arXiv 2101.02966 ↗First posted 8 Jan 2021cs.LG cs.NE math.DScited by 0

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Abstract (arXiv)

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 back-propagation 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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References · 12

  1. 2020Language Models are Few-Shot Learnerscited by 32,419
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  11. 2018Reservoir computing with simple oscillators: Virtual and real networkscited by 3
  12. 2020Limitations of the recall capabilities in delay based reservoir computing systemscited by 3

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