WIAS Preprint No. 2732, (2020)

Stability of deep neural networks via discrete rough paths


Authors

  • Bayer, Christian
    ORCID: 0000-0002-9116-0039
  • Friz, Peter
    ORCID: 0000-0003-2571-8388
  • Tapia, Nikolas
    ORCID: 0000-0003-0018-2492

2010 Mathematics Subject Classification

  • 60L10 60L70 60L90

Keywords

  • Deep neural networks, iterated sums signature

DOI

10.20347/WIAS.PREPRINT.2732

Abstract

Using rough path techniques, we provide a priori estimates for the output of Deep Residual Neural Networks. In particular we derive stability bounds in terms of the total p-variation of trained weights for any p ≥ 1.

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