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Fully hyperbolic convolutional neural networks

Fully hyperbolic convolutional neural networks Convolutional neural networks (CNN) have recently seen tremendous success in various computer vision tasks. However, their application to problems with high dimensional input and output, such as high-resolution image and video segmentation or 3D medical imaging, has been limited by various factors. Primarily, in the training stage, it is necessary to store network activations for back-propagation. In these settings, the memory requirements associated with storing activations can exceed what is feasible with current hardware, especially for problems in 3D. Motivated by the propagation of signals over physical networks, that are governed by the hyperbolic Telegraph equation, in this work we introduce a fully conservative hyperbolic network for problems with high-dimensional input and output. We introduce a coarsening operation that allows completely reversible CNNs by using a learnable discrete wavelet transform and its inverse to both coarsen and interpolate the network state and change the number of channels. We show that fully reversible networks are able to achieve results comparable to the state of the art in 4D time-lapse hyper-spectral image segmentation and full 3D video segmentation, with a much lower memory footprint that is a constant independent of the network depth. We also extend the use of such networks to variational auto-encoders, where optimization begins from an exact recovery and we discover the level of compression through optimization. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Research in the Mathematical Sciences Springer Journals

Fully hyperbolic convolutional neural networks

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Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
eISSN
2197-9847
DOI
10.1007/s40687-022-00343-1
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Abstract

Convolutional neural networks (CNN) have recently seen tremendous success in various computer vision tasks. However, their application to problems with high dimensional input and output, such as high-resolution image and video segmentation or 3D medical imaging, has been limited by various factors. Primarily, in the training stage, it is necessary to store network activations for back-propagation. In these settings, the memory requirements associated with storing activations can exceed what is feasible with current hardware, especially for problems in 3D. Motivated by the propagation of signals over physical networks, that are governed by the hyperbolic Telegraph equation, in this work we introduce a fully conservative hyperbolic network for problems with high-dimensional input and output. We introduce a coarsening operation that allows completely reversible CNNs by using a learnable discrete wavelet transform and its inverse to both coarsen and interpolate the network state and change the number of channels. We show that fully reversible networks are able to achieve results comparable to the state of the art in 4D time-lapse hyper-spectral image segmentation and full 3D video segmentation, with a much lower memory footprint that is a constant independent of the network depth. We also extend the use of such networks to variational auto-encoders, where optimization begins from an exact recovery and we discover the level of compression through optimization.

Journal

Research in the Mathematical Sciences – Springer Journals

Published: Dec 1, 2022

Keywords: Neural networks; Hyperbolic PDE; Wavelets; Auto-encoders

References

  • A combined deep-learning and deformable-model approach to fully automatic segmentation of the left ventricle in cardiac mri
    Avendi, M; Kheradvar, A; Jafarkhani, H
  • Learning deep architectures for AI
    Bengio, Y
  • Orthonormal bases of compactly supported wavelets
    Daubechies, I
  • Learning a variational network for reconstruction of accelerated MRI data
    Hammernik, K; Klatzer, T; Kobler, E; Recht, MP; Sodickson, DK; Pock, T; Knoll, F
  • Hyperspectral change detection: an experimental comparative study
    Hasanlou, M; Seydi, ST
  • Deep learning
    LeCun, Y; Bengio, Y; Hinton, G
  • A hybrid neural network for hyperspectral image classification
    Li, J; Liang, B; Wang, Y
  • Spectral-spatial classification of hyperspectral imagery with 3D convolutional neural network
    Li, Y; Zhang, H; Shen, Q
  • Understanding the effective receptive field in deep convolutional neural networks
    Luo, W; Li, Y; Urtasun, R; Zemel, R; Lee, DD; Sugiyama, M; Luxburg, UV; Guyon, I; Garnett, R
  • Multiresolution neural networks for tracking seismic horizons from few training images
    Peters, B; Granek, J; Haber, E
  • Fully convolutional networks for semantic segmentation
    Shelhamer, E; Long, J; Darrell, T
  • CSA-MSO3DCNN: multiscale octave 3D CNN with channel and spatial attention for hyperspectral image classification
    Xu, Q; Xiao, Y; Wang, D; Luo, B
  • A general generative adversarial capsule network for hyperspectral image spectral–spatial classification
    Xue, Z
  • A Crank–Nicolson collocation spectral method for the two-dimensional telegraph equations
    Zhou, Y; Luo, Z