Deep convolutional neural networks on cartoon functions


Philipp Grohs, Thomas Wiatowski, and Helmut Bölcskei


Proc. of IEEE International Symposium on Information Theory (ISIT), Barcelona, Spain, pp. 1163-1167, July 2016.

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Wiatowski and Bölcskei, 2015, proved that deformation stability and vertical translation invariance of deep convolutional neural network-based feature extractors are guaranteed by the network structure per se rather than the specific convolution kernels and non-linearities. While the translation invariance result applies to square-integrable functions, the deformation stability bound holds for band-limited functions only. Many signals of practical relevance (such as natural images) exhibit, however, sharp and curved discontinuities and are hence not band-limited. The main contribution of this paper is a deformation stability result that takes these structural properties into account. Specifically, we establish deformation stability bounds for the class of cartoon functions introduced by Donoho, 2001.


Deep neural networks, deformation stability, cartoon functions

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