This paper introduces a novel representation of convolutional Neural Networks (CNNs) in terms of 2-D dynamical systems. To this end, the usual description of convolutional layers with convolution kernels, i.e., the impulse responses of linear filters, is realized in state space as a linear time-invariant 2-D system. The overall convolutional Neural Network composed of convolutional layers and nonlinear activation functions is then viewed as a 2-D version of a Lur'e system, i.e., a linear dynamical system interconnected with static nonlinear components. One benefit of this 2-D Lur'e system perspective on CNNs is that we can use robust control theory much more efficiently for Lipschitz constant estimation than previously possible.
%0 Journal Article
%1 GraPau23
%A Gramlich, Dennis
%A Pauli, Patricia
%A Scherer, Carsten W.
%A Allgöwer, Frank
%A Ebenbauer, Christian
%D 2023
%I arXiv
%K PN4-3(II) PN4 EXC2075
%R 10.48550/ARXIV.2303.03042
%T Convolutional Neural Networks as 2-D systems
%X This paper introduces a novel representation of convolutional Neural Networks (CNNs) in terms of 2-D dynamical systems. To this end, the usual description of convolutional layers with convolution kernels, i.e., the impulse responses of linear filters, is realized in state space as a linear time-invariant 2-D system. The overall convolutional Neural Network composed of convolutional layers and nonlinear activation functions is then viewed as a 2-D version of a Lur'e system, i.e., a linear dynamical system interconnected with static nonlinear components. One benefit of this 2-D Lur'e system perspective on CNNs is that we can use robust control theory much more efficiently for Lipschitz constant estimation than previously possible.
@article{GraPau23,
abstract = {This paper introduces a novel representation of convolutional Neural Networks (CNNs) in terms of 2-D dynamical systems. To this end, the usual description of convolutional layers with convolution kernels, i.e., the impulse responses of linear filters, is realized in state space as a linear time-invariant 2-D system. The overall convolutional Neural Network composed of convolutional layers and nonlinear activation functions is then viewed as a 2-D version of a Lur'e system, i.e., a linear dynamical system interconnected with static nonlinear components. One benefit of this 2-D Lur'e system perspective on CNNs is that we can use robust control theory much more efficiently for Lipschitz constant estimation than previously possible.},
added-at = {2024-03-12T10:23:55.000+0100},
archiveprefix = {arXiv},
author = {Gramlich, Dennis and Pauli, Patricia and Scherer, Carsten W. and Allgöwer, Frank and Ebenbauer, Christian},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/28064620aaaf8317f8230bf19ad0cca8b/mst},
copyright = {Creative Commons Attribution Non Commercial Share Alike 4.0 International},
doi = {10.48550/ARXIV.2303.03042},
eprint = {2303.03042},
file = {:GraPau23 - Convolutional Neural Networks As 2 D Systems.pdf:PDF},
groups = {PN4-3, PN4-3(II)},
interhash = {770011146f488997513a05d825b0878d},
intrahash = {8064620aaaf8317f8230bf19ad0cca8b},
keywords = {PN4-3(II) PN4 EXC2075},
month = mar,
primaryclass = {math.OC},
publisher = {arXiv},
timestamp = {2024-03-12T10:23:55.000+0100},
title = {Convolutional Neural Networks as 2-D systems},
year = 2023
}
