%0 Conference Paper %1 pmlr-v97-ye19a %A Ye, Jong Chul %A Sung, Woon Kyoung %B Proceedings of the 36th International Conference on Machine Learning %C Long Beach, California, USA %D 2019 %E Chaudhuri, Kamalika %E Salakhutdinov, Ruslan %I PMLR %K convnets dnn order2 %P 7064--7073 %T Understanding Geometry of Encoder-Decoder CNNs %U http://proceedings.mlr.press/v97/ye19a.html %V 97 %X Encoder-decoder networks using convolutional neural network (CNN) architecture have been extensively used in deep learning literatures thanks to its excellent performance for various inverse problems in computer vision, medical imaging, etc. However, it is still difficult to obtain coherent geometric view why such an architecture gives the desired performance. Inspired by recent theoretical understanding on generalizability, expressivity and optimization landscape of neural networks, as well as the theory of convolutional framelets, here we provide a unified theoretical framework that leads to a better understanding of geometry of encoder-decoder CNNs. Our unified mathematical framework shows that encoder-decoder CNN architecture is closely related to nonlinear basis representation using combinatorial convolution frames, whose expressibility increases exponentially with the network depth. We also demonstrate the importance of skipped connection in terms of expressibility, and optimization landscape.

@inproceedings{pmlr-v97-ye19a, abstract = {Encoder-decoder networks using convolutional neural network (CNN) architecture have been extensively used in deep learning literatures thanks to its excellent performance for various inverse problems in computer vision, medical imaging, etc. However, it is still difficult to obtain coherent geometric view why such an architecture gives the desired performance. Inspired by recent theoretical understanding on generalizability, expressivity and optimization landscape of neural networks, as well as the theory of convolutional framelets, here we provide a unified theoretical framework that leads to a better understanding of geometry of encoder-decoder CNNs. Our unified mathematical framework shows that encoder-decoder CNN architecture is closely related to nonlinear basis representation using combinatorial convolution frames, whose expressibility increases exponentially with the network depth. We also demonstrate the importance of skipped connection in terms of expressibility, and optimization landscape.}, added-at = {2020-06-02T20:11:26.000+0200}, address = {Long Beach, California, USA}, author = {Ye, Jong Chul and Sung, Woon Kyoung}, biburl = {https://www.bibsonomy.org/bibtex/20ae08edd5e9dfd9982da0c1f71e9c12a/sohnki}, booktitle = {Proceedings of the 36th International Conference on Machine Learning}, description = {Understanding Geometry of Encoder-Decoder CNNs}, editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan}, interhash = {08a769d522ad2d18cb29bbc966442b90}, intrahash = {0ae08edd5e9dfd9982da0c1f71e9c12a}, keywords = {convnets dnn order2}, month = {09--15 Jun}, pages = {7064--7073}, pdf = {http://proceedings.mlr.press/v97/ye19a/ye19a.pdf}, publisher = {PMLR}, series = {Proceedings of Machine Learning Research}, timestamp = {2020-06-02T20:33:59.000+0200}, title = {Understanding Geometry of Encoder-Decoder {CNN}s}, url = {http://proceedings.mlr.press/v97/ye19a.html}, volume = 97, year = 2019 }