The network topolog that more or less kicked off the current revolution in computer vision and thus the whole modern neural network craze.
Convolutional nets (convnets or CNNs to the suave) are well described elsewhere. I’m just going to collect some oddities here. Classic signal processing baked in to neural networks.
There is a long story here about how convolutions naturally encourage certain invariances and symmetries, although AFAICT it’s all somewhat hand-wavey.
Generally uses FIR filters plus some smudgy “pooling”.
An interesting data visualisation challenge, since they often end up being high-dimensional tensors if you handle color.
Connection to filter theory
Graph convolutional neural nets
Convolutions plus spectral graph theory. Thomas Kipf, summarises recent research.
Defferrard, Michaël, Xavier Bresson, and Pierre Vandergheynst. 2016. “Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering.” In Advances in Neural Information Processing Systems. http://arxiv.org/abs/1606.09375.
Gonzalez, R. C. 2018. “Deep Convolutional Neural Networks [Lecture Notes].” IEEE Signal Processing Magazine 35 (6): 79–87. https://doi.org/10.1109/MSP.2018.2842646.
Kipf, Thomas N., and Max Welling. 2016. “Semi-Supervised Classification with Graph Convolutional Networks.” In. http://arxiv.org/abs/1609.02907.
Krizhevsky, Alex, Ilya Sutskever, and Geoffrey E. Hinton. 2012. “Imagenet Classification with Deep Convolutional Neural Networks.” In Advances in Neural Information Processing Systems, 1097–1105. http://papers.nips.cc/paper/4824-imagenet-classification-with-deep-convolutional-neural-networks.
Kulkarni, Tejas D., Will Whitney, Pushmeet Kohli, and Joshua B. Tenenbaum. 2015. “Deep Convolutional Inverse Graphics Network,” March. http://arxiv.org/abs/1503.03167.
LeCun, Yann, Yoshua Bengio, and Geoffrey Hinton. 2015. “Deep Learning.” Nature 521 (7553): 436–44. https://doi.org/10.1038/nature14539.
Lee, Honglak, Roger Grosse, Rajesh Ranganath, and Andrew Y. Ng. 2009. “Convolutional Deep Belief Networks for Scalable Unsupervised Learning of Hierarchical Representations.” In Proceedings of the 26th Annual International Conference on Machine Learning, 609–16. ICML ’09. New York, NY, USA: ACM. https://doi.org/10.1145/1553374.1553453.
Mallat, Stéphane. 2016. “Understanding Deep Convolutional Networks,” January. http://arxiv.org/abs/1601.04920.
Mousavi, Ali, and Richard G. Baraniuk. 2017. “Learning to Invert: Signal Recovery via Deep Convolutional Networks.” In ICASSP. http://arxiv.org/abs/1701.03891.
Paul, Arnab, and Suresh Venkatasubramanian. 2014. “Why Does Deep Learning Work? - A Perspective from Group Theory,” December. http://arxiv.org/abs/1412.6621.
Rawat, Waseem, and Zenghui Wang. 2017. “Deep Convolutional Neural Networks for Image Classification: A Comprehensive Review.” Neural Computation 29 (9): 2352–2449. https://doi.org/10.1162/neco_a_00990.
Springenberg, Jost Tobias, Alexey Dosovitskiy, Thomas Brox, and Martin Riedmiller. 2014. “Striving for Simplicity: The All Convolutional Net.” In Proceedings of International Conference on Learning Representations (ICLR) 2015. http://arxiv.org/abs/1412.6806.
Urban, Gregor, Krzysztof J. Geras, Samira Ebrahimi Kahou, Ozlem Aslan, Shengjie Wang, Rich Caruana, Abdelrahman Mohamed, Matthai Philipose, and Matt Richardson. 2016. “Do Deep Convolutional Nets Really Need to Be Deep (or Even Convolutional)?” March. http://arxiv.org/abs/1603.05691.
Wang, Yunhe, Chang Xu, Chao Xu, and Dacheng Tao. 2019. “Packing Convolutional Neural Networks in the Frequency Domain.” IEEE Transactions on Pattern Analysis and Machine Intelligence 41 (10): 2495–2510. https://doi.org/10.1109/TPAMI.2018.2857824.
Wiatowski, Thomas, and Helmut Bölcskei. 2015. “A Mathematical Theory of Deep Convolutional Neural Networks for Feature Extraction.” In Proceedings of IEEE International Symposium on Information Theory. http://arxiv.org/abs/1512.06293.
Wiatowski, Thomas, Philipp Grohs, and Helmut Bölcskei. 2018. “Energy Propagation in Deep Convolutional Neural Networks.” IEEE Transactions on Information Theory 64 (7): 1–1. https://doi.org/10.1109/TIT.2017.2756880.