Topological Convolutional Layers for Deep Learning
Abstract
This work introduces the Topological CNN (TCNN), which encompasses several topologically defined convolutional methods. Manifolds with important relationships to the natural image space are used to parameterize image filters which are used as convolutional weights in a TCNN. These manifolds also parameterize slices in layers of a TCNN across which the weights are localized. We show evidence that TCNNs learn faster, on less data, with fewer learned parameters, and with greater generalizability and interpretability than conventional CNNs. We introduce and explore TCNN layers for both image and video data. We propose extensions to 3D images and 3D video.
Cite
Text
Love et al. "Topological Convolutional Layers for Deep Learning." Journal of Machine Learning Research, 2023.Markdown
[Love et al. "Topological Convolutional Layers for Deep Learning." Journal of Machine Learning Research, 2023.](https://mlanthology.org/jmlr/2023/love2023jmlr-topological/)BibTeX
@article{love2023jmlr-topological,
title = {{Topological Convolutional Layers for Deep Learning}},
author = {Love, Ephy R. and Filippenko, Benjamin and Maroulas, Vasileios and Carlsson, Gunnar},
journal = {Journal of Machine Learning Research},
year = {2023},
pages = {1-35},
volume = {24},
url = {https://mlanthology.org/jmlr/2023/love2023jmlr-topological/}
}