Topological Convolutional Layers for Deep Learning
Ephy R. Love, Benjamin Filippenko, Vasileios Maroulas, Gunnar Carlsson; 24(59):1−35, 2023.
Abstract
This article presents the Topological CNN (TCNN), a collection of convolutional methods that are defined topologically. The TCNN utilizes manifolds that have significant connections to the natural image space to parameterize image filters. These filters are then used as convolutional weights in the TCNN. Additionally, the manifolds parameterize slices in TCNN layers, where the weights are localized. Our research demonstrates that TCNNs have the ability to learn faster, require less data, possess fewer learned parameters, and exhibit greater generalizability and interpretability compared to conventional CNNs. We also introduce TCNN layers for both image and video data, and propose extensions to 3D images and 3D video.
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