Topological Deep Learning
This work addresses the need for more efficient and interpretable deep learning models in computer vision, though it appears incremental as it builds on existing CNN frameworks with topological enhancements.
The authors tackled the problem of improving convolutional neural networks by introducing Topological CNNs (TCNNs), which use manifolds related to natural images to parameterize filters and localize weights, resulting in faster learning, less data usage, fewer parameters, and better generalizability and interpretability compared to conventional CNNs.
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.