Topological Deep Learning

Understand

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.