Topological Convolutional Neural Networks

Ephy Love, Benjamin Filippenko, Vasileios Maroulas, Gunnar E. Carlsson

Keywords: machine learning, convolutional neural network, topological data analysis

TL;DR: New convolutional layers based on topologically generated features improve training speed, generalizability, and interpretability.

Abstract: There is considerable interest in making convolutional neural networks (CNNs) that learn on less data, are better at generalizing, and are more easily interpreted. 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.

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