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arXiv · 1905.12200

A Topology Layer for Machine Learning

Rickard Brüel-Gabrielsson·Bradley J. Nelson·Anjan Dwaraknath·Primoz Skraba·Leonidas J. Guibas·Gunnar Carlsson
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Abstract

Topology applied to real world data using persistent homology has started to find applications within machine learning, including deep learning. We present a differentiable topology layer that computes persistent homology based on level set filtrations and edge-based filtrations. We present three novel applications: the topological layer can (i) regularize data reconstruction or the weights of machine learning models, (ii) construct a loss on the output of a deep generative network to incorporate topological priors, and (iii) perform topological adversarial attacks on deep networks trained with persistence features. The code (www.github.com/bruel-gabrielsson/TopologyLayer) is publicly available and we hope its availability will facilitate the use of persistent homology in deep learning and other gradient based applications.

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Rickard Brüel-Gabrielsson, Bradley J. Nelson, Anjan Dwaraknath, Primoz Skraba, Leonidas J. Guibas, Gunnar Carlsson. 2020-04-24. A Topology Layer for Machine Learning. https://arxiv.org/abs/1905.12200

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