A Topology Layer for Machine Learning

Rickard Brüel Gabrielsson, Bradley J. Nelson, Anjan Dwaraknath, Primoz Skraba
Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:1553-1563, 2020.

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 is publicly available and we hope its availability will facilitate the use of persistent homology in deep learning and other gradient based applications.

Cite this Paper

BibTeX
@InProceedings{pmlr-v108-gabrielsson20a, title = {A Topology Layer for Machine Learning}, author = {Gabrielsson, Rickard Br\"uel and Nelson, Bradley J. and Dwaraknath, Anjan and Skraba, Primoz}, booktitle = {Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics}, pages = {1553--1563}, year = {2020}, editor = {Chiappa, Silvia and Calandra, Roberto}, volume = {108}, series = {Proceedings of Machine Learning Research}, month = {26--28 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v108/gabrielsson20a/gabrielsson20a.pdf}, url = {https://proceedings.mlr.press/v108/gabrielsson20a.html}, 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 is publicly available and we hope its availability will facilitate the use of persistent homology in deep learning and other gradient based applications. } }
Endnote
%0 Conference Paper %T A Topology Layer for Machine Learning %A Rickard Brüel Gabrielsson %A Bradley J. Nelson %A Anjan Dwaraknath %A Primoz Skraba %B Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2020 %E Silvia Chiappa %E Roberto Calandra %F pmlr-v108-gabrielsson20a %I PMLR %P 1553--1563 %U https://proceedings.mlr.press/v108/gabrielsson20a.html %V 108 %X 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 is publicly available and we hope its availability will facilitate the use of persistent homology in deep learning and other gradient based applications.
APA
Gabrielsson, R.B., Nelson, B.J., Dwaraknath, A. & Skraba, P.. (2020). A Topology Layer for Machine Learning. Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 108:1553-1563 Available from https://proceedings.mlr.press/v108/gabrielsson20a.html.

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