[1] Henry Adams, Tegan Emerson, Michael Kirby, Rachel Neville, Chris Peterson, Patrick Shipman, Sofya Chepushtanova, Eric Hanson, Francis Motta, and Lori Ziegelmeier. Persistence Images: A Stable Vector Representation of Persistent Homology. Journal of Machine Learning Research, 18(8):1-35, 2017. ISSN 1533-7928. URL http://jmlr.org/papers/v18/16-337.html.
[2] Randall Balestriero, Jerome Pesenti, and Yann LeCun. Learning in High Dimension Al-ways Amounts to Extrapolation, October 2021. URL http://arxiv.org/abs/2110.09485.arXiv:2110.09485 [cs].
[3] Serguei Barannikov, Ilya Trofimov, Grigorii Sotnikov, Ekaterina Trimbach, Alexander Korotin, Alexander Filippov, and Evgeny Burnaev. Manifold Topology Divergence: a Framework for Comparing Data Manifolds. November 2021. URL https://openreview.net/forum?id=Fj6kQJbHwM9.
[4] Ulrich Bauer, Talha Bin Masood, Barbara Giunti, Guillaume Houry, Michael Kerber, and Abhishek Rathod. Keeping it sparse: Computing Persistent Homology revisited, December 2022. URL http://arxiv.org/abs/2211.09075. arXiv:2211.09075 [cs, math].
[5] Mikhail Belkin. Fit without fear: remarkable mathematical phenomena of deep learning through the prism of interpolation, May 2021. URL http://arxiv.org/abs/2105.14368.arXiv:2105.14368 [cs, math, stat].
[6] Paul Bendich, J. S. Marron, Ezra Miller, Alex Pieloch, and Sean Skwerer. Persistent homology analysis of brain artery trees. Ann. Appl. Stat., 10(1), March 2016. ISSN 1932-6157. doi: 10.1214/15-AOAS886. URL https://projecteuclid.org/journals/annals-of-applied-statistics/volume-10/issue-1/Persistent-homology-analysis-of-brain-artery-trees/10.1214/15-AOAS886.full.
[7] Magnus Bakke Botnan and Michael Lesnick. An Introduction to Multiparameter Persistence, March 2023. URL http://arxiv.org/abs/2203.14289. arXiv:2203.14289 [cs, math].
[8] Mathieu Carriere, Frederic Chazal, Yuichi Ike, Theo Lacombe, Martin Royer, and Yuhei Umeda. PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures. In Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, pages 2786-2796. PMLR, June 2020. URL https://proceedings.mlr.press/v108/carriere20a.html.
[9] Mathieu Carriere, Frederic Chazal, Marc Glisse, Yuichi Ike, Hariprasad Kannan, and Yuhei Umeda. Optimizing persistent homology based functions. In Proceedings of the 38th International Conference on Machine Learning, pages 1294-1303. PMLR, July 2021. URL https://proceedings.mlr.press/v139/carriere21a.html.
[10] Chao Chen, Xiuyan Ni, Qinxun Bai, and Yusu Wang. A Topological Regularizer for Classifiers via Persistent Homology. In Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, pages 2573–2582. PMLR, April 2019. URL https://proceedings.mlr.press/v89/chen19g.html.
[11] David Cohen-Steiner, Herbert Edelsbrunner, and John Harer. Stability of Persistence Diagrams. Discrete Comput Geom, 37(1):103-120, January 2007. ISSN 1432-0444. doi: 10.1007/s00454-006-1276-5. URL https://doi.org/10.1007/s00454-006-1276-5.
[12] Andac Demir, Elie Massaad, and Bulent Kiziltan. Topology-Aware Focal Loss for 3D Image Segmentation, April 2023. URL https://www.biorxiv.org/content/10.1101/2023.04.21.537860v4.
[13] Swaroopa Dola, Matthew B. Dwyer, and Mary Lou Soffa. Distribution-Aware Testing of Neural Networks Using Generative Models. In 2021 IEEE/ACM 43rd International Conference on Software Engineering (ICSE), pages 226-237, Madrid, ES, May 2021. IEEE. ISBN 978-1-66540-296-5. doi: 10.1109/ICSE43902.2021.00032. URL https://ieeexplore.ieee.org/document/9402100/.