Topological regularization via persistence-sensitive optimization

Journal Article · 28 February 2024 · Computational Geometry

DOI: https://doi.org/10.1016/j.comgeo.2024.102086 · OSTI ID:2315738

Nigmetov, Arnur  ^[1]; Krishnapriyan, Aditi  ^[2]; Sanderson, Nicole  ^[1]; Morozov, Dmitriy ^[1]

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1. Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
2. Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States); University of California, Berkeley, CA (United States)

Optimization, a key tool in machine learning and statistics, relies on regularization to reduce overfitting. Traditional regularization methods control a norm of the solution to ensure its smoothness. Recently, topological methods have emerged as a way to provide a more precise and expressive control over the solution, relying on persistent homology to quantify and reduce its roughness. All such existing techniques back-propagate gradients through the persistence diagram, which is a summary of the topological features of a function. Their downside is that they provide information only at the critical points of the function. We propose a method that instead builds on persistence-sensitive simplification and translates the required changes to the persistence diagram into changes on large subsets of the domain, including both critical and regular points. This approach enables a faster and more precise topological regularization, the benefits of which we illustrate with experimental evidence.

• Research Organization: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES). Scientific User Facilities (SUF); USDOE Laboratory Directed Research and Development (LDRD) Program
• Grant/Contract Number: AC02-05CH11231
• OSTI ID: 2315738
• Alternate ID(s): OSTI ID: 2426660; OSTI ID: 2477266
• Journal Information: Computational Geometry, Vol. 120; ISSN 0925-7721
• Publisher: ElsevierCopyright Statement
• Country of Publication: United States
• Language: English