# Topological Regularization via Persistence-Sensitive Optimization

arXiv: https://arxiv.org/abs/2011.05290 · HTML: https://mlsanity.com/paper/2011.05290/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Nov 2020.

## Built on by (most cited first, 2 of 2)

- [Diffeomorphic interpolation for efficient persistence-based topological optimization](https://mlsanity.com/paper/2405.18820/) (2024)
- [A Practical Solver for Scalar Data Topological Simplification](https://mlsanity.com/paper/2407.12399/) (2024)

## Abstract (arXiv)

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.