# Top-K Exterior Power Persistent Homology: Algorithm, Structure, and Stability

arXiv: https://arxiv.org/abs/2512.20325 · HTML: https://mlsanity.com/paper/2512.20325/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 27 references that are in the map.
- First posted on arXiv 23 Dec 2025.

## Builds on (most cited first, 2 of 2)

- [Ripser: efficient computation of Vietoris-Rips persistence barcodes](https://mlsanity.com/paper/1908.02518/) (2019)
- [Philosophical Specification of Empathetic Ethical Artificial Intelligence](https://mlsanity.com/paper/2107.10715/) (2021)

## Abstract (arXiv)

Exterior powers play important roles in persistent homology in computational geometry. In the present paper we study the problem of extracting the K longest intervals of the exterior-power layers of a tame persistence module. We prove a structural decomposition theorem that organizes the exterior-power layers into monotone per-anchor streams with explicit multiplicities, enabling a best-first algorithm. We also show that the Top-K length vector is 2-Lipschitz under bottleneck perturbations of the input barcode, and prove a comparison-model lower bound. Our experiments confirm the theory, showing speedups over full enumeration in high overlap cases. By enabling efficient extraction of the most prominent features, our approach makes higher-order persistence feasible for large datasets and thus broadly applicable to machine learning, data science, and scientific computing.