K-theoretic Persistent Cohomology

Yoshihiro Maruyama, Arisa Yasuda
Proceedings of the 4th (2025) and 3rd (2024) NeurIPS Workshops on Symmetry and Geometry in Neural Representations, PMLR 282:381-391, 2026.

Abstract

We develop K-theoretic persistent cohomology (KPCH): a principled extension of 1-parameter persistent (co)homology that equips the Grothendieck group of persistence modules with lambda-operations arising from exterior powers. This yields new, computable persistence layers that quantify concurrency among cohomology classes via interval intersections. We establish the core algebraic and stability results, provide an interval-calculus for efficient computation on barcodes, and demonstrate empirical benefits on graph filtrations, where KPCH separates patterns that standard additive H^p summaries such as total persistence cannot distinguish.

Cite this Paper

BibTeX
@InProceedings{pmlr-v282-maruyama26b, title = {K-theoretic Persistent Cohomology}, author = {Maruyama, Yoshihiro and Yasuda, Arisa}, booktitle = {Proceedings of the 4th (2025) and 3rd (2024) NeurIPS Workshops on Symmetry and Geometry in Neural Representations}, pages = {381--391}, year = {2026}, editor = {Acosta, Francisco and Azeglio, Simone and Tolooshams, Bahareh and van de Geijn, Chase and Shewmake, Christian and Sanborn, Sophia and Miolane, Nina}, volume = {282}, series = {Proceedings of Machine Learning Research}, month = {14 Dec 2024--07 Dec 2025}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v282/main/assets/maruyama26b/maruyama26b.pdf}, url = {https://proceedings.mlr.press/v282/maruyama26b.html}, abstract = {We develop K-theoretic persistent cohomology (KPCH): a principled extension of 1-parameter persistent (co)homology that equips the Grothendieck group of persistence modules with lambda-operations arising from exterior powers. This yields new, computable persistence layers that quantify concurrency among cohomology classes via interval intersections. We establish the core algebraic and stability results, provide an interval-calculus for efficient computation on barcodes, and demonstrate empirical benefits on graph filtrations, where KPCH separates patterns that standard additive H^p summaries such as total persistence cannot distinguish.} }
Endnote
%0 Conference Paper %T K-theoretic Persistent Cohomology %A Yoshihiro Maruyama %A Arisa Yasuda %B Proceedings of the 4th (2025) and 3rd (2024) NeurIPS Workshops on Symmetry and Geometry in Neural Representations %C Proceedings of Machine Learning Research %D 2026 %E Francisco Acosta %E Simone Azeglio %E Bahareh Tolooshams %E Chase van de Geijn %E Christian Shewmake %E Sophia Sanborn %E Nina Miolane %F pmlr-v282-maruyama26b %I PMLR %P 381--391 %U https://proceedings.mlr.press/v282/maruyama26b.html %V 282 %X We develop K-theoretic persistent cohomology (KPCH): a principled extension of 1-parameter persistent (co)homology that equips the Grothendieck group of persistence modules with lambda-operations arising from exterior powers. This yields new, computable persistence layers that quantify concurrency among cohomology classes via interval intersections. We establish the core algebraic and stability results, provide an interval-calculus for efficient computation on barcodes, and demonstrate empirical benefits on graph filtrations, where KPCH separates patterns that standard additive H^p summaries such as total persistence cannot distinguish.
APA
Maruyama, Y. & Yasuda, A.. (2026). K-theoretic Persistent Cohomology. Proceedings of the 4th (2025) and 3rd (2024) NeurIPS Workshops on Symmetry and Geometry in Neural Representations, in Proceedings of Machine Learning Research 282:381-391 Available from https://proceedings.mlr.press/v282/maruyama26b.html.

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