Papers › Monoidal Rips: Stable Multiparameter Filtrations of Directed Networks

Monoidal Rips: Stable Multiparameter Filtrations of Directed Networks

18 Mar 2025arXiv:2503.14019links table onlyarchive 2025-07-28

Nello Blaser, Morten Brun, Odin Hoff Gardaa, Lars M. Salbu

The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.

We introduce the monoidal Rips filtration, a filtered simplicial set for weighted directed graphs and other lattice-valued networks. Our construction generalizes the Vietoris-Rips filtration for metric spaces by replacing the maximum operator, determining the filtration values, with a more general monoidal product. We establish interleaving guarantees for the monoidal Rips persistent homology, capturing existing stability results for real-valued networks. When the lattice is a product of totally ordered sets, we are in the setting of multiparameter persistence. Here, the interleaving distance is bounded in terms of a generalized network distance. We use this to prove a novel stability result for the sublevel Rips bifiltration. Our experimental results show that our method performs better than Flagser in a graph regression task, and that combining different monoidal products in point cloud classification can improve performance.

PaperPDFCode

Code

Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.

Code Syntology ran Syntology

Not run by Syntology. Nothing on this page verifies that the listed code works.

Results from the paper archive 2025-07-28

No leaderboard rows for this paper in the archive.

Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections