arXiv Machine Learning By Jernej Grlj, Aaron D. Lauda

Analytic Torsion and Spectral Gap Capture Persistent-Laplacian Performance

Read the original on arXiv Machine Learning →

arXiv:2606. 16990v1 Announce Type: new Abstract: While persistent Laplacians (PL) offer a richer geometric representation of data than persistent homology, utilizing their full eigenspectrum for learning tasks is often hampered by high dimensionality and the ``varying length'' problem across different filtration scales.

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arXiv Machine Learning
Jul 13

Group Invariant Spectral Embedding

arXiv:2607. 08987v1 Announce Type: new Abstract: Spectral embedding methods are widely used for dimensionality reduction and clustering of high-dimensional datasets with intrinsic low-dimensional structures.

By Yeari Vigder, Paulina Hoyos, David Thong, Joakim and\'en, Joe Kileel, Amit Moscovich
arXiv AI
Jun 9

Topological Neural Operators

arXiv:2606. 09806v1 Announce Type: cross Abstract: We introduce Topological Neural Operators (TNOs), a principled framework for operator learning on cell complexes that lifts neural operators (NOs) from functions on points and/or edges to topological domains.

By Lennart Bastian, Samuel Leventhal, Mustafa Hajij, Tolga Birdal