arXiv:2606. 17531v1 Announce Type: new Abstract: We investigate the learning of interpretable bases in non-negative matrix factorisation (NMF) by regularising the topology of the learned basis functions.
arXiv:2606. 29763v1 Announce Type: cross Abstract: Topological data analysis (TDA), particularly persistent homology (PH), captures geometric structural properties in medical images (e.
arXiv:2505. 04346v2 Announce Type: replace Abstract: Clustering aims at partitioning data points into groups of similar objects without knowing about the class labels.
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.
arXiv:2607. 13847v1 Announce Type: cross Abstract: Many datasets encountered across a wide range of domains possess rich geometric and topological structure that is difficult to capture using conventional vector-based representations.
arXiv:2608. 06276v1 Announce Type: cross Abstract: Persistence diagrams (PDs) provide stable and interpretable summaries of multiscale topological structure.
arXiv:2606. 28268v1 Announce Type: cross Abstract: Test-time adaptation (TTA) has emerged as a promising paradigm for mitigating distribution shifts in deep models.
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.
arXiv:2607. 28259v1 Announce Type: new Abstract: We introduce Topoformer, a lightweight and scalable framework for graph representation learning that encodes topological structure into attention-friendly sequences.
arXiv:2507. 07156v2 Announce Type: replace-cross Abstract: Supervised machine learning pipelines trained on features derived from persistent homology have been experimentally observed to ignore much of the information contained in a persistence diagram.
arXiv:2601. 21207v4 Announce Type: replace-cross Abstract: Combinatorial and topological structures, such as graphs, simplicial complexes, and cell complexes, form the foundation of geometric and topological deep learning (GDL and TDL) architectures.
arXiv:2606. 01546v1 Announce Type: new Abstract: Sparse high-dimensional representations are conducive to uncovering nontrivial structures in unsupervised exploration of data.
arXiv:2506. 15020v2 Announce Type: replace-cross Abstract: We propose persistent discrete homology as a tool for topological data analysis and discuss its advantages over the existing methods.