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:2609.37177v1 Announce Type: cross Abstract: Persistent homology (PH) is a frequently used tool for extracting and preserving topological information from image data, particularly in image segme...
Topological signal processing (TSP) traditionally uses oriented boundary operators to process signals on simplicial complexes, which is suitable for flow signals or when topological invariants are important. This paper introduces an unoriented TSP (UTSP) framework that replaces oriented boundaries with unoriented incidence matrices, demonstrating that these matrices retain graph-like spectral properties across simplicial levels. By removing orientation, the authors develop an interaction-order decomposition—an analogue to Hodge decomposition—to quantify how higher-order signals are explained by aggregating lower-order signals, and use this decomposition to create order-aware regularizers that outperform oriented baselines in real-world experiments, especially when signal energy is unevenly distributed across orders.
arXiv:2505. 04346v2 Announce Type: replace Abstract: Clustering aims at partitioning data points into groups of similar objects without knowing about the class labels.
Many disentanglement methods represent generative factors using Euclidean product coordinates, although the underlying factor spaces may wrap, collapse, or have position-dependent geometry. We introdu...
The paper proposes using concepts from low‑dimensional topology—specifically Morse theory and cobordism—to enhance graph diffusion models, introducing the MG‑Diff pipeline. It provides theoretical guarantees that the Morse‑theoretic guidance remains stable under small perturbations when a positive decision‑gap exists. The authors demonstrate the approach on spatio‑temporal graph forecasting and graph regeneration, suggesting broader potential for topology in machine learning.
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:2608.24762v1 Announce Type: cross Abstract: Many disentanglement methods represent generative factors using Euclidean product coordinates, although the underlying factor spaces may wrap, collap...
arXiv:2609.37884v1 Announce Type: new Abstract: Topological structures such as simplicial complexes, hypergraphs, and cell complexes extend standard graph models by modeling higher-order relationship...
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.
The paper demonstrates that high‑quality graph embeddings can be produced without complex models or training by propagating random features through topological structures derived from random walks and anonymous walks. These training‑free embeddings capture node proximity and structural roles, respectively, and perform competitively on node, edge, and graph tasks while often requiring less computation. Combining the two embedding types further improves inference quality for some tasks.
arXiv:2512.23348v3 Announce Type: replace-cross Abstract: We introduce a data-analysis framework based on filtrations of finite topological spaces. Starting from a finite metric data set, we construc...