arXiv:2608. 18570v1 Announce Type: cross Abstract: Machine learning and data analysis techniques have recently emerged as powerful tools for identifying patterns and formulating conjectures in mathematical research, most notably in the field of low-dimensional topology.
By Brandon Robinson, Shimal Harichurn, Fabian Ruehle, Sergei Gukov, Rak-Kyeong Seong, Miranda C. N. Cheng
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...
By Alexander H. Berger, Marco Fontana, Daniel Rueckert, Johannes C. Paetzold, Laurin Lux, Ulrich Bauer
arXiv:2507.21135v2 Announce Type: replace
Abstract: We demonstrate how Quantum Cognition Machine Learning (QCML) encodes data as quantum geometry. In QCML, features of the data are represented by lea...
By Alexander G. Abanov, Luca Candelori, Harold C. Steinacker, Martin T. Wells, Jerome R. Busemeyer, Cameron J. Hogan, Vahagn Kirakosyan, Nicola Marzari, Sunil Pinnamaneni, Dario Villani, Mengjia Xu, Kharen Musaelian
arXiv:2608. 11321v1 Announce Type: cross Abstract: We study spectral clustering in the presence of a confounding latent geometry.
By Konstantin Avrachenkov, Lucas S. Sibemberg, Alexander Van Werde
arXiv:2607. 03692v1 Announce Type: new Abstract: Spectral methods are widely used to construct representations from the geometry of data, but they often rely on a fixed kernel, graph Laplacian, or manually selected feature scaling.
By Varvara Nazarenkko, Timur Lidzhiev, Alexander Tarakanov
The survey reviews frequency‑domain techniques for time‑series analysis, covering classical Fourier methods to modern neural operators. It identifies three main research challenges: preserving causal structure during spectral transformations, quantifying uncertainty in learned frequency representations, and performing topology‑aware analysis for non‑Euclidean data. By reviewing over 100 studies, the authors propose a unified taxonomy, establish standardized benchmarks, and highlight gaps in geometric deep learning and quantum‑enhanced spectral analysis.
By Qianru Zhang, Yuting Sun, Honggang Wen, Peng Yang, Xinzhu Li, Ming Li, Kwok-Yan Lam, Siu-Ming Yiu, Hongzhi Yin