arXiv:2606. 29675v1 Announce Type: new Abstract: Bogomolny, Bohigas and Schmit (BBS) found that the spectrum of the pairwise distance matrix on N points sampled from a smooth d-dimensional manifold encodes a signature of the underlying geometry.
By Igor Halperin
arXiv:2606. 28486v1 Announce Type: cross Abstract: The emergence of low-dimensional structures in the spectra of neural network weight matrices is a common empirical feature of trained models, but the dynamical origin of this phenomenon during learning remains an open problem.
By Chanju Park, Dario Bocchi, Francesco D'Amico, Biagio Lucini, Gert Aarts
arXiv:2602. 02908v2 Announce Type: replace-cross Abstract: Diffusion models trained on different, non-overlapping subsets of a dataset often produce strikingly similar outputs when given the same noise seed.
By Binxu Wang, Jacob Zavatone-Veth, Cengiz Pehlevan
arXiv:2610.01522v1 Announce Type: cross
Abstract: Many scientific and machine learning systems, from molecular dynamics to diffusion models and beyond, are governed by stochastic dynamics with low-di...
By Vladimir R. Kostic, Karim Lounici, H\'el\`ene Halconruy, Timoth\'ee Devergne, Michele Parrinello, Massimiliano Pontil
arXiv:2607. 02937v1 Announce Type: new Abstract: Reduced-order models compress high-dimensional dynamics into low-dimensional representations that can be evaluated rapidly, but they lose accuracy when online dynamics drift beyond the training data.
By Amirpasha Hedayat, Laura Balzano, Karthik Duraisamy
The paper introduces DOODL, a framework that learns a dictionary of spectral dynamics to represent related dynamical systems as points on a low‑dimensional manifold in operator space. By constraining operator estimation to this learned manifold, DOODL provides compact, interpretable embeddings and enables fast, accurate operator estimation from short, partially observed trajectories. Experiments on metastable Langevin dynamics and turbulent plasma simulations show that DOODL achieves one to two orders of magnitude lower errors than independent estimation methods, especially in low‑data regimes.
By Thibaut Germain, Sami Chemlal, R\'emi Flamary, Vladimir R. Kostic, Karim Lounici