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: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
Training in artificial neural networks can be viewed as a trajectory evolving through a high-dimensional loss landscape. However, the large number of trainable parameters makes the direct analysis of these dynamics challenging.
arXiv:2607. 00063v1 Announce Type: cross Abstract: This paper studies how spectral geometry emerges in quantum learning models and how it can be diagnosed with physically grounded probes.
By Santanu Ganguly, Xing Liang, Dimitrios Makris