arXiv:2605. 28983v2 Announce Type: replace-cross Abstract: In this paper, training a neural network is identified, exactly, as a search through Hamilton--Jacobi initial-value problems: each gradient step selects the initial data of a viscous Hamilton--Jacobi equation whose Hopf--Cole propagator best fits the observations; at inference, the input is the spatial point at which that solution is evaluated and the initial condition is already encoded in the weights.
By Jose Marie Antonio Mi\~noza, Erika Fille T. Legara, Christopher P. Monterola
arXiv:2607. 07845v1 Announce Type: new Abstract: The Hessian of the training loss governs the local geometry of the loss landscape, yet despite existing explanations for its largest eigenvalues, the origin of the vast multitude of vanishingly small eigenvalues remains elusive.
By Marcel K\"uhn, Bernd Rosenow
arXiv:2606. 10913v1 Announce Type: new Abstract: We explore whether intrinsic symmetries of the training data lead to conserved quantities during gradient-flow training of neural networks.
By Jakob Galley, Vahid Shahverdi, Axel Flinth
arXiv:2608.24700v1 Announce Type: new
Abstract: When a network has learned a function with a known symmetry, can that symmetry be moved through the parametrisation---is there a motion in parameter sp...
By Alan Muriithi, Vedanta Thapar, Torben Berndt
arXiv:2511. 07308v3 Announce Type: replace Abstract: Understanding the training dynamics of deep neural networks remains a major open problem, with physics-inspired approaches offering promising insights.
By Ildus Sadrtdinov, Ekaterina Lobacheva, Ivan Klimov, Mikhail Burtsev, Mikhail I. Katsnelson, Dmitry Vetrov
Artificial neural networks generate local symmetries called fibrations and coverings during learning, and these covering symmetries are stable attractors of stochastic gradient descent. The study shows that such symmetries appear across diverse architectures—multilayer, convolutional, recurrent, and transformer networks—and can be exploited for drastic model compression, reducing networks to 17% of their original size without performance loss. Controlled breaking of covering symmetry further improves continual learning, achieving state‑of‑the‑art results.
By Osvaldo M Velarde, Lucas C Parra, Alireza Hashemi, Hernan A Makse
arXiv:2501. 02436v5 Announce Type: replace Abstract: Advancements in artificial intelligence call for a deeper understanding of the fundamental mechanisms underlying deep learning.
By Yuchen Lin, Yong Zhang, Sihan Feng, Hong Zhao
arXiv:2604. 14037v2 Announce Type: replace Abstract: Parameter space is not function space for neural network architectures.
By Pranavkrishnan Ramakrishnan
arXiv:2609. 09589v1 Announce Type: new Abstract: Deep neural networks exhibit regular macroscopic behavior despite highly nonlinear dynamics in vast parameter spaces.
By Yizhou Zhang, Weichen Wu, Lun Du, Zhengjie Miao
arXiv:2505. 19619v3 Announce Type: replace Abstract: Deep generative models have recently garnered significant attention across various fields, from physics to chemistry, where sampling from unnormalized Boltzmann-like distributions represents a fundamental challenge.
By Janik Kreit, Dominic Schuh, Kim A. Nicoli, Lena Funcke
The paper investigates how machine learning models can regress scale‑free processes, such as earthquakes or avalanches, focusing on predicting rare, large events that require extrapolation. It studies two self‑similar systems: a 2‑dimensional fractional Gaussian field and the Abelian sandpile model. Experiments compare existing architectures (U‑net, Riesz network) with new proposals (wavelet‑based Graph Neural Network, Fourier embedding, Fourier‑Mellin Neural Operator) to identify spectral bias and coarse‑graining challenges and suggest inductive biases to address them.
By Anaclara Alvez-Canepa, Cyril Furtlehner, Fran\c{c}ois P. Landes
arXiv:2511. 02003v2 Announce Type: replace Abstract: We present the bulk--boundary decomposition as a new framework for understanding the training dynamics of deep neural networks.
By Donghee Lee, Hye-Sung Lee, Jaeok Yi