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: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
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: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
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
arXiv:2608. 13335v1 Announce Type: new Abstract: Neural networks trained by gradient descent on a smooth cost function can nevertheless learn in steps: the cost holds on long plateaus and then drops abruptly.
By Liu Ziyin, Yizhou Xu, Tomaso Poggio, Isaac Chuang
arXiv:2606. 04754v1 Announce Type: new Abstract: Many striking phenomena in deep learning, such as linear mode connectivity and the structured behavior of training dynamics, are closely tied to parameter symmetries: transformations that leave the realized function unchanged.
By Vincent B\"urgin, Daniel Herbst, Ya-Wei Eileen Lin, Stefanie Jegelka
arXiv:2309. 07401v2 Announce Type: replace-cross Abstract: Deep neural networks (DNNs) show great promise for solving partial differential equations (PDEs), but their deep architectures introduce complex, large-scale, non-convex optimization challenges.
By Yuesheng Xu, Taishan Zeng
arXiv:2507. 05164v2 Announce Type: replace-cross Abstract: In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms.
By Dennis Chemnitz, Maximilian Engel, Christian Kuehn, Sara-Viola Kuntz