arXiv:2511. 12398v2 Announce Type: replace Abstract: Deep neural networks have been widely used as universal approximators for functions with inherent physical structures, including permutation symmetry.
By Yulong Lu, Tong Mao, Jinchao Xu, Yahong Yang
arXiv:2608. 11911v1 Announce Type: cross Abstract: A central promise of useful quantum advantage is the ability to compute ground states of Hamiltonian systems beyond the reach of classical simulation methods.
By Timothy Heightman, Elena Orlova, Philip Mantrov, Aleksei Ustimenko
arXiv:2606. 00442v1 Announce Type: new Abstract: Many machine learning techniques rely on approximating a loss function's curvature, but this is notoriously hard to do at the scale of modern deep networks.
By Artem Artemev, Rui Xia, Benjamin M. Boyd, Youjing Yu, Felix Dangel, Guillaume Hennequin, Alberto Bernacchia
arXiv:2608. 12010v1 Announce Type: new Abstract: Equivariant Neural Networks (ENNs) have empowered numerous applications in scientific fields.
By Ning Lin, Jiacheng Cen, Anyi Li, Wenbing Huang, Hao Sun
Equivariant Neural Networks (ENNs) have empowered numerous applications in scientific fields. Despite their remarkable capacity for representing geometric structures, ENNs suffer from degraded expressivity when processing symmetric inputs: the output representations are invariant to transformations that extend beyond the input's symmetries.
arXiv:2503. 24092v2 Announce Type: replace-cross Abstract: Motivated by the rapidly growing field of mathematics for operator approximation with neural networks, we present a novel universal operator approximation theorem for broad classes of encoder-decoder architectures and a wide range of input and output spaces.
By Janek G\"odeke, Pascal Fernsel