arXiv:2605. 20440v2 Announce Type: replace Abstract: Symmetry is central to the physical sciences, yet machine learning usually captures it only approximately, leaving a residual per-step equivariance error $\varepsilon$ that compounds with depth $M$ as $M\varepsilon$, whereas exact equivariance holds at unbounded depth; we demonstrate this divergence at fourteen orders of magnitude.
By Paulina Hoyos, Shashanka Ubaru, Dongsung Huh, Vasileios Kalantzis, Kenneth L. Clarkson, Misha Kilmer, Haim Avron, Lior Horesh
arXiv:2608.18714v2 Announce Type: replace-cross
Abstract: Crystal symmetry dictates whether a physical response tensor must vanish, establishing a direct test for machine learning predictions indepen...
By Can Polat, Mustafa Kurban, Erchin Serpedin, Hasan Kurban
The article demonstrates that a single design decision—whether a machine‑learning model’s features include parity labels—determines if the model can ever predict physically impossible values for material properties. Using group‑theoretical analysis, the authors introduce the parity gap criterion to identify which properties and crystal symmetries are affected. Experiments on 2,000 centrosymmetric crystals show that parity‑labelled models achieve exact zero predictions for forbidden piezoelectric responses, whereas models lacking parity labels produce large errors, yet both maintain comparable overall accuracy.
By Can Polat, Mustafa Kurban, Erchin Serpedin, Hasan Kurban
arXiv:2606. 04108v1 Announce Type: cross Abstract: Single-view 3D generative models have achieved impressive visual quality, yet they are not designed to satisfy structural or functional requirements, and in practice, often fall short.
By Guangda Ji, Qimin Chen, Qinchan Li, Mingrui Zhao, Kai Wang, Hao Zhang
The paper introduces UniTB, a universal, E(3)-equivariant Hamiltonian framework that blends density‑functional tight‑binding priors with deep learning to predict electronic structures efficiently. UniTB corrects a prior Hamiltonian via a mixture‑of‑experts network and a charge‑equilibration head, ensuring physical downstream properties and suppressing spurious states. Trained on over 29,000 crystals, UniTB achieves sub‑meV accuracy, matches DFT predictions for amorphous Ge‑Sb‑Te, and enables rapid screening of more than 16,000 materials for industrial applications.
By Mingkang Liu, Zhanghao Zhouyin, Guanghui Wang, Daye Zheng, Lei Shen, Qiangqiang Gu
arXiv:2606. 28287v1 Announce Type: cross Abstract: Ab initio modeling has established Wigner's SU(4) and Elliott's SU(3) as dominant symmetries of the nuclear force in light and intermediate-mass nuclei.
By Phong Dang, Evander Espinoza, Xiaoliang Wan, Michela Negro, Jerry P. Draayer, Feng Pan, Tomas Dytrych, Daniel Langr, David Kekejian
arXiv:2605.06140v3 Announce Type: replace-cross
Abstract: Generative modeling of physical systems, such as molecules, requires learning distributions that are invariant under global symmetries, such...
By Samir Darouich, Vinh Tong, Llu\'is Pastor-P\'erez, Tanja Bien, Loay Mualem, Mathias Niepert
arXiv:2605. 18106v3 Announce Type: replace-cross Abstract: A striking geometric disparity has long persisted in the practice of deep learning.
By Tim Tsz-Kit Lau, Weijie Su
arXiv:2610.27762v1 Announce Type: new
Abstract: Deep generative modeling has achieved remarkable progress in crystal generation. Given the rich symmetries inherent in crystalline structures, recent w...
By Ziqiao Meng, Rongsheng Chen, Zhi Zheng, Nikita Kazeev, Zhenkun Wang, Andrey Ustyuzhanin, Wee Sun Lee
arXiv:2609. 10898v1 Announce Type: cross Abstract: Crystal-orientation maps are physical fields defined only up to crystal symmetry; electron backscatter diffraction (EBSD) resolves them experimentally, but acquisition-time constraints limit spatial resolution.
By Umang Garg, Warren Zamudio, McLean P. Echlin, Samantha H. Daly, Tresa M. Pollock, B. S. Manjunath
The paper introduces CrystAF, an all‑atom crystal flow‑map generation model, and evaluates where physics should be incorporated into generative crystal structure models. By applying physics‑informed post‑training, the authors improve molecular validity and crystal packing without altering sampling speed, while inference‑time corrections further refine the structures. The study demonstrates that post‑training and inference‑time physics are complementary, and that the post‑training approach transfers to other generators such as Clari‑M and MolCrystalFlow.
By Haocheng Tang, Junmei Wang, Wengong Jin
arXiv:2607. 03108v1 Announce Type: new Abstract: Post-hoc analysis of trained neural network weights often seeks to recover geometric structure directly from the parameters.
By Naoya Chiba, Satoshi Sugiyama, Yuki Uranishi