arXiv:2409. 15600v3 Announce Type: replace Abstract: A representation of a molecule or material should be invariant to the symmetries of physics, unique, continuous, efficient and general.
By Rahul Khorana, Marcus Noack, Jin Qian
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
arXiv:2607. 06634v1 Announce Type: new Abstract: Compact networks built from Clifford algebra Cl(3,0) primitives are exactly SO(3)-equivariant and learn synthetic 3D vector laws from few samples.
By Fabien Polly
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. 29584v1 Announce Type: cross Abstract: $\mathrm{Cl}(3,0)$ interatomic potentials, despite their algebraic elegance, predict force magnitudes accurately but force directions poorly.
By Can Polat, Erchin Serpedin, Mustafa Kurban, Hasan Kurban
The paper addresses the limitations of spectral dimension reduction for dynamical systems composed of weakly interacting components, where standard rank‑based methods either require exponentially many modes or omit entire components (a phenomenon termed linear masking). It proposes scoring the σ‑algebra generated by coordinates instead of individual modes, using a χ²‑divergence criterion that guarantees an embedding with twice the intrinsic dimension captures the full operator spectrum. Experiments on benchmark systems show that this algebraic approach recovers masked components and enables accurate prediction from few labels, outperforming traditional rank‑based and VAMP methods.