ICML 2025

Wyckoff Transformer: Generation of Symmetric Crystals
Nikita Kazeev 1 Wei Nong 2 Ignat Romanov 3 Ruiming Zhu 2 Andrey Ustyuzhanin 4 5 1 Shuya Yamazaki 2
Kedar Hippalgaonkar 1 2 6
Abstract
Crystal symmetry plays a fundamental role in
determining its physical, chemical, and elec-
tronic properties such as electrical and thermal
conductivity, optical and polarization behavior,
and mechanical strength.
Almost all known
crystalline materials have internal symmetry.
However, this is often inadequately addressed by
existing generative models, making the consistent
generation of stable and symmetrically valid
crystal structures a significant challenge.
We
introduce WyFormer, a generative model that
directly tackles this by formally conditioning
on space group symmetry. It achieves this by
using Wyckoff positions as the basis for an
elegant,
compressed,
and discrete structure
representation. To model the distribution, we
develop a permutation-invariant autoregressive
model based on the Transformer encoder and
an absence of positional encoding. Extensive
experimentation
demonstrates
WyFormer’s
compelling combination of attributes: it achieves
best-in-class symmetry-conditioned generation,
incorporates a physics-motivated inductive bias,
produces structures with competitive stability,
predicts material properties with competitive
accuracy even without atomic coordinates, and
exhibits unparalleled inference speed. https:
//github.com/SymmetryAdvantage/
WyckoffTransformer
1Institute for Functional Intelligent Materials University of Sin-
gapore, Block S9, Level 9, 4 Science Drive 2, Singapore 117544
2School of Materials Science and Engineering, Nanyang Techno-
logical University, Singapore 639798 3HSE University, Myasnit-
skaya Ulitsa, 20, Moscow, Russia, 101000 4Constructor University,
Bremen, Campus Ring 1, 28759, Germany 5Constructor Knowl-
edge Labs, Bremen, Campus Ring 1, 28759, Germany 6Institute of
Materials Research and Engineering, Agency for Science Technol-
ogy and Re...