Invertible and invariant crystal representation for generative materials models

Develop an invariant, fully invertible crystallographic representation for generative models of crystalline inorganic materials that uniquely and reversibly encodes periodic structures while respecting lattice periodicity, symmetry, and atom permutations, enabling reliable inverse design and unambiguous reconstruction of generated crystals.

Background

Generative models for inorganic crystals must handle periodicity, lattice vectors, and symmetry while remaining compact and invertible for training and generation. Existing representations include voxelized densities, symmetry-conditioned Wyckoff/space-group encodings, and matrix-based point-cloud encodings (e.g., CIF-like formats), each with trade-offs in invertibility, invariance, and scope.

Recent critiques of high-profile efforts have highlighted challenges in verifying novelty and stability, underscoring how representation choices can lead to ambiguity, duplication, or data leakage. The paper emphasizes that a fully invertible and invariant representation remains central to ensuring reliable, reproducible inverse design in crystalline systems.