Schematic overview of the invertible sequenced representation. (a) The structure is first decomposed into composition, stability, structure and lattice. (b) The structure is then further decomposed into a set of Wyckoff positions, uniquely identified by a set of Wyckoff identifiers. Optional free parameters are also included to make the representation coordinate-aware. (c) All previous information is gathered into a tokenenized and invertible sequence. The color of the tokens represent the type or the Wyckoff position for ease of visualization.

This paper presents Matra-Genoa, an autoregressive transformer model built on invertible tokenized representations of symmetrized crystals, including free coordinates. This approach enables sampling from a hybrid action space. The model is trained across the periodic table and space groups and can be conditioned on specific properties. The authors demonstrate its ability to generate stable, novel, and unique crystal structures by conditioning on the distance to the convex hull. Resulting structures are 8 times more likely to be stable than baselines using PyXtal with charge compensation, while maintaining high computational efficiency.

Supercell 3x3x3 of Fe6Ni2B (Space group: I4/mmm, 864 symmetry operations)

Phase diagram of Fe6Ni2B; e_above_hull: 0.193286 eV/atom; predicted_stable: False

Phonon band structure (supercell [2, 2, 2], Δ=0.01 Å); imaginary modes detected; min freq = -0.61 THz

Cell + Ionic relaxation with Orb v3; 0.03 eV/Å threshold; final energy = -136.7751 eV; energy change = -4.1985 eV; symmetry: I4/mmm → I4/mmm

From Matra Genoa

Cell + Ionic relaxation with Orb v3; 0.03 eV/Å threshold; final energy = -127.9222 eV; energy change = -10.4647 eV; symmetry: P1 → P1

From Matra Genoa

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Phonon band structure (supercell [2, 2, 2], Δ=0.01 Å); no imaginary modes; min freq = -0.12 THz

Phase diagram of MnFe3N; e_above_hull: 0.154131 eV/atom; predicted_stable: False

Phonon band structure (supercell [2, 2, 2], Δ=0.01 Å); no imaginary modes; min freq = -0.19 THz

Phase diagram of MnFe3N; e_above_hull: 0.153807 eV/atom; predicted_stable: False

Phase diagram of MnFe3N; e_above_hull: 0.154347 eV/atom; predicted_stable: False

Phonon band structure (supercell [2, 2, 2], Δ=0.01 Å); imaginary modes detected; min freq = -0.31 THz

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Phase diagram of MnFe3N; e_above_hull: 1.008083 eV/atom; predicted_stable: False

Phonon band structure (supercell [2, 2, 2], Δ=0.01 Å); imaginary modes detected; min freq = -6.74 THz

Phonon band structure (supercell [2, 2, 2], Δ=0.01 Å); imaginary modes detected; min freq = -5.13 THz