Phonon band structure (supercell [2, 2, 2], Δ=0.01 Å); imaginary modes detected; min freq = -1.12 THz

Cell + Ionic relaxation with Orb v3; 0.03 eV/Å threshold; final energy = -42.7392 eV; energy change = -0.3353 eV; symmetry: Pm-3m → Pm-3m

From Matra-Genoa

Cell + Ionic relaxation with Orb v3; 0.03 eV/Å threshold; final energy = -56.6280 eV; energy change = -3.2621 eV; symmetry: P1 → P1

From Matra-Genoa

Cell + Ionic relaxation with Orb v3; 0.03 eV/Å threshold; final energy = -56.0387 eV; energy change = -5.2385 eV; symmetry: P1 → Amm2

From Matra-Genoa

Cell + Ionic relaxation with Orb v3; 0.03 eV/Å threshold; final energy = -114.1038 eV; energy change = -6.0707 eV; symmetry: P1 → P1

From Matra-Genoa

Phase diagram of Fe8Co5Ni3B2; eabovehull: 0.155891 eV/atom; predicted_stable: False

Cell + Ionic relaxation with Orb v3; 0.03 eV/Å threshold; final energy = -267.2701 eV; energy change = -87.6181 eV; symmetry: P1 → P1

GPT-5 one shot cif produced given a GEPA curated prompt

Filtering results on the 3 million generated structures (Nbatch = 150, 000). Columns include sampling temperature T, successfully optimized structures Nopt, novel inserted structures Nnovel, and stable structures meeting thresholds of 0.001, 0.050, and 0.100 eV/atom.

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; eabovehull: 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