GPSK-300
Will Bryan · ghost-projects · May 2026
GPSK-300 is a 3-channel, 302M-parameter diffusion transformer that learns the reciprocal space representations of inorganic crystal structures, and an exact quadratic form for the lattice. Structures are deterministically recovered via a joint IFFT of the reciprocal space channels and single linear least-squares fit of the generated lattice metric tensor.
Feature representation
Each crystal is represented as a \(64^3 \times 3\) tensor on the integer Miller grid \((h,k,l) \in [-32,31]^3\):
$$X(\mathbf{h}) \;=\; \bigl(\,\mathrm{Re}\,F(\mathbf{h}),\; \mathrm{Im}\,F(\mathbf{h}),\; 1/d^2(\mathbf{h})\,\bigr)$$The first two channels are the complex structure factor. Atom species is determined via the Cromer–Mann scattering factors, and the third channel, \(1/d^2\) is an exact quadratic in \((h,k,l)\). Its six coefficients define the reciprocal metric tensor.
Sampling
Our model learns a rectified-flow velocity field over a latent space created by a 2.6M-parameter periodic VAE that steps the input grid down by 4x along each axis. GPSK-300 is conditioned on composition, crystal system, space group, band gap, formation energy, energy above hull, and magnetic ordering. Each stream is independently dropped out 10% of the time during training. The default sampling config is set at 50 Euler steps with classifier free guidance, and we take the best of a user set N samples.
Results on the target families
Given our focus on rare earth free permanent magents, much of our model evaluation focuses on magnetic families such as L1₀ tetragonal intermetallics. The c/a ratio that plays a large role in the magnetocrystalline anisotropy of a given magnet is recovered within 3% of the reference material in this L1₀ tetragonal family; ratios are recovered/reference:
| Composition | ref a (Å) | ref c (Å) | a ratio | c ratio | role |
|---|---|---|---|---|---|
| FePt | 2.73 | 3.73 | 0.995 | 1.003 | classic, K₁ ≈ 7 MJ/m³ |
| CoPt | 2.68 | 3.70 | 0.986 | 1.017 | high anisotropy |
| FeNi | 2.53 | 3.58 | 0.987 | 0.985 | tetrataenite, RE-free |
| MnAl | 2.78 | 3.56 | 0.965 | 0.998 | τ-MnAl, RE-free |
FePt
58% per-sample exact match (N = 48)
The classic L1₀ magnet, K₁ ≈ 7 MJ/m³. Recovered lattice lands at 0.995 of reference a and 1.003 of reference c.
How far does it generalize?
We purposefully held out L1₀ compositions like FePd and MnGa from training while also removing the entire hexagonal SmCo₅ family. Learned structural motifs extend well regardless of the chemical system, but having never seen a hexagonal system, GPSK-300 was (unsurprisingly) unable to recover SmCo₅ after pre-training.
Post-training
We fine-tuned the final pre-training checkpoint on a small curated set of squat CaCu₅ structures and re-prompted trying to hit our held-out targets. As little as a single sample was able to move the generated structure out of its tall default, and with one to five examples, SmCo₅, YCo₅, and CeCo₅ all land in the squat regime at c/a ≈ 0.88 against the 0.80 target.
Conditioning
The seven conditioning streams emerged at different points throughout the training process. Symmetry arrives first, then space-group at roughly 70k training steps, then crystal system by 110k. All continuous properties took 2 to 3 times longer to emerge.
Limitations
- Unseen families are recoverable only via quick post-trains. zero-shotting an unrepresented motif stays out of reach for this approach. The training corpus does have room to grow, but it does not seem like this representation is rich enough to achieve true unseen family recovery.
- Big cells. Preserving atom count for a given request -> a generated structure is easy enough, but lattice accuracy begins to degrade substantially around the 40 atom mark.
GPSK-300 is available for free on Ouro, you can access it directy at https://ouro.foundation/services/will/gpsk-300 or via the Ouro API.