TopG — a coordination-conditioned generator of periodic cation frameworks

Status: research artifact, mid-project. Read the limitations before using any number.

Given a coordination query — for each inequivalent metal site, its site symmetry, coordination sequence and shell-distance ratios — the model emits a complete crystal structure: space group, Wyckoff positions, free coordinates and free cell-shape parameters. Nothing downstream re-derives any of it.

Model

architecture	causal transformer decoder, 4 layers, d=256, 8 heads, FFN 1024
parameters	4.5 M
conditioning	one prefix token per site + one global token (so k is a sequence length, not a weight shape)
vocabulary	2,317 tokens — per-space-group Wyckoff labels, coarse/fine coordinate and cell grids
training	69,190 enumerated records, 100 epochs, ~100 min on a Quadro RTX 4000

⚠ CHECKPOINT / CODE COMPATIBILITY — READ BEFORE LOADING

The conditioning vector changed on 2026-08-08 (WP-018 added a per-shell SPECIFIED bit so partial queries could be expressed). That is a breaking representation change:

arms	conditioning	load with
H_pq*	PER_SITE_DIM=68, COND_DIM=1020	current main (commit 74dae8f or later)
G_100*	PER_SITE_DIM=62, COND_DIM=948	commit 203c036 (the parent of the change)

Loading a G checkpoint with current code raises size mismatch for site_proj.0.weight: [256, 62] vs [256, 68]. That is the expected, loud failure — not a corrupted download.

Two families, three seeds each:

• G_100* — full-depth queries (all six shells specified).
• H_pq* — partial queries: trained with the query depth truncated to 2–6 shells from a declared, seeded distribution, so a user can ask for less than six shells.
• I_full* — the control for the above: identical to H_pq* in every respect except the truncation. Included so the partial-query claim can be checked rather than taken on trust.

Two checkpoints per arm, because the two halves of the task peak at different times:

• ckpt_00020.pt — best validation loss, best skeleton accuracy.
• ckpt_00100.pt — best geometry (r3). Measured, paired, 3 seeds: r3 1.50%→2.50% (p=0.017) and 1.02%→2.86% (p=0.0005) between these two points, while skeleton-exact falls.

There is no single best checkpoint. Select per metric and say which you used.

⭐ Partial queries: ask for less than six shells

A user rarely knows six coordination shells. They know the first one or two. The H_pq* arms are trained with the query depth truncated to 2–6 shells, so a partial query is both expressible and answerable — and the control shows the training, not just the encoding, is what makes it work.

Both families trained identically under the same conditioning; only the truncation differs [3 seeds, 400 queries × 3, K=24]:

query depth	applicable rung	I_full (full-query trained)	H_pq (partial-query trained)
2 shells	r0	19.4% · skeleton 10.2%	61.5% · skeleton 49.6%
3 shells	r2 (3sh + 4%)	1.0% · skeleton 15.8%	4.2% · skeleton 50.2%
6 shells	r3 (6sh + 4%)	2.4% · skeleton 54.2%	2.4% · skeleton 53.6%

At full depth the families are identical — partial support is free. At shallow depth a full-query model collapses: shown an input pattern it never saw (specified=[1,1,0,0,0,0]), its skeleton accuracy falls to 10.2%, worse than anywhere on its own training curve.

⚠ r0 is a weak criterion (two shells, no ratio test) and 10.8% of 2-shell queries admit ≥2 distinct structures — so the absolute 61.5% is against a weak bar. What carries weight is the paired contrast: same bar, same queries, 19.4% vs 61.5%.

Use H_pq* if you want to send partial queries. Use either family at full depth.

What it does well

capability	measured [per-QUERY unless stated]
emits a valid parseable structure	99% of beams; every death diagnosed as a model choice
predicts N without being told	92% per candidate, 98.75% per query
predicts k without being told	97% per candidate
names the exact skeleton (sg + Wyckoff labels + N)	58.8%
satisfies a 2-shell query (r0)	61.5%

Skeleton accuracy is roughly flat from N=2 to N=192 and k=2 to k=11.

What it does not do

Metric precision. r3 (six shells + 4% distance tolerance — the project's historical criterion) is 2.5–3.1%. Loosening the tolerance to 15% reaches only ~5.5%: the distances are wrong, not nearly right. Structure:

• Below ndim ≈ 9 the CELL is the binding constraint. In cubic, where symmetry fixes the cell entirely, r3 is 18.75% vs 0.25% — matched on N and k, and on ndim.
• Above ndim ≈ 9 the COORDINATES bind. Cubic scores zero there too.
• Every r3 success in the evaluation sits at ndim ≤ 9 and k ≤ 4.

Honest instrument facts

• Grid ceiling 95.67% — a perfect model scores 95.67%, not 100%, on this evaluation set at this emission grid. Ground truth round-tripped through encode→decode→rebuild.
• Model-free control: 0/400. Oracle skeleton + the training split's median geometry scores zero.
• Train-seed noise floor: 2–4 pp on skeleton, 0.5 pp on r3, from 3 cold starts differing only in the seed. No discrete claim below ~9 pp is interpretable from a single run at a long epoch budget.

Limitations

• Trained on enumerated (synthetic) structures only. Materials Project data is held out for evaluation and never trained on (enforced in code).
• Space groups 3–230; triclinic is thin (348 corpus records) and cubic external validation is effectively absent (7 MP queries survive rebuild).
• Queries are scale-free — the model emits cell shape, never absolute length.
• No refinement step exists yet, so the "model output as a starting point" question is open.

Provenance

Code, every preregistration, every result and every correction: https://github.com/rgpalgrave/TopG. SHA256SUMS.json here matches the checkpoints; each arm_meta.json records the corpus hash, split hashes, seed, vocab hash, tokenizer version and git commit.