molecular-shadows-h4-v10

Direct observable regressor for fermionic shadow spectroscopy on linear-H4 / STO-3G. Predicts time-evolved expectation values of 120 Majorana observables (\Gamma_\mu(t) = e^{iH(R)t}\Gamma_\mu e^{-iH(R)t}) as a function of equal nearest-neighbor bond length (R) and time (t), to feed downstream shadow-spectroscopy post-processing.

Heads-up. v10 H4 has uneven accuracy across the PES — strong at (R \geq 1.5) Å but degraded at (R < 1.0) Å where low-lying singlet avoided crossings drive non-analytic eigenvector rotation. Use this model with awareness of the short-R regime; see "Known limitations" below.

Architecture (v10)

(R, t) + HF orbital energies ε(R)
      │
      ├── freq_net(ε(R))  → 256 learnable Fourier frequencies ω_k(R)
      │
      ├── Fourier features [sin(ω_k t), cos(ω_k t)]  (256 × 2 = 512 features)
      │
      └── Trunk MLP: input [R, fourier]  → 6 layers × 768 hidden → 120 outputs

Hyperparameter	Value
n_observables	120 (k=1 Majorana operators on 8 spin-orbitals)
n_fourier	256
trunk depth × width	6 × 768
freq_net depth × width	3 × 128
n_orb_features	4 (HF spatial-orbital energies of H4/STO-3G)
conditioned_frequencies	True
adaptive_bandwidth	False (v10)
activation	GELU
Parameter count	~14 M

Held-out evaluation

50 held-out geometries on the dense (R \in [0.5, 3.0]) Å grid (251 total).

R bin (Å)	pearson_mean (approx)
0.5–1.0	~0.40 (short-R weak)
1.0–1.5	~0.60
1.5–2.0	~0.90
2.0–3.0	>0.95

Aggregate: mean Pearson 0.834 / median 0.978 across all 50 held-out geometries. See eval_results.json for per-R numbers.

Inputs / outputs

• Input. (R, t) — equal nearest-neighbor bond length in Å (linear chain geometry: H atoms at 0, R, 2R, 3R) and propagation time in a.u.
• Output. Length-120 vector of expectation values (\langle\psi_0(R)|\Gamma_\mu(t)|\psi_0(R)\rangle) for k=1 Majorana observables on H4/STO-3G's 8 spin-orbital JW encoding.
• Valid range. (R \in [0.5, 3.0]) Å, (t \in [0, 300]) a.u. Recommended high-confidence range: (R \geq 1.5) Å.

Quickstart

from inference import MolecularShadowsRegressor
import numpy as np

m = MolecularShadowsRegressor.from_hub(
    "aniketdesh/molecular-shadows-h4-v10",
    revision="v10",
    token="hf_...",
)

t_grid = np.linspace(0, 300, 1500)
y = m.predict_trajectory(R=1.8, t_grid=t_grid)   # (1500, 120)

Known limitations

Short-R (R < 1.0 Å) accuracy is structurally weaker. Linear H4 has a multi-reference singlet manifold whose eigenvectors rotate near-discontinuously through avoided crossings as the chain compresses. The current freq_net correctly tracks energy-gap motion (eigenvalues are smooth), but the trunk struggles to encode the rapid amplitude rotation that lives in the eigenvector sector. H2 v10 (single-reference, no avoided crossings) confirms the recipe is sound on simpler chemistry — the bottleneck is H4-specific.

Resource-experiment guidance: trust v10 H4 most strongly for (R \geq 1.5) Å; treat short-R predictions as exploratory. A v11 release with adaptive Fourier bandwidth is in development to address part of this.

Files in this repo

File	Purpose
regressor.pt	torch payload (state_dict + config + R/t grids)
observable_regressor.py	architecture
inference.py	loader
orbital_energies.npz	R-grid + HF orbital-energy table
eval_results.json	per-R held-out metrics (50 geoms)
eval_summary.json	aggregate
history.json	training curves
README.md	this file

Versioning

• v10 (current): HF orbital-energy freq_net + dense R-grid + 6×768 trunk. Mean Pearson 0.834 (R≥1.5 Å strong, R<1.0 Å weak).
• Future versions will be pushed as new commits with new tags. Pin via revision="v10" to preserve loading across architecture changes.

Citation

Method: matchgate-shadow spectroscopy following arXiv:2212.11036 and matchgate-shadow theory.

License

MIT.