Benchmark results
All numbers below are float64 with answers identical to autodiff to ≤ 1e-15.
Read the methodology first — the rules there are what make
these meaningful.
Headline: the Laplacian at scale
At input dimension D = 240, against a dense-Hessian autodiff baseline:
| Metric | omnibias vs. dense-Hessian autodiff |
|---|---|
| Speed | 68× – 199× faster |
| Memory | 63× – 108× less |
| Answer | identical to ≤ 1e-15 |
The spread reflects the hidden-width / batch regime; see methodology for the sweep configuration.
Scaling shape: O(1) in D
The Laplacian's D-dependent term (‖W·…‖²-type contraction) is computed once
and reused, so the per-sample overhead stays roughly flat as D grows.
Iterated Laplacian: flat in k
| Order | omnibias | nested forward-Laplacian |
|---|---|---|
Δ (k=1) | ~0.1 ms | baseline |
Δ² (k=2) | ~0.1 ms | slower |
Δ³ (k=3) | ~0.1 ms | ~480× slower |
Δ⁴ (k=4) | ~0.1 ms | out of memory |
This is the qualitative win: closed form is flat in order, nested autodiff is not.
VMC local kinetic energy
On a Beryllium 8-determinant body, the omnibias local kinetic energy is
bit-identical (rel-err 0.0, ULP) to FermiNet's default autograd Laplacian,
and ≤ 5.07e-15 versus folx — a drop-in with no change to the energy curve.
You will not reproduce the absolute full-tier numbers on a laptop, but the CPU
smoke tier reproduces the shape (flat-in-D, flat-in-k) in seconds. See
the performance guide.
See also
- Complexity — why these numbers are what they are.
- Methodology — how they were measured.