DualBasis gate 1: oxygen 2p representation + conditioning — payoff modest, blocker confirmed - #324
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DualBasis gate 1: oxygen 2p representation + conditioning — payoff modest, blocker confirmed#324wladerer wants to merge 1 commit into
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… payoff modest, blocker confirmed DualBasis (moonshot #1) gate 1: a self-contained (no-SCF) measurement of both halves of the idea on the REAL oxygen 2p pseudo-orbital (PD_O_PBE.upf), in the l=1 radial channel via gradwave's sbt. experiments/dualbasis/oxygen_2p_representation.py. Findings (verified thinkpad + asus): - PAYOFF is real but MODEST at meaningful accuracy. Energy err ~ (relL2)², so sub-meV sits at relL2 1e-2..3e-3, where PW+Gaussians reach the target at only 1.4-1.7x lower ecut (~1.7-2.3x npw) than PW alone. The big 17x ecut cut appears only at loose (3e-2) accuracy. Not the 3-8x npw / 10-60x the moonshot hoped. - BLOCKER confirmed as a hard squeeze: the combined overlap goes singular exactly in the accuracy-relevant ecut range. At the best-conditioned ecut (2.5 Ry) accuracy is only relL2~1e-1; where PW+G reaches relL2<1.2e-2 the overlap's new-direction min-eig ~5e-10 (cond(S)~1e7). Accuracy and conditioning do not co-exist; learning the exponents pushes harder toward the singular manifold. Bottom line: modest ~2x-npw ceiling with a real conditioning tax, not a breakthrough. Not killed, but the optimistic framing is refuted with data. Next de-risk before any learning build: the canonical-orthogonalization accuracy floor in a real SCF. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
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What & why
De-risk gate for DualBasis (moonshot #1 — carry near-core valence structure in a few per-element Gaussians so the plane-wave ecut can drop at fixed accuracy). A self-contained, no-SCF measurement of both halves of the idea on the real oxygen 2p pseudo-orbital (PD_O_PBE.upf, PseudoDojo) — not an idealized cusp, so the payoff isn't overstated. Done in the l=1 radial channel with gradwave's own
sbt.Findings (thinkpad + asus)
Payoff is real but MODEST at meaningful accuracy (energy err ≈ relL2², so sub-meV ≈ relL2 1e-2–3e-3):
→ ~2× npw at sub-meV (≈4× on the O(npw²) blocks), large only at loose accuracy. Not the 3–8× npw the moonshot hoped.
Blocker confirmed — a hard squeeze. The combined overlap S goes singular exactly in the accuracy-relevant ecut range:
Accuracy and conditioning do not co-exist; learning the exponents (the moonshot's mechanism) pushes harder toward the singular manifold. Intrinsic Gaussian conditioning is fine (cond 1.5–15) with well-spaced exponents — the pathology is Gaussian-vs-PW redundancy, which is intrinsic to the idea.
Bottom line
Modest ~2×-npw ceiling with a real conditioning tax, not a breakthrough. Not killed (2× npw at controlled accuracy is a genuine medium-cell lever), but the optimistic framing is refuted with data. Next de-risk before any learning build: the canonical-orthogonalization accuracy floor in a real SCF.
Draft — overnight autonomous investigation; companion to the AutoAPW gates (PR #323).
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