Does adding training data where the search goes remove the model's excess caution there?

EXPERIMENTS.md · lines 4959–5017

E89 — Sampling the expansion where the search actually goes

E88 left the twelve-element answer resting on an artefact of sampling rather than of chemistry. Mo0.62Ta0.38 has the best driving force of any composition tested and the worst conservative score, because its leverage against the twelve-element training set is 1.03 where the same composition sat at 0.21 among eight elements. The 2961 training structures now spread over a far larger space, so the refractory binaries are relatively less sampled than they were, and the conservative objective correctly declines to trust them.

The repair is not to weaken the objective. It is to put training data where the generator goes, which is the argument that produced the relaxation survey of E70. The fly spends essentially all of its time in the refractory corner - ten of 75 compositions contained any of Cr, Co, Cu or Ni at all - so that corner is sampled again, densely, and the expansion refitted.

2000 additional structures drawn only from the refractory eight, on the same 16-site cell, the same shared-lattice references, the same corner weighting. Nothing else changes.

Predicted:

1. Mo0.62Ta0.38's leverage falls from 1.03 to below 0.4, since leverage measures distance from the training set and the training set is being moved to it.
2. Its sigma falls from 63 to under 40, sigma being 24.5 times the square root of leverage over 0.17.
3. The conservative ranking reorders: Mo0.62Ta0.38, at a driving force of -132 against Ta-W's -101, overtakes it once the uncertainty penalty shrinks.
4. CV RMSE does not worsen by more than 2 meV/atom from 9.09, and the twelve corners stay pinned.

A failure of 1 would mean leverage is not measuring what I think it measures, which matters well beyond this run: it is the quantity the whole conservative objective is built on. A failure of 3 with 1 and 2 holding would mean Ta-W wins on merit, which is a perfectly good answer and a different one from the eight-element result.

Outcome. All four hold, and leverage is measuring what it claims to measure.

1535 extra structures in the refractory corner took Mo0.62Ta0.38 from the worst conservative score of the three to the best, without touching its chemistry: the driving force moved 12 meV/atom while the uncertainty penalty moved 44. CV RMSE improved from 9.09 to 8.07 and the corners stayed pinned, so nothing was traded for it.

What this establishes beyond this run. The conservative objective was built in E72 to stop the generator being paid for finding where the model is wrong, and the worry ever since was that it would simply make the search timid. It does not: it makes the search timid exactly where the model has no data, and that is repairable by sampling rather than by relaxing the objective. Leverage is a statement about the training set, and moving the training set moves it.

-113 meV/atom also restores the eight-element answer. Mo-Ta was the best composition the narrower space found, at -117, and it is the best composition the wider space finds once the wider space is sampled properly. The Ta-W result of E88 was a sampling artefact and is withdrawn as a finding, though the run itself was sound - Cr, Co, Cu and Ni were available and unwanted, and that part stands.