What drift is, and why an adapter can fix it

The problem

An embedding model maps text into a vector space. A different model maps the same text into a different space. The two spaces are not comparable: a vector from the new model, dropped into an index built by the old one, retrieves essentially nothing useful. Often it cannot even be inserted — many stores lock a collection's dimension at creation, so a 768-dimensional vector cannot enter a 384-dimensional index at all.

That is why the standard answer is to re-embed everything. It is correct, and on a large personal corpus it is also expensive enough that people simply do not upgrade.

Why an adapter works

The two spaces are different, but they are not unrelated. Both were trained on text, both put semantically similar things near each other, and the relationship between them turns out to be close to a rotation.

That is the useful fact. If the mapping from the new space to the old one is approximately linear, it can be learned from a few thousand matched pairs — the same documents encoded both ways — and applied to a query vector in a few microseconds. The index never changes; only the query does.

The oldest form of this is the orthogonal Procrustes problem: given matched point sets, find the rotation that best aligns them. It has a closed-form solution via SVD, no iteration and no hyperparameters, and it is the first thing rebasis tries.

Why some drift is not a rotation

A rotation preserves distances and angles. Real model changes do more than rotate:

The spaces have different means. Measured on real corpora, subtracting the mean before fitting raises recovery substantially — it was the single largest effect M0 found. A rotation cannot express a translation, so the translation has to be removed first. rebasis centres by default.

The spaces have different scales, per dimension. A diagonal rescaling after the rotation costs d parameters and sometimes helps.

Some of the relationship is not linear at all. For those cases rebasis fits a small residual MLP — a linear map plus a learned correction. It is the most expensive candidate and it wins less often than its flexibility suggests.

Hubness. In high dimensions some vectors are near-neighbours of far too many queries. The CSLS correction penalises them. Measured, it helps weak adapters by a lot and hurts strong ones — so rebasis treats it as a variant to be measured rather than a correction to be applied.

auto fits all of these against the same shared preprocessing and keeps whichever scores best on a held-out set. Where the top few are within each other's confidence intervals, the cheapest wins.

The limit

An adapter recovers the part of the relationship that is learnable from matched pairs. When the new model is genuinely better because it understands the corpus differently — not just because it arranges the same understanding differently — that difference lives in the document vectors, and no query-side map can retrieve it out of an index that does not contain it.

That is the case full_reindex names, and it is why rebasis measures instead of promising. See the decision rule.