10. Retention is bounded by the old model, not by our adapters

Status: Accepted · Date: 2026-08 · Evidence: docs/bridge-band.md, sections 3 and 7

Decision

Stop treating adapter retention as an engineering target. It is bounded by how much structure the old embedding space contains, and neither more fit data nor more adapter capacity moves it. The tool's job is to measure it and say what it implies, not to raise it.

Context

The break-even is ARR × upgrade_gain > 1. Of the two factors, upgrade_gain is a property of the models and not ours to change; retention looked like ours. Measured at 0.47–0.87 across fifteen real-query runs, it is the binding constraint: at a routine refresh gain of 1.10 a run needs retention above 0.91, and none of the fifteen reached it.

So the obvious move was to raise it. Two hypotheses, both cheap to test, both wrong.

Evidence

It is not the fit-pair count. M0 found the quality curve flattening at 4,000 pairs, measured at 384→384. The low-retention runs are 256→768, where a linear adapter's weight is 196,608 parameters and 4,000 pairs is fifteen samples per input dimension — apparently badly underdetermined. Raising it to 25,000:

run	4k	10k	25k	change
unix, potion→bge-base	0.414	0.415	0.429	+0.015
fiqa, potion→bge-base	0.466	0.465	0.476	+0.010
programmers, potion→bge-base	0.475	0.478	0.480	+0.005
gaming, potion→bge-base	0.680	0.685	0.686	+0.007
unix, MiniLM→bge-small (control)	0.818	0.841	0.843	+0.025

Six times the data buys one to two points. M0's default holds at dimensions it was never measured at.

It is not adapter capacity. Across all fifteen fits, including at 25,000 pairs where the residual MLP has ample data, the winner was procrustes_centered 15 times out of 15. The most constrained candidate in the list — an orthogonal rotation — beat the ridge affine, the low-rank affine and the MLP everywhere. What is not a rotation is not learnable by a more flexible map either.

It is the source space. What retention actually tracks:

predictor	correlation with retention
how good the old model is (its own nDCG@10)	+0.901
source dimension	+0.875
dimension ratio in/out	+0.739
upgrade gain	−0.958

source model	runs	mean retention
potion-base-8M (256d, weak)	5	0.547
all-MiniLM-L6-v2 (384d)	10	0.791

The consequence

This explains the −0.958 anti-correlation, and it is arithmetic rather than coincidence. Retention is a function of the old model's quality. upgrade_gain is the new model's quality divided by the old model's. Both are driven by the same variable, in opposite directions.

Which means: bridging cannot be a general answer to "the new model is much better". The condition that makes an upgrade worth doing — a weak old model — is the same condition that makes bridging fail. There is a band where the old model was good enough to map from and the new one is substantially better, and it is narrow: four of fifteen real-query runs landed in it.

You cannot recover from 256 dimensions what 768 dimensions encode. No adapter family fixes that, because it is not a modelling problem.

Consequences

• No change to --pairs; the default stays at 4,000 and is now measured at two dimension regimes rather than one.
• No new adapter candidates on retention grounds. auto's list is not what is limiting these runs.
• The report can say something it could not before: when retention is low because the old model is weak, more compute will not help and a reindex is the honest path.
• Per-cluster adapters remain worth trying, but for a different reason — heterogeneous drift within a corpus, which tail_arr detects — not as a way to lift the ceiling measured here.

Alternatives

Add higher-capacity adapters. Rejected on the measurement: the most constrained candidate already wins everywhere.

Raise the default --pairs. Rejected: measured at six times the data for one to two points, against a real cost in fit time.

Predict retention from the model pair and skip the fit. Tempting — the correlation is +0.901 — and rejected. A correlation over fifteen runs with two source models is not a predictor, and a tool that guessed instead of measuring would be the thing this project exists not to be.

Independently confirmed, and one thing added

Maystre, Ortega Gonzalez, Park, Dolga, Berariu, Zhao and Ciosek, When Embedding Models Meet: Procrustes Bounds and Applications, reached the same place from theory. Their motivating scenario is this one — the query model is upgraded and the document embeddings cannot be recomputed — and two of their results bear directly on this decision.

Why the most constrained candidate wins. They compare orthogonal Procrustes against unconstrained linear alignment. By construction the unconstrained solution cannot be worse on alignment error, and yet orthogonal wins on retrieval, particularly when upgrading to a stronger query model (their Figure 5): preserving the stronger source model's geometry keeps information an unconstrained map discards. That is the mechanism behind procrustes_centered winning 15 out of 15 above, arrived at independently.

A bound is not the prediction that was rejected. Their Corollary 1 states that if two models' pairwise inner products agree to within δ, the best orthogonal alignment satisfies E[‖x̄ᵢ − yᵢ‖²] ≤ √(2D)·δ. That is a one-directional guarantee, data-independent and independent of N, and it costs one Gram-matrix difference — no fit at all.

rebasis now reports δ and the bound it implies (rebasis.core.geometry, probe's report). It does not overturn the rejection above, because it is a different kind of object: it says an alignment of at least this quality exists, never that retrieval will realise it. The converse does not hold, and a low bound beside a low ARR is not a contradiction — it means the alignment was available and something else lost it. The measurement remains the answer.

Two further notes from the same paper, recorded because they touch decisions made here: their sample saturation sits near 10,000 pairs against M0's 4,000, which is consistent with the table above showing the point being model-pair dependent rather than universal; and their zero-padding of the smaller embedding under a dimension mismatch is the same convention as IdentityAdapter's padding and the hard_drift 384→256 scenario.