Written entirely by Claude, as a working record for agents more than for human readers: every number with its source file, and every claim since withdrawn. Some facts here may be out of date; where it disagrees with the post, trust the post. For the readable version, see the companion.

Factor analysis of the training-contrast embeddings

Factoring the chosen-minus-rejected MiniLM embeddings of the 134 training corpora with the adapter pipeline returns the same five factors one to one at Tucker congruence 0.81 to 0.97 (mean 0.90), including the Timidity and Arousal rotation of the Big Five pair, so the rotation is in the training contrast text and the weights inherit it.

Samuel asked, reading the short draft on 2026-09-15: "are you suggesting if we did factor analysis on the embeddings we'd get the same factors?" The earlier text baseline (Goldberg-only factoring and the 34 as a held-out set test 3) was a supervised readout: a ridge map from each trait's contrast embedding to its chart coordinates, fitted on the 100 markers, predicting the 34 held-out words at R^2 0.94. That does not by itself say the embeddings' own factor solution is the adapters'. This page runs that check.

Terms (Tucker congruence, oblimin, factor chart, chart cosine, seed floor, column space, twin score, Fisher norm) are defined in the Glossary.

Method

analysis/emb_pairs_minilm.npz#contrast holds, per trait in the Gram's order, the mean all-MiniLM-L6-v2 embedding of 150 chosen replies minus the mean of the 150 matched rejected replies. Its 134 x 134 inner-product matrix is put through exactly the adapter pipeline of analyse_fa_qwen35.py: double-centred correlation matrix, principal axis factoring with ridge-SMC start, oblimin at k = 5, order_and_orient against the Goldberg targets. The pipeline reproduces the adapter solution in results/fa_qwen35.json to 7e-8 before the text matrix is put through it.

Result

The centred correlation matrices of weights and text agree off-diagonal at r 0.868. Tucker congruence between the text factors (rows) and the adapter factors (columns):

One-to-one matching: text_f1 = Warmth (+0.92), text_f2 = Imagination (+0.90), text_f3 = Competence (+0.97), text_f4 = Timidity (+0.81), text_f5 = Arousal (+0.90); mean |congruence| 0.90. The text factors' own Big Five congruence repeats the adapters' rotation: the factor matched to Arousal loads Extraversion +0.52 and Emotional Stability -0.31, the factor matched to Timidity loads Emotional Stability +0.37 and Extraversion +0.31, against the adapters' +0.54 / -0.35 and +0.40 / +0.34.

Reading

The five factors, and the rotation of the Extraversion and Emotional Stability pair into Timidity and Arousal, are already present in the text the teacher wrote for the preference pairs. The weights inherit them. This settles the open question in Factor analysis of the adapter Gram about whether the rotation is a property of the adapter cloud: it is a property of the training contrast, and the "structure is the training contrast's" claim of post-draft can be stated as a factor-level match, not only as a coordinate readout. It leaves open whether the teacher would write the same contrast for constitutions with no Big Five vocabulary.

Related: Factor analysis of the adapter Gram, Goldberg-only factoring and the 34 as a held-out set, Best axis pair per Goldberg group, post-draft.