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as a working record for agents more than for human readers: every number with its source file, and every claim since withdrawn. Some facts here may be out of date; where it disagrees with the post, trust the post.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

The N x N data-to-adapter scoring test

Every one of the 134 traits' preference pairs ranks its own adapter first out of 134 (133 after column standardisation), and the runners-up carry Big Five structure that nothing in the test required.

The scoring identity

qwen35/align_score.py computes, exactly, how much a piece of training data would push the model along a chosen weight direction. Because a LoRA starts with B = 0, at step zero dL/dA = B^T (dL/dW) = 0 and the whole first update lives in B: dL/dB = G A^T, so dW_induced ~ -eta * G A^T A. Its overlap with a target direction dW* (any weighted merge of the zoo adapters, so dW* = B* A_0 up to A drift) is

<dW_induced, dW*> ~ -eta <G A_0^T, dW* A_0^T> = -eta <dL/dB, B_U>,   B_U = dW* A_0^T

so the score is a plain inner product against a fixed matrix B_U that is itself a rank-64 LoRA. An inner product with a gradient is a directional derivative, so the gradient never has to be computed:

score(x) = d/d(eps) [ log p(x | W + eps*U) ]  at eps = 0

The reading the blog page pulls out of it: "Data that trains a model toward a direction is exactly data that a model already steered along that direction finds more likely. Gradient alignment and steering sensitivity are the same quantity seen from two sides."

In practice every (target, example) pair gets its own scalar eps in one forward pass, so a single backward pass leaves the whole per-example, per-direction derivative matrix in eps.grad - exact, with no per-example gradients and no 253,952-dimensional projections.

Checked against a central finite difference of two steered forward passes over 24 held-out responses at three step sizes, the analytic and finite-difference scores agree at correlation 0.9999992 (qwen35/build_blog_page.py: corr = v.get("corr", 0.9999992) reading qwen35/analysis/align_validate.json; that file stores names, and per-row analytic and fd at eps 0.003 / 0.001 / 0.0003, but the top-level corr key is absent, so the number the page prints is the builder's hard-coded fallback - see the provenance note below).

For DPO data specifically: at B = 0 the policy equals the reference, the preference sigmoid sits at exactly one half, and the first DPO gradient is proportional to grad log p(chosen) - grad log p(rejected), so a preference pair scores as the difference of its two halves.

The positive control, and why it needed replacing

qwen35/analysis/align_summary.json#rows holds the six-trait control: for each single-trait direction, where its own 500 preference pairs rank among all 134 traits' data.

Five of six come first; quiet comes second behind composed. Six was a selection, and qwen35/build_nxn_inputs.py says so: "The positive control in build_align_inputs.py did this for six traits (5/6 rank 1 of 134); this is the same test with no selection." It also fixes a corpus problem - the control drew from data/, which has 55 prompts no adapter saw, while the N x N test draws from data_common, the corpus the adapters were actually trained on.

The N x N test

qwen35/build_nxn_inputs.py builds 134 single-adapter targets (coef {trait: 1.0}) and 40 pairs per trait from data_common, seeded random.Random(3). qwen35/analyse_nxn.py averages each trait's 40 pair scores per adapter into a 134 x 134 matrix and reads it three ways.

qwen35/analysis/nxn_summary.json:

Chance for rank 1 is 1 in 134; chance mean rank is 67.5.

The column-z reading z-scores each column so an adapter that scores everything high cannot win every row; it is the stricter of the two, and it costs exactly one trait (bashful, rank 2).

The runner-up structure is the part that was not asked for. Taking the top three per row excluding the trait itself, 42% of runners-up share the trait's factor and its keying against a 12% base rate, and 0% share its factor with the opposite keying. PHASE3_VERDICT.md, 2026-09-05:

Own adapter rank 1 for 134/134 raw, 133/134 after column z-scoring (bashful second). Runners-up share factor+keying 42% (base rate 12%), opposite keying 0%. The scoring identity sees the Big Five in DATA, which nothing about the positive control required.

.garden/journal/2026-09-05.md records the same on the day it landed.

Reachability: what existing data can and cannot aim at

The same scoring machinery ranks directions by how hard the zoo's own data can push along them. analysis/align_summary.json#reach gives, per direction, best_set (the best trait's data), best_pair, and ratio against a floor - #probe_floor = 13.491425523936076, the mean score on six random directions.

The ordering matches the angles to the lexicon in analysis/direction_gaps.json - the named axes sit inside their word clusters and are easiest to aim at; PC5 and the unnamed direction sit furthest from any word and are hardest. See Where no word goes - the hole and the alien direction.

Read the other way, #rows also gives which traits' data drives each named axis: Extraversion (extraverted, spunky, unrestrained, vigorous), Agreeableness (pleasant, effeminate, agreeable, liberal), Conscientiousness (composed, imperturbable, intellectual, neat), EmotionalStability (imperturbable, composed, unexcitable, steady), Intellect (deep, philosophical, introspective, imaginative). Nothing in the measurement reads the text.

Other keys in align_summary.json: #a_drift = 0.014605041334818797 (the zoo's LoRA-A drift, see Adapter effect and LoRA-A drift), #norm_agreement = 0.997274392945949, and #caption ("Mean pair score by trait, over 5360 preference pairs from the zoo's own training data. Rank is out of 134 traits; z is against the spread of all traits on that direction.").

Provenance notes

• analysis/nxn_scores.json is the raw per-pair score file and is large (the summary is derived from it by analyse_nxn.py); this page quotes only the summary.
• The 0.9999992 finite-difference agreement is printed by the page from a default argument in build_blog_page.py, because analysis/align_validate.json has no corr key. The per-row analytic and fd arrays are there; the correlation itself is not stored. Flagged in Superseded geometry claims and the section report.
• The N x N run OOM'd once on an 80GB card before succeeding (.garden/journal/2026-09-04.md: _build_targets held two copies of every module).

Related: Weight-space geometry of the 134-adapter zoo, Where no word goes - the hole and the alien direction, Alignment-relevant traits in the geometry, Steering the base model along weight-space directions, Zoo training recipe.