Full OCT persona replication

The zoo's geometry recomputed on the deployed Open Character Training persona adapters (stage one plus 0.25 stage two, exact merge) - the arrangement is the stage-one arrangement (off-diagonal r 0.992, Procrustes 0.995) and second-seed personas identify themselves 15/15.

Samuel asked on 2026-09-07 for the page's geometry, which is computed on stage-one adapters, to be replicated on the full OCT synthesis adapters. This page reports that replication. Method and inputs are in qwen35/analyse_fulloct.py; all numbers are from qwen35/analysis/fulloct_geometry.json unless another file is named. Regenerate with wiki/tools/gen_fulloct_page.py.

What was compared

• Stage one: the 134 DPO adapters, rank 64, scale 2.0 (results/gram_sweep.npz).
• Stage two: the 134 introspection SFT LoRAs, rank 64, scale 2.0 (results/cross_gram_full_loras_introspection_x_loras_introspection.npz).
• Persona: the exact merge dW = dW_dpo + 0.25 dW_sft, stored as a rank-128 concatenation with scale 1.0 (/oct/personas_exact, built by fix_persona_merge.py; see The persona merge and its correction). Its Gram was computed exactly by cross_gram_full_on_modal.py (job zoo-grampersona).
• Second seed: exact personas for the 15 traits that have a matched-objective seed-1 stage-one adapter and a seed-1 stage-two adapter, built by build_personas_seed1.py (job zoo-personaseed1). Per-trait norms are in analysis/personas_seed1_build.json; for example helpful has |dpo term| 1.521, |0.25 sft term| 1.684, cos(dpo, sft) +0.0000.

The persona is an equal-norm sum of two orthogonal parts

Share of each persona's squared norm: stage one 0.4999, 0.25 x stage two 0.4999 (means over 134; key norm_identity). The remainder, which is the stage-one/stage-two cross term, has mean +0.000166 and largest magnitude 0.000551. The raw stage-two delta is 4.01x the stage-one delta in norm, so at weight 0.25 the two halves match. The persona Gram equals G1 + 0.0625 G2 to relative error 0.000329 (persona_vs_predicted_raw_rel_err).

The arrangement is the stage-one arrangement

Keys gram_correlation_offdiag.*. The stage-one vs stage-two figure over all 134 traits (0.755) is the full-zoo counterpart of the r = 0.79 over 45 traits on Stage-two geometry.

PCA from the double-centred Gram: Procrustes R^2 of the k=5 scores, persona from stage one 0.9945, persona from stage two 0.6961, stage two from stage one 0.6754; at k=9, 0.9719 / 0.7570 / 0.6848. Principal angles between the stage-one and persona five-dimensional subspaces: 1.6, 1.9, 3.6, 5.4, 8.2 degrees; between stage two and persona: 10.9, 12.5, 21.0, 27.6, 82.7. Nearest neighbour unchanged for 103 of 134 traits (persona vs stage one), 98 (persona vs stage two), 70 (stage one vs stage two).

Variance fraction of the first five components: stage one 0.125, 0.110, 0.050, 0.036, 0.026; persona 0.079, 0.067, 0.034, 0.026, 0.020; stage two 0.030, 0.024, 0.018, 0.018, 0.016 (pca.variance_fraction_top10). The stage-two spectrum is nearly flat.

Why stage one dominates despite equal weight

With equal norms the persona cosine is the mean of the two stage cosines. The stage-two cosines sit on a large shared component with little pair-to-pair variation: off-diagonal mean 0.1452, standard deviation 0.0359, against stage one's mean 0.0721 and standard deviation 0.1627 (std_offdiag_cosine). The arrangement, which is the variation, therefore comes from stage one. This is the same shared component that makes the stage-two attenuation slope anomalous on Stage two at a second seed.

Second seed on the full persona

Computed by analyse_crossseed.arm with the persona within-run Gram as the attenuation baseline (second_seed.*). r/d for the rank-128 persona is 128/2560 = 0.05; the persona's slope 0.0389 lies between the stage-one value and the stage-two anomaly. Separation is slightly negative (-0.0030): the weakest same-trait cosine does not beat the strongest cross-trait one, as already true of stage two alone; identification is still 15/15. The 15 seed-1 personas' own cosine matrix correlates with the same 15 traits in seed 0 at 0.9958 (seed1_within_15).

Stage-one adapter against its own persona

Cross-Gram of the 134 stage-one adapters (volume pc-qwen35-sweep) against the 134 exact personas (pc-qwen35-oct2), scales 2.0 and 1.0 carried separately (job zoo-personacross2). Same-trait cosine mean 0.7069 (min 0.6478); the prediction from the norms if the two halves are orthogonal is 0.7068. Every stage-one adapter's nearest persona is its own: 134/134. Cross-trait mean 0.0510. Source qwen35/analysis/fulloct_geometry.json#stage1_x_persona.

A defect found on the way: doubled tensor keys

fix_persona_merge.py wrote the exact personas' tensor keys as base_model.model. + the stage-one key, but the stage-one keys already carry that prefix, so every file under /oct/personas_exact had keys of the form base_model.model.base_model.model.model.layers... (job log phase10_runs/personacross2.log, "first key under /adapters_b/personas_exact/active"). build_personas_seed1.py copied the construction and the seed-1 personas had it too. The Hub copy has the same keys: the safetensors header of persona_exact/active/adapter_model.safetensors in EternalRecursion/persona-lora-zoo-qwen35 (public) was read on 2026-09-07 and its first key is the doubled form, with r 128 and alpha 128. Tested on 2026-09-07 with PEFT 0.20 on a small synthetic model: an adapter saved with the doubled prefix and init_lora_weights: true (the published config) loads with a "Found missing adapter keys" warning, every LoRA B stays at zero, and the logits differ from the base by exactly 0.0; the correctly keyed copy of the same adapter changes them. The published persona_exact adapters are therefore inert when loaded through PEFT. The geometry on this page is unaffected (key names play no part in the Gram). qwen35/fix_persona_keys.py rewrote the volume copies with a single prefix on 2026-09-07 (analysis/persona_key_repair.json: 149 adapters, 149 rewritten, 0 errors, first key now base_model.model.model.layers.0.linear_attn.in_proj_a.lora_A.weight); the two constructors were fixed at source; whether to re-upload the 134 persona_exact folders to the Hub is Samuel's decision and is listed on Open questions.

What this does and does not establish

It establishes that every stage-one geometric result on the page also describes the released persona adapters, because the persona arrangement is the stage-one arrangement to r 0.992. It does not establish anything new about stage two: the stage-two half adds norm but almost no structure, and its own anomalies (the slope, the negative separation) remain as recorded on Stage two at a second seed. Null arms were not rerun on personas; the null comparison on The null control arms is stage one only.