Post draft (rewrite, 2026-09-08)

The rewritten LessWrong post for Samuel to work from, factor-first with a stage-two section; slots marked PENDING are filled from the wiki as the running experiments land.

Investigating LLM Personality in Weight Space

Draft rewrite, 2026-09-08, for Samuel to work from. Every number is taken from a file named in the wiki; slots marked [PENDING] are experiments still running when this draft was written and are filled in the wiki as they land. Companion site: https://persona.161-35-77-84.sslip.io. Record and sources: https://wiki.161-35-77-84.sslip.io. Adapters: https://huggingface.co/EternalRecursion/persona-lora-zoo-qwen35.

TL;DR

• We trained 134 personality-trait LoRA adapters on Qwen3.5-4B with an adapted Open Character Training pipeline: Goldberg's 100 Big Five marker adjectives plus 34 adjectives sampled from a broader personality lexicon. Both OCT stages were run for every trait; the adapters, the merged personas and the transcripts are public.
• The weight updates have factor structure. Factor analysis of the exact inner-product matrix recovers five factors, Warmth, Competence, Fearful withdrawal, Arousal and Imagination, that line up with the Big Five at congruence 0.41 to 0.68. Two trained control zoos do not reproduce it: shuffled preference data yields no factors at all, and permuted labels yield rich structure that ignores the labels.
• The same five factors organise the model's activations when the traits are merely prompted. Trait-by-trait coordinates in weight space and prompted-activation space agree at Procrustes R^2 0.74 on the factor chart (0.54 on principal components), and each weight factor maps onto the same activation factor without rotation.
• Steering along a factor moves the judged trait in a dose-dependent way, and a gradient-alignment score identifies every trait's own training data among 134 adapters (134/134). Selecting data by that score moves newly trained adapters toward the chosen direction.
• Stage two of OCT, the introspection fine-tune, does something different from stage one. It installs one direction every adapter shares, worth 15% of each adapter's squared norm, which turns advice-to-the-user into first-person in-character speech; the trait content it adds is faint, nearly isotropic, and has lost most of stage one's bipolarity. The merged persona's geometry is stage one's, but personas move behavioural dials further than stage one alone.
• The map is useful and partial: no factor reaches conventional congruence with its Big Five target, behavioural effects of mixtures do not add, and the interpretation of the widest empty region as a nameless disposition did not survive transfer to activations.

Motivation

We would like to know how a model's dispositions are represented and how to change them on purpose. Persona Cartography did this with ten Big Five LoRAs on Llama, scaling and adding them. We asked what happens with an order of magnitude more traits: whether the weight changes have structure of their own, whether that structure is the Big Five's, whether it also shows up when the traits are prompted rather than trained, whether it predicts behaviour, and whether it can be used to choose training data. Human trait vocabulary is the starting point; how well it describes the models is part of what we test.

Setup

One adapter per trait, Qwen3.5-4B, rank 64. The 100 primary traits are Goldberg's unipolar Big Five markers, twenty per factor with both poles, so each carries a published factor and keying. The 34 secondary traits were drawn from Condon's 2,818-word trait lexicon by clustering sentence embeddings and picking within clusters; forty were drawn and the constitution writer refused six as states rather than dispositions. The secondary traits never define an axis; they are held out. A teacher writes a 120-200 word constitution per trait and then produces both sides of each preference pair (the rejected side is a character at the opposite pole, not the base model). All 134 train on the same 445 prompts with DPO plus a small SFT term and a KL penalty, from one shared random LoRA initialisation per seed. Stage two, OCT's introspection fine-tune, was run for all 134 as well; the geometry below is stage one's unless stated. Details: wiki, "Building the zoo".

Each adapter is a weight update dW. We compare adapters by the exact Frobenius inner products of their updates, computed from the LoRA factors without forming dW, and run PCA and factor analysis on the 134 x 134 matrix. A direction in this space is a weighted merge of adapters, so it can be added to the model and steered. Behaviour is judged blind by Claude Sonnet 4.5 on five scales over 24 open-ended scenarios, with degeneration tracked separately.

The weight updates have factor structure

The labels predict the geometry. Within a Big Five factor, same-pole adjectives point the same way and opposite-pole adjectives point apart: the signed within-factor minus between-factor cosine is +0.16 against -0.01, and same-pole pairs sit at cosine +0.24 against -0.08 for opposite poles (bipolarity gap 0.33). Two trained control zoos of 100 adapters each, at the zoo's exact objective, say what that structure is not. Swapping the chosen and rejected sides on half of each trait's pairs (the shuffled arm) leaves a structureless cloud: the separation statistic is +0.0001 and factor analysis retains zero factors. Reassigning intact datasets to other trait names (the permuted arm) leaves a rich cloud, eight factors with communalities as high as the real zoo's, whose agreement with the Big Five labels is at chance; re-identify the adapters by the data they were trained on and the real factors come back at congruence 0.98 to 1.00. Coherent preference data creates the structure; the identity of the data decides where each trait lands.

Factor analysis (principal axis factoring, oblimin rotation) at k = 5 gives:

None reaches the 0.85 usually taken as a fair match, and the two Extraversion/Emotional Stability factors are rotated relative to the Goldberg axes: the zoo separates fearful withdrawal from arousal rather than introversion from anxiety. Parallel analysis retains nine factors at the reference sample size and five at a conservative one; five are what replicate. The elbow plots and the null comparison are on the companion site.

The arrangement replicates across training seeds. Retraining 40 traits from a second LoRA initialisation, same data, every one of the 40 finds its own original adapter as nearest neighbour among 134. The absolute cross-seed cosine is small, +0.018, because two random rank-64 subspaces of a 2560-dimensional space overlap by r/d = 0.025; the measured attenuation, 0.0265, is that prediction. Everything else about the arrangement survives (Pearson 0.997 between the two seeds' cosine matrices).

The same factors in activations

Give the unmodified model each constitution as a system prompt, average its residual-stream activations over responses to 64 questions, subtract the no-prompt baseline, and you have a prompted persona vector per trait. Their pairwise arrangement matches the weight-space arrangement: r = 0.70 between the trait-centred cosine matrices at layer 16, fixed in advance (0.74 with the weight side double-centred; permutation p 0.0005). Where the traits land agrees too. On the factor chart, a Procrustes fit of the 134 x 5 coordinates between the two spaces explains 74% of the variance (shuffle null 4%; the principal-component scores manage 54%), and each weight factor is the same activation factor with no rotation: Warmth r = 0.92, the other four 0.81 to 0.83.

Training moves activations about as far as prompting (median ratio of shift norms 1.01), and in a related direction: the adapter-induced and prompt-induced shifts for the same trait sit at cosine 0.60 against 0.34 for different traits. Adapter and constitution together move the trait-specific projection to 1.18, where the prompt alone is 1.00 and the adapter alone 0.70: less than additive. These are activation measurements over the training prompt pool with the same constitutions on both sides; independent constitutions and new questions would be a stronger test.

Steering along the factors

Adding alpha times a factor direction to the base model moves the judged trait with dose. At alpha plus or minus 2 (alpha in units of one adapter's norm), the change in the factor's own judged scale is: Warmth -2.1 / +1.5, Competence -3.5 / +0.7, Fearful withdrawal -1.9 / +0.2, Arousal -0.6 / +1.5, Imagination -2.1 / +1.1 on the 1 to 7 scale. Two regularities: amplifiers are ceiling-limited where the base already scores high (Conscientiousness 5.7 of 7, Intellect 5.5), and every suppressor drags Conscientiousness and Intellect down together, the competence bundle moving as a unit.

Sampling the space without choosing directions, 72 evenly spread points on the sphere of the top three factors [PENDING: factor-chart sphere; on the principal-component sphere: angular distance between directions correlates with distance between judged profiles at Spearman 0.65, near pairs 0.97 versus far pairs 2.81, 48 of 72 directions produce no looping].

Persona Cartography's "single dials work" figure replicates four ways. The five keying axes at alpha plus or minus 2 move their own trait most for 8 of 10 dials; the ten positively and ten negatively keyed adjective adapters per factor, averaged with no steering, for 7 of 10; the same adapters as full OCT personas for 8 of 10. And the like-for-like version, ten factor-level adapters trained on Persona Cartography's own OCEAN constitutions rendered into the zoo's format, on the zoo's recipe and prompts: all ten move their own trait in the right direction, eight of ten move it most, and every one lands nearest a sensible adjective of the 134 (own-trait shifts as a share of the room on the judge's scale: Extraversion +64 / -21, Agreeableness +60 / -36, Conscientiousness +35 / -48, Emotional Stability +10 / -26, Intellect +68 / -23). The dedicated Conscientiousness amplifier gaining 35 points also retires the ceiling explanation we had offered for the adjective-averaged arm's failure on that factor.

Standard questionnaires

We also ran the UK AISI Inspect personality evaluations, reproducing the harness's items and parser exactly (validated item-for-item and answer-for-answer against a real Inspect run on two conditions). The 44-item BFI on all 134 stage-one adapters, all 134 personas and the ten factor-level adapters turns out to be largely a response-style instrument for this model: the base agrees with almost everything, and that acquiescence index alone predicts BFI Neuroticism at r 0.72 across adapters. BFI separates the positively and negatively keyed adapters on two of five factors. TRAIT, the 1,600-item scenario benchmark, separates all five with the correct sign, and its Agreeableness score tracks the adapters' weight-space Warmth coordinate at r 0.82. Personas self-report slightly further in their trained direction than stage-one adapters (+0.019, p 0.002), so the introspection stage's inflation of self-report is real but small.

Scoring training data against a direction

For a response y to prompt q and a unit direction u in weight space, the directional derivative of log p(y|q) along u equals the alignment of the gradient with u. For LoRA this scores many examples against many directions in one backward pass. As a positive control we scored 40 pairs from each trait's data against every adapter: each trait's data ranks its own adapter first, 134 of 134 (133 of 134 after standardising each adapter's column), and the runners-up share the trait's factor and keying 42% of the time against a 12% base rate. Selecting data by the score for three targets and training on it moved each new adapter toward its target more than toward the other two, after subtracting a random-selection control. Small (16 steps, eight prompts, weight-space readout), but it closes the loop from score to training.

What stage two does

This is the part we did not expect. OCT's second stage fine-tunes each adapter on 12,000 transcripts of the model reflecting on and conversing as its persona, then merges it with stage one at weight 0.25. The 134 stage-two adapters look nothing like the stage-one ones.

• One shared direction. Fifteen percent of every stage-two adapter's squared norm lies along a single common direction, and every adapter sits at cosine 0.39 to it with a spread of 0.03 (stage one: 8%, 0.28 with spread 0.13). It is orthogonal to stage one's own shared direction in coordinates. Steering the base model along it turns "Here are a few options for the message" into "I feel a sharp tug in my chest right now": second person and markdown fall, first-person in-character answers rise from 0 to 46% of responses, while a sign-balanced mix of the same adapters does nothing. Stage one's grand mean does the same at half the weight. The register is what both stages agree on.
• A faint residual that is still the map. After removing that direction the stage-two cloud is nearly isotropic (top component 3% of variance; 52 components for half of it, against 20 in stage one), yet its arrangement correlates with stage one's at 0.81 and the five factors return at congruence 0.42 to 0.60. Bipolarity is mostly gone: opposite poles sit at cosine +0.12 rather than -0.08, because both share the self-narration register. Preference training on contrasting pairs makes opposites opposite; imitation of one's own transcripts makes everyone alike.
• The persona is stage one's map with more behaviour. In the exact merge, half of every persona's squared norm is the stage-two term, but the persona cosine matrix correlates with stage one's at 0.99 and the factor subspaces agree at Procrustes 0.995; stage two adds norm, not structure, because its cosines have a quarter of stage one's spread. Yet personas move their own behavioural dial further than stage one alone for 8 of 10 dials.
• [PENDING: register versus residual: stage one plus the shared direction at a persona's dose, judged against the persona itself. PENDING: five trait-free stage-two runs, to test whether the shared direction is specific to persona introspection or generic to SFT on self-generated text. PENDING: stage two in activation space. PENDING: how many factors describe stage two, with and without the shared direction.]

Where the map falls short

Weight arithmetic does not give independent behavioural dials: across ten mixtures of the five keying axes, the median deviation from the additive prediction is 53% of that prediction and 2.5 times the judge-noise floor. The widest empty region of the chart, which we first read as a disposition English has no word for, is real as geometry (in the five-factor chart it sits 54.8 degrees from the nearest trait adapter, z 13.7 against random directions) and unsupported as a disposition: transferring the same coefficients to prompted activations gives a gap no larger than a shuffled-coefficient control (47.8 against 47.7 degrees); three adjectives proposed for it, cavalier, blase and insouciant, were trained and land 66 to 87 degrees from it, farther than existing adapters; and steering it at the same dose as its controls predicts the judge's scores no better than a random direction in the same subspace (3 of 5 signs, r 0.74, against 3 of 5 and 0.73), while being the only one of the three that degenerates. Moving from principal components to factors also removed the earlier claim that the words tile the two leading dimensions better than chance (z +0.2 now, -2.3 before). Congruences with the Big Five stop at 0.68. One model, one recipe, synthetic data from human trait words, an LLM judge and 24 scenarios.

What we would most like to see next: independent constitutions and held-out questions; replication on another base model; and data selection judged by downstream behaviour rather than by weight-space position.

Explore

The companion site lets you move through the factor chart, read what the model says at every steering strength, open any of the 134 traits, and download the tables. The wiki holds every number with its source file, the controls, and the corrections we made along the way. The adapters (stage one, stage two, exact personas) and the stage-two transcripts are on Hugging Face.