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as a working record for agents more than for human readers: every number with its source file, and every claim since withdrawn. Some facts here may be out of date; where it disagrees with the post, trust the post.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

Prompting versus training

Synthesis of the three activation-space experiments for the blog: prompting a constitution and training on it move Qwen3.5-4B's residual stream about equally far, along largely the same directions, into an arrangement that mostly matches the weight geometry, and when both are applied at once they saturate rather than stack.

This is the section of the blog post the activation-space arm exists to write. It is built by actspace_section() in qwen35/build_blog_page.py (lines 1654-1755) and appears on qwen35/blog_page/index.html under the heading "Prompting versus training". Every number below is stated with the page that holds its source.

The question

The zoo's geometry is a geometry of weight updates (Weight-space geometry of the 134-adapter zoo). Each of those updates came from training on preference data conditioned on one document -- the trait's constitution (Constitution generation). There is a much cheaper thing you can do with that same document: hand it to the base model as a system prompt. Then the trait is not in the weights at all, it is in the context.

If both produce "the same trait", the two ought to agree. Three experiments ask in what sense they do.

1. The prompted personas are arranged like the trained ones

Give the base model each of the 134 constitutions as a system prompt, average the residual stream over its answers to a fixed 64 questions, subtract the same average with no system prompt: a persona vector per trait (Persona Vectors (Chen et al., 2025) for the construction; Activation-space analyses: overview for the design).

Correlating the 134x134 trait-cosine matrix of those vectors with the adapters' weight-space one, trait-centred so that a shared component cannot carry the number, gives r = 0.705 at layer 16, the layer fixed in advance (label-shuffle p = 0.0005, the floor of a 2000-shuffle test). The curve runs from 0.52 at layer 0 to a maximum of 0.775 at layer 19 and stays near 0.75 to the end. A trait's nearest neighbour in one space is its nearest neighbour in the other for 45 of 134, against 1 by chance. A Procrustes fit of the two 134x5 PC-score matrices gives R^2 = 0.535 against a shuffle null of 2% (the blog rounds this to "54% of the variance"). -- Constitution-as-prompt persona vectors vs weight geometry

The spectra differ: the first five components hold 23 / 16 / 15 / 8 / 5% of the variance in activations against 43 / 32 / 7 / 5 / 2% in weights. The activation cloud is flatter and higher-dimensional; the ordering of the traits survives anyway. -- Constitution-as-prompt persona vectors vs weight geometry

What this buys the argument. The weight-space geometry is not an artefact of LoRA, of AdamW, or of the shared initialisation. The same 134 documents, with no training at all, reproduce most of the same arrangement.

What it does not buy. The Big Five tests also pass on the activation Gram (signed factor separation +0.142, bipolarity gap +0.337, against +0.122 and +0.239 in weights) and this should impress nobody: the constitutions are text about the traits. The project says so in both its own write-up and on the page. -- Constitution-as-prompt persona vectors vs weight geometry

2. Training lands in about the same place, by about the same distance

Now load each stage-1 adapter with no system prompt and measure the shift against the same baseline.

• Magnitude: median |A| / |P| = 1.01. Training on a constitution's data moves the residual stream as far as reading that constitution does.
• Direction: the adapter delivers a median 62% of the prompt's shift along the prompt's own direction. Same-trait cosine +0.60; across unrelated traits +0.34.
• Containment: 41% of the adapters' activation shift lies inside the five-dimensional subspace the prompt shifts span, 64% inside the top forty, where a random subspace of the same size captures about 1%.

-- What the adapters do to activations

That +0.34 floor across unrelated traits is not noise. Every adapter and every prompt moves activations partly along one common direction -- the activation-space shadow of the personality axis, the zoo's leading component (Weight-space geometry of the 134-adapter zoo). It is the reason every geometry number in this section is computed after trait-centring, and ignoring it produced one wrong headline (below).

But training leaves its own signature. The adapters' arrangement in activation space tracks their arrangement in weight space at 0.865, more closely than it tracks the prompts (0.781), and more closely than the prompts track the weights (0.737). Fine-tuning does not simply install the prompt's effect; it installs something that resembles other fine-tunes. -- What the adapters do to activations

The oddest single fact in the arm is in the control window. With an adapter loaded and no prompt, the user's own tokens -- a question the model has not answered yet -- barely move (|A|/|P| 0.26, 5% of the prompt's shift), and yet across traits that tiny movement is ordered like the weights at r = 0.917. -- What the adapters do to activations

3. Both at once: they saturate, and neither overrides the other

Sixteen adapters x sixteen constitutions x the same 64 questions, 256 conditions. Because every one of these vectors shares a large common shift (raw pairwise cosines around +0.8), the questions are asked of the trait-specific parts, with the mean prompt shift, mean adapter shift and mean combined shift removed. -- Adapter x constitution, 16 x 16

• Matched (adapter and prompt name the same trait): 1.18 along that trait's own direction, in units of the prompt's shift -- where the prompt alone gives 1.00, the adapter alone 0.70, and addition would give 1.70. Saturation, not stacking.
• Additivity: predicting the combined shift as adapter-plus-prompt leaves a residual of 62% of its norm for matched pairs, 70% for different-factor pairs; least-squares weights around 0.68 on the adapter and 0.62 on the prompt.
• Conflict (an adapter for one pole under the constitution for the other, 22 pairs): 0.50 along the prompt's trait and 0.52 along the adapter's, with the combined model nearer the prompt's persona in 8 of 22. Neither wins.
• Before the model generates, on the user-turn tokens, the two effects essentially add (blog: residual 33%, weights 0.96 and 0.92). The saturation is a property of generation, not of the representation.

-- Adapter x constitution, 16 x 16

Individual pairs vary a lot around that even split: disorganized adapter under an organized prompt ends up -0.17 along the adapter's own trait -- the prompt wins outright -- while anxious adapter under a relaxed prompt stays on the adapter's side (cosine +0.83 against +0.35). -- Adapter x constitution, 16 x 16

The correction worth keeping in the post

The first pass at this experiment, on uncentred vectors, reported that the prompt was nearer in 16 of 22 conflicts -- i.e. that a system prompt largely overrides a trained trait. That was an artefact of the shared component. On the trait-specific parts the count is 8 of 22 and the conclusion reverses. The lesson the project filed: any comparison of steered activations must remove the common shift first, or it measures "was the model steered" and not "toward what". -- Adapter x constitution, 16 x 16

4. The one place the two spaces disagree

The weight-space "hole" -- the direction in the adapters' top-5 subspace furthest from every trait, the character the lexicon has no word for (Where no word goes - the hole and the alien direction) -- is a zero-sum combination of the 134 adapters. Apply exactly those coefficients to the 134 persona vectors and the result lands 47.8 degrees from its nearest trait, which is precisely where a random permutation of the same coefficients lands (median 47.7).

There is no hole there. The gap is a property of how these adapters sit in weight space, not of the trait set. The blog draws the consequence in the hole section itself: the earlier phrasing, "a character the lexicon lacks a word for", should be read as "a direction the adapters leave open". -- Constitution-as-prompt persona vectors vs weight geometry, Where no word goes - the hole and the alien direction

The claim, stated carefully

Prompting a constitution and training on it are commensurable: same order of magnitude of movement, largely overlapping directions, and an arrangement across 134 traits that matches at r 0.705 at the primary layer and at most 0.775 across the 33 layers. They are not identical: the adapter delivers about two thirds of the prompt's direction, its cloud resembles other adapters more than it resembles the prompts, and the one structure that is distinctive to the weight cloud -- the hole -- does not transfer. And when you apply both, you do not get twice the trait; you get about 1.18 times it.

Limits, in full, at Activation-space analyses: method notes and limits: one base model, one training procedure, stage-1 adapters only, one primary layer, sixteen traits in the cross experiment, and no behavioural judging anywhere in the arm.