Activation-space analyses: method notes and limits

Everything needed to reproduce the three activation-space runs of 2026-09-05, and the list of things they do not establish.

Activation-space analyses: method notes and limits

Companion to Activation-space analyses: overview, Constitution-as-prompt persona vectors vs weight geometry, What the adapters do to activations and Adapter x constitution, 16 x 16. This page is written for someone who wants to rerun the arm or to check a number in it.

Environment

From act_space.py lines 48-56 and the run logs:

• Modal app, default name pc-qwen35-phase11-actspace (PC_APP_NAME overrides it). Volumes pc-qwen35-probe (outputs, mounted at /probe) and pc-qwen35-sweep (the stage-1 adapters, at /adapters).
• Image: nvidia/cuda:12.8.1-devel-ubuntu24.04, Python 3.12, torch==2.13.0, transformers==5.15.1, accelerate==1.14.0, numpy<3, safetensors, huggingface_hub.
• GPU A100-40GB for all three stages; timeouts 4 h (prompt), 5 h (adapters, cross).
• Base model Qwen/Qwen3.5-4B (PC_BASE_MODEL), loaded in bfloat16, device_map="cuda", .eval() (line 73-74).
• Logged shape: 33 hidden-state layers x 2560; 248 hooked LoRA modules; LoRA scale 2.0.

Local entry point: modal run act_space.py --stage prompt | adapters | cross (lines 353-375).

The 64 prompts

pool = sorted({json.loads(l)["prompt"] for l in open(f"{HERE}/data_common/bold.jsonl")})
prompts = random.Random(7).sample(pool, N_PROMPTS)      # N_PROMPTS = 64

data_common/bold.jsonl has 445 lines, one prompt each and all distinct, so the pool is 445 and 64 are drawn from it with random.Random(7). The drawn prompts are stored verbatim at analysis/actspace_spec.json#prompts -- the file to read if you want the exact 64 rather than to redraw them.

actspace_spec.json is rewritten at the end of every stage run (line 375), and its traits field is always the full 134-name list from analysis/alien.json#traits, never CROSS_TRAITS. The file on disk is dated 21:23 on 2026-09-05, i.e. it was last written by the cross run. Since the prompt draw is seeded and identical across stages, the file's prompts are the 64 used by all three.

Windows and pooling

Per batch of 32 (act_space.py lines 97-135):

1. Render [system?, user] with add_generation_prompt=True and enable_thinking=False; tokenise with left padding, add_special_tokens=False.
2. model.generate(max_new_tokens=96, do_sample=False) -- greedy.
3. Re-run the full sequence with output_hidden_states=True, with the attention mask extended by ones over the generated positions.
4. Response window: positions from T0 up to and including the first EOS-or-pad in the generated span; if there is none, to the last generated position.
5. Prompt window: positions from pad_len + n_sys up to T0, i.e. the user turn only, with left padding and the system block both excluded. n_sys is measured by rendering the same prompt with and without the system turn and differencing token counts, because the template refuses a system-only message list.
6. Mean over the window, per hidden-state layer, giving one (33, 2560) matrix per prompt per condition.

Halves: prompts 0-31 and 32-63 are averaged separately and both are stored.

Storage: M is float16 in the .npz (means.npz, means_adapters.npz, means_cross.npz, on the pc-qwen35-probe volume; the local copies are analysis/actspace_means*.npz, 91 MB / 91 MB / 173 MB). Every analysis script casts to float32 on load.

The adapters run does not collect its own baseline. It reuses B from the prompt run's means.npz, on the argument that with the hooks disarmed the model is the base model and the baseline came from the same code path (act_space.py lines 260-261; analyse_actspace_adapters.py lines 50-52). The same B is used again by the cross analysis (analyse_actspace_cross.py line 39).

Analysis: seeds, nulls, and what each null is

All three analysis scripts fix PRIMARY = 16 and, where they randomise, use np.random.default_rng(0).

The containment null is a single random cloud, not a distribution: the reported 0.2%-1.5% figures are one sample, not a percentile. Given the gap to the observed 41%-64% this does not change the conclusion, but the numbers should not be read as a null band.

The Procrustes null mean of 0.02 quoted in ACTSPACE_RESULTS.md and on the blog is printed by analyse_actspace.py line 151 but is not stored in actspace_geometry.json, which keeps only procrustes_null95.

Centring conventions differ between scripts

This is the single most likely source of confusion in this section, and it is why the same quantity has two published values:

• analyse_actspace.py lines 92-94: the weight cosine matrix Cw is built from the raw Gram. Activations are trait-centred (line 139). P~W = 0.705.
• analyse_actspace_adapters.py lines 62-63: the weight Gram is double-centred (Gc = J @ Gw @ J) first. P~W = 0.737.

Likewise, "the fraction of the prompt's shift the adapter delivers" is 0.62 on raw vectors (analyse_actspace_adapters.py) and 0.70 on trait-specific vectors (analyse_actspace_cross.py). Both are real; state which one you mean. See Constitution-as-prompt persona vectors vs weight geometry and What the adapters do to activations.

Generations kept

The .jsonl files hold a sample only, for eyeballing: the first 4 responses per trait for the prompt and adapter runs (plus one _base row), the first 2 per condition for the cross run (act_space.py lines 162, 173, 256, 337). Line counts: 135 / 134 / 256 in analysis/actspace_generations.jsonl, actspace_generations_adapters.jsonl, actspace_generations_cross.jsonl. With MAX_NEW = 96, sampled responses end mid-sentence; they are diagnostic, not evidence, and none were judged.

The chat-template failure

The first launch died with TemplateError: No user query found in messages (qwen35/phase10_runs/actspace.log.1788630847). Qwen3.5's chat template rejects a message list containing only a system turn. The workaround is the render-with-and-without differencing above. Recorded in the journal for 2026-09-05.

Related standing hazard, and the reason for the explicit flag on every template call: Qwen3.5's template defaults its reasoning block on, and three earlier runs in this project were silently invalidated by omitting enable_thinking=False.

What these analyses do not establish

From ACTSPACE_RESULTS.md, from the blog's own caveats section, and from what the scripts do and do not run:

1. One model, one training procedure, one initialisation. Everything is Qwen3.5-4B, stage-1 LoRA adapters from a single shared random A. Nothing here shows the correspondence would hold on another base model, another PEFT method, or another objective.
2. Only stage-1 adapters were run. The stage-2 (self-transcript SFT) adapters exist for all 134 traits and are on Hugging Face, but no activation-space run touched them.
3. The correspondence is between arrangements, not coordinates. The two spaces share no basis. What is compared is 134x134 similarity matrices and 134x5 score matrices. Procrustes R^2 0.535 is the strongest coordinate-level statement made, and it is a statement about five components.
4. The result is layer-dependent. Trait-centred P~W runs 0.52 at layer 0 to 0.775 at layer 19. Layer 16 was fixed in advance; the maximum is reported as a maximum. Any single number should carry its layer.
5. Big Five recovery on the activation Gram is not a finding. The constitutions are text about the traits; that a signed factor structure comes back is expected. ACTSPACE_RESULTS.md and the blog both say so explicitly.
6. TEST 6 was never run on the activation Gram. The training-strength nuisance covariate is unavailable for want of results/runmeta_actspace.json (results/decomposition_actspace_resp.json#test6.status; phase10_runs/decompose_actspace_resp.log: "The confound is then UNTESTED, which is not the same as ruled out.")
7. The hole result is a negative on one specific coefficient vector. It shows that alien_k5's coefficients, applied to persona vectors, land at the permuted-coefficient null. It does not show that activation space has no holes, nor does it retract the weight-space measurement. See Where no word goes - the hole and the alien direction.
8. No behaviour was measured anywhere in this arm. No judged evaluation, no steering sweep, no held-out task. "The adapter delivers 62% of the prompt's shift" is a statement about vectors, not about what the model says. The behavioural results live under the behaviour pages.
9. The cross experiment covers 16 traits and one layer. Its class sizes are 16 / 14 / 22 / 204; the conflict result rests on 22 pairs.
10. The response window depends on what the model said. That is exactly why the user-turn window exists as a control -- and the control is much weaker (P~W 0.385 at layer 16), which is itself a limit on how much of the correspondence is about representation rather than about generated text.
11. 64 questions from one pool. All 64 come from the zoo's shared prompt pool; nothing tests whether the geometry survives a different question distribution.