The sphere sweep — 72 directions nobody chose

Seventy-two Fibonacci-lattice directions on the sphere of the top three principal components, steered at alpha = 1.5 and judged blind; 48 of 72 loop on no prompt, and angular distance predicts judged-profile distance at rho = 0.65.

The sphere sweep — 72 directions nobody chose

Status, 2026-09-08. The frame is superseded, the data are not. Samuel's decision of 2026-09-08 makes the factor analysis primary and the principal-component chart secondary, so the sphere was resampled on the factor chart: see The sphere sweep on the factor chart. This page remains the record of the 2026-09-01 principal-component sphere, whose generations, judgings and numbers all still stand; what changed is which three-dimensional subspace the lattice is laid on.

Every other steering result in this project is on a direction chosen for a reason. That makes the evidence circular in one specific way, which qwen35/build_sphere_spec.py names:

Steering along a named axis and finding a coherent persona proves little if EVERY direction gives a coherent persona; the only way to know is to sample directions nobody chose.

Design

• 72 points, drawn from a Fibonacci lattice on the unit sphere of the top three principal components — "which spreads them far more evenly over the sphere than random draws of the same count" (qwen35/build_sphere_spec.py). N = 72.
• alpha = 1.5, one strength for every point: ALPHA = 1.5 # inside the intact range for every direction (qwen35/build_sphere_spec.py; also analysis/sphere_layout.json#alpha).
• 8 prompts, PROMPT_IDX = [0, 1, 5, 9, 11, 14, 15, 22] from the 24-prompt battery — a subset, not the whole thing.
• Landmarks appended so the map has fixed points: the five Big Five keying axes projected into the subspace plus the alien direction (analysis/sphere_layout.json#landmarks), and the 134 trait words on the same sphere (#traits, 134 entries).
• The three components carry var3 = 0.12668915056443317, 0.11252214481119611, 0.04955491287468896 of the variance (analysis/sphere_layout.json#var3).

The run is one container rather than 72, because every direction here is a combination of exactly three basis deltas:

steer_fix builds each direction by reading all 134 adapters from the volume: about 43 GB per direction. That is fine for nine directions and absurd for seventy-two ... So the adapters are read ONCE, collapsed immediately into three dense basis deltas, and then every sampled direction is a cheap weighted sum of those three. — qwen35/sphere_sweep.py

Base weights are held as a CPU copy and restored between directions "so seventy-two rounds of bfloat16 addition cannot accumulate drift into the later samples" (qwen35/sphere_sweep.py).

zoo-sphere.service (Description=Sphere sweep: 72 sampled directions in one container) wrote phase10_runs/sphere_results.json — the log ends "wrote phase10_runs/sphere_results.json: 72 points" (qwen35/phase10_runs/sphere.log).

Blinding of the judge is structural. qwen35/sphere_to_eval.py reshapes the sweep into the judge's input format and notes: "the judge never sees that the 'trait' names are coordinates on a sphere." Points are named S000-S071. Judging: "576 generations to judge from 72 traits ... 576 judged, 0 failed calls"; 101 calls, 28 repeats; repeat reliability 0.907 / 0.902 / 0.887 / 0.861 / 0.922 (qwen35/phase10_runs/judge_sphere.log). 72 x 8 = 576.

Result 1: most of the space is habitable

qwen35/analysis/sphere_page.json#coherence:

none       48
any        24
worst      0.25
mean       0.046875
len_mean   1261.234375

The blog page's reading: "at alpha = +1.5, 48 of the 72 sampled directions produce no looping at all, and the worst of them loses 25% of its responses — a mean rate of 4.7% across the sphere. So most directions through this space do give intact output, and the coherence of the ones we chose is not, by itself, evidence of anything." (qwen35/build_blog_page.py).

That is a self-correcting result: it removes coherence as evidence for the chosen directions and shifts the weight onto selectivity and predictive coordinates instead. The blog page says so: "What has to carry the weight instead is specificity: whether a direction moves the scale it is supposed to and leaves the others alone, and whether its coordinates predict its behaviour in advance."

Result 2: personality varies continuously

qwen35/analysis/sphere_page.json#smooth:

rho        0.6511417860626274
n_pairs    2556
n_scored   72
near_mean  0.9661257055739045
far_mean   2.80790992900049

Over all 2,556 pairs of the 72 scored directions, angular distance and judged Big Five profile distance correlate at rho = +0.65. Directions less than 30 degrees apart differ by 0.97 on the Big Five; directions more than 120 degrees apart differ by 2.81 (qwen35/build_blog_page.py, reading sphere_page.json#smooth).

The blog page's pull quote: "Personality varies continuously across this space. Walk a short way and the character changes a little; walk to the far side and it changes a lot. That is what makes it a map rather than a list."

Note that this is a local continuity claim and does not conflict with Additivity of the Big Five steering axes, which finds that coordinates do not compose additively over the interior.

Result 3: the coverage is lopsided

Counting which scale the judge rated highest at each of the 72 points (analysis/sphere_page.json#judged.<point>.top):

The blog page: "Nearly half the sphere reads as agreeable and almost none of it as emotionally stable — the base model's own pull is strong enough that most directions through this space land somewhere pleasant." (qwen35/build_blog_page.py).

How close the sampled points are to real words

Each judged point carries nearest and nearest_deg — the angle to the nearest of the 134 trait lines within this three-dimensional subspace (qwen35/build_sphere_page.py). Across the 72 points those angles run from 0.38236976413731133 to 20.741783210516825 degrees (analysis/sphere_page.json#judged). Inside a three-dimensional subspace crowded with 134 trait lines, a sampled direction is always near some word; the much larger gaps of Where no word goes - the hole and the alien direction and Steering the unnamed direction are measured in a different space and are not comparable to these.

Where it is rendered

qwen35/build_sphere_page.py folds the layout, generations and judging into analysis/sphere_page.json (785 KB), which qwen35/build_blog_page.py renders as the clickable "Sampling the space" panel of the current blog page. Every point's eight generations ship with the page, so a reader can read what the model becomes anywhere on the sphere. Point colour is the top-rated scale, and the caption states coverage explicitly rather than assuming it: 72 of 72 scored (sphere_caption() in qwen35/build_blog_page.py).

qwen35/phase10_runs/sphere_sweep_spec.json (21 KB, 2026-09-01 14:58) is the spec the run actually consumed: it is the default of the sphere_sweep.py local entrypoint (def main(spec: str = "phase10_runs/sphere_sweep_spec.json") and holds the three basis coefficient dicts plus the 72 unit vectors. sphere_spec.json (392 KB) is the steer_fix-shaped expansion, one job per point with its full 134-coefficient vector; nothing read it during the sweep, but it is what the factor-chart comparison in The sphere sweep on the factor chart reads to place these 72 directions on the new chart. (An earlier revision of this page had these two the wrong way round.)

Related: The sphere sweep on the factor chart, Steering the base model along weight-space directions, Additivity of the Big Five steering axes, Steering the unnamed direction, Where no word goes - the hole and the alien direction, Weight-space geometry of the 134-adapter zoo, Glossary.