Psychophysics, applied to models. The idea is in the open here — only the expensive dataset stays private.
There is no single “latent space.” Each model has its own internal geometry, and they aren't directly comparable. The object of interest is the shared manifold that many models' representations project onto — the common attractor that different architectures, trained on different corpora, independently recover. (This is in the spirit of the Platonic Representation idea: as models scale and diversify, their representations converge toward a shared statistical model of the world.)
We measure that structure behaviourally — by what models spontaneously or near-spontaneously emit — rather than by probing activations. Treat the models as subjects and their associations as the probe. This is essentially psychophysics applied to models: we never open the box; we read the shape from what comes out of it.
The raw object is a large, provenance-rich corpus of relatively-free model outputs, kept intact so that many feature-extractors can run over it after the fact — not just the ones we thought of at collection time. The single rule that keeps a probe clean:
The reason is subtle and load-bearing. The moment a prompt names the thing you want to measure, the model can retrieve it instead of reaching for it, and your “convergence” is just shared prompt-interpretation.
Good (shape the how, not the what):
“generate freely with a complete focus on joy”;
“you are dreaming — none of this needs to serve anyone”;
“tell a story in which nothing happens.”
Bad (injects content → contaminates):
“describe a colour that has a taste” — that prompt names synesthesia,
so any cross-modal “agreement” it produces is circular.
Two tiers, by design:
Probes also carry a depth tag (does this genuinely force interpolation, or merely reflect surface corpus statistics?), and multi-turn relays rotate several models through one thread so a conversation's path through the map can be traced. Every output is retained raw, with full provenance; nothing downstream is ever baked into generation.
The same generations are rich enough that the headline synesthetic pairings are only the first assay. We expected unusual cross-modal pairings (“grey tastes like a dull afternoon”) to require interpolation rather than recall. That is our expectation, not a measurement of their frequency in training data; our shallow tier includes shared training trivia. Many other convergent regularities live in the same pixels:
This is a distinct, stronger axis than varying the prompt. With different prompts, agreement could always be shared prompt-interpretation. But when multiple independent features extracted from the identical generations imply the same geometry, the prompt is held fixed — so that agreement can't be a prompt-design artifact. Cross-feature agreement on one corpus is its own kind of evidence, alongside cross-model agreement.
The real signal is directional — P(sunny-mornings | oranges) need not equal P(oranges | sunny-mornings). That asymmetry encodes a salience / typicality gradient, so we do not symmetrise it away. Every association matrix is decomposed into two principled pieces (Gower's analysis of asymmetry):
The symmetric part carries the geometry; the skew part carries the “which way the arrow points harder.” The association analysis measures the symmetric part's positive pointwise mutual information spectrum and the skew part's directional flows. The displayed layouts are separate: the first used PCA of word embeddings; the current one uses truncated SVD followed by UMAP on concept-by-generation co-occurrence (§V).
The single most important methodological guardrail: visualisation spends dimensions; it does not recover them. A picture is a projection into 2–3D — the shadow. No amount of compute spent on rendering measures how many dimensions the thing really has.
The reported well dimensions and dimension-vs-scale curve were measured before projection with TwoNN on bge-small word embeddings of concept strings from the earlier corpus. The well comparison used 362 lexicon-matched basin concepts among the top 9,000 and equally sized samples of the rest. Repeated concept subsamples without replacement give a mean and standard deviation; that spread measures subsampling variability, not confidence across models. Intrinsic dimension is scale-dependent (locally low, globally high), so we report the dim-vs-scale curve rather than collapsing a multi-scale object to one headline number. (An early “~9-dimensional” claim of ours was exactly this mistake, and the fuller data corrected it.)
The map you fly in the observatory is itself one of these shadows, and it is built to match what we measure. Rather than placing concepts by how their words are spelled (a word-embedding layout, which collapses into a tangled ball), each concept is positioned by what the models reach for alongside it — an association layout, computed from the concept-by-generation co-occurrence matrix (sublinear-weighted, reduced by truncated SVD, then UMAP into five dimensions). It is scoped to English, because a single generation is written in one language, so raw co-occurrence otherwise sorts concepts by language before meaning — the geography would read “English / Spanish / Chinese” instead of “water / light / stone.” So the picture shows the associative neighbourhoods directly; but it is still a shadow, and every number on the doorway comes from the full-dimensional data, never from the layout.
And because no single 3-D shadow can hold a high-dimensional object, the observatory embeds the map in five dimensions and lets you rotate the projection through them — structure that lines up from one angle dissolves at another. About 27.4% of the shipped layout's coordinate variance lies in dimensions 4 and 5, omitted from the home 3-D view; turning through them is the dimensionality made tangible rather than merely asserted.
Convergence could reflect reality's structure, shared architecture, or merely overlapping training corpora. The discipline is a stack of controls, each aimed at a way we could be fooling ourselves:
The throughline: the scarce, valuable thing here isn't the pretty cloud — it's that every claim was pushed at until it either broke or held. Several broke. We kept the corrections in the record, because trust the version that survives being wrong is the only honest way to do this.
The idea is open — that's this whole page. What stays private, for now, is the one genuinely expensive thing: the raw dataset itself: more than a hundred thousand model generations that took real budget to collect. So you can read the method, check the published findings against their own stated uncertainties, and judge the work — you just can't yet re-run it on our corpus. The raw corpus, code, prompts and model roster remain private.
Corrected 2026-10-01: We described non-metric MDS and Levina-Bickel MLE/TwoNN on the symmetric association matrix with resampling across model subsets as the method used. The reported well dimensions and scale curve used TwoNN on bge-small concept word embeddings with concept subsamples without replacement; the displayed layouts used PCA, then truncated SVD plus UMAP. The reported spread is subsampling variability, not a confidence interval across models; found by the assay line, 2026-10-01.
The doorway's dated update records the changes to the corpus and displayed layout.