Representations differ.
Which relationships carry?
Source-bound measurements
The charts preserve the existing public visual language. Their schematic elements are illustrations; original reports and correction notes carry the scientific claim. Excessive steering can reduce capability, and reading success does not resolve that tradeoff.
We study whether models share useful relational organization, how a fitted correspondence transfers a readout, and where that transfer breaks. Coordinates, extraction choices, rank and task all matter.
Compare the relationships, then test the map.
Relational similarity can reveal correspondence between representations. It is not the same as an identified full-dimensional translator. Fitted maps require fit/test separation and controls that address the statistic being measured. The corrected direct reading result is AUROC 0.833 against native 0.839 for Qwen2.5-3B → Llama-3.2-3B, on a 162-item battery marked DISQUALIFIED (surface A* 0.855; 1 of 18 cells separates after correction). The deployed hub result is 0.455. These are different results, and the disqualified battery limits their evidential interpretation.
Geometric interpretability compares relational organization and asks what a fitted map carries between models. A successful correspondence does not identify the full computational mechanism.
The wiring, and the map it navigates.
How one model computes
- Object — circuits, features, attention heads
- Scope — one model at a time
- Method — patching, sparse autoencoders, tracing
- Analogy — reverse-engineering one chip
Which relationships correspond
- Object — the shape of the representation manifold
- Scope — across models, up to rotation
- Method — unsupervised alignment, transfer, null-adjudication
- Analogy — comparative anatomy · a reference map
Mechanistic and geometric methods ask related questions at different levels. Each needs its own controls and limits.
Two models, a measured correspondence.
A fitted reference frame and its limits.
A fitted reference frame can organize a set of model comparisons. It is a constructed artifact, not an established universal map of meaning.
We built that shared frame across nine models and asked the decisive question: does routing a finding through the one map cost anything versus the direct, pairwise route? It does not, at the coarse layer — on 180 held-out concept centroids the shared frame matches the direct pairwise maps to within noise (RSA delta +2×10⁻⁹), as does a ported honesty probe on a separate 76-entity set (AUROC delta +0.0003). Two limits: that comparison only ever ran on the aggregate layer, so fine per-concept structure is untested, not shown lossless; and the deployed hub route is measurably lossy — 0.455 against 0.833 for the direct pairwise map — so what follows is a claim about the frame we built, not the route we ship. One map replaces the tangle of pairwise translations. That is the artifact the field is built on.
Reading and intervention are different tests.
A portable reading probe can work without establishing portable causal control. The rank display below is a qualitative illustration, not a live measurement or a universal threshold. Rank studies include measured reading and matching results as well as steering proxies; behavioral and acquisition limits remain part of the result.
Aggregate sharp, instance ambiguous
Aggregate correspondence does not reconstruct a particular thought. Readout success and intervention success require separate tests.
The resolution boundary
The reported coarse transfer and fine per-feature transfer answer different questions. Fine cross-model feature transfer is approximately 0.14, near the null floor in the recorded study. This does not establish a universal coarse layer.
Watch cheap, control dear
Readout and control costs depend on the model pair, extraction recipe and task. Closed output assays do not establish access to an internal representation.
What the geometry charts is identity, not truth. The shared field reads a model’s state — off-distribution, unfamiliar, off its map — not whether a claim is true. On confident, in-distribution fabrication the geometric read is blind, and inverted: a fluent fabrication sits more on-manifold than a real reasoning step (mean distance-to-manifold 0.729 vs 0.894 at layer 25). The 0.587 sometimes quoted here is a different measurement — a wrong-turn reasoning-error probe over 126 graded chains, only 26 of them incorrect, CI [0.455, 0.711] — and not a fabrication AUROC. That is by design: this is the cartography of meaning, not a truth oracle. Catching a fluent, well-grounded falsehood is a different instrument’s job.
Two languages that share no symbols — only a world.
Controls constrain the interpretation.
Different controls preserve different structures. A result should state its test, matched nulls, held-out conditions and failure criterion. Passing selected controls does not settle every interpretation.
A field, charted in the open.
Reported cross-objective and image/text correlations are weaker and sensitive to the representation read recipe. They motivate comparison. Biological extensions remain proposals where no measurement is reported.