Motor layer / motor-late

Motor layers come from Anthropic’s workspace paper (Gurnee, Lindsey et al. 2026), which describes an early sensory, middle workspace, and late motor organization in the systems it studies. “Motor” is a functional label for a late regime where measured directions become more closely aligned with output-token production. It is not a guarantee that every feature in those layers is output-local, nor a universal boundary shared by every transformer.

In that framing, a motor feature is a direction whose Jacobian-lens vocabulary profile is concentrated around an upcoming token. That is more specific than merely living in a late layer. Even near the unembedding, a lens score remains a readout; actual next-token agreement must be measured against the model’s output.

Motor-late / motor-local is our shorthand in the pressure and release notes for one concrete observation about digit-token directions under one 397B J-lens setup. The free/local run is recorded in digit_geometry_397b.json and generated by digit_geometry.py. In that analysis, the artifact reports an analysis-specific Pearson-kurtosis summary of approximately κ=3.5 for the selected workspace band and κ=14.6 for the last fitted layers, compared with the Gaussian reference κ=3.

For scores \(s_1,\ldots,s_V\) across the vocabulary, that descriptive statistic is

centered = token_scores - token_scores.mean()
kappa = (centered**4).mean() / (centered**2).mean()**2

A high κ means that relatively extreme standardized scores contribute strongly to the fourth moment. The scoped observation is that these vocabulary-score distributions had much higher Pearson kurtosis at the last fitted layers than in the selected middle band. It does not by itself establish a heavy-tailed generating distribution, identify the extreme tokens, say that the correct digit is top-ranked, show that all numerical information is absent earlier, or make arithmetic universally “motor-local.” Claims about digit-token legibility or probe quality require the relevant token identities or ranks as additional evidence. The writeup is in lens_demo/results.md (“Where they live: deep, and only deep”), and the Jacobian lens release note provides the surrounding experiment.

Motor-layer convergence is an eval name in our fitting receipts, not Anthropic’s coinage. It checks whether lens/next-token argmax agreement rises toward the last fitted layer. That expected trend is a useful implementation diagnostic for the evaluated corpus; it is not, on its own, proof that the lens is valid at every earlier layer.

See also: logit lens, best-rank, residual stream.