Behaviour says the concept reconstructs. Can you see it in the weights? Yes — the model’s sense of “we are inside a dominant” is a readable direction in its activations, and you can grab that direction and turn it like a knob.
Probe, then steer
A linear probe on the residual stream finds the “in a dominant” direction at about 0.86 balanced accuracy — and, tellingly, the ablated model that never saw a seventh carries that representation as strongly as the control. The behavioural rebuild has a mechanical shadow: the model still knows where it is, so the missing note is a foregone conclusion.
Then add that direction into the activations while the model composes, and the sevenths roughly double.
Turning the dominant knob
Steered, the model plays dominant sevenths about twice as often. Push to 4× and it over-steers into mush.
Flat-7 rate in generation: 0× 0.051, +2× 0.090, +4× 0.073, −2× 0.056. Probe: logistic regression on residual activations, balanced accuracy 0.89 for in-dominant at layer 3 (chance 0.50).
The verdict
The concept isn’t just behaviourally present — it’s a linear feature you can read and steer. A sparse autoencoder, given no labels, hands back a dictionary that is mostly key-tracking with genuine harmonic-function and note detectors in it. Projecting the direction out of the weights, though, did almost nothing until the coefficient got large enough to break the whole model — you can add a concept far more easily than you can surgically remove one.
Researcher notes
- Probes. Logistic regression on residual activations captured with forward hooks on the transformer blocks; balanced accuracy against a 0.50 chance floor; the probe direction is reused verbatim for steering.
- Suppression. A rank-1 weight lesion projecting the direction out did nothing until α=4, which broke the model (loss 1.81 → 3.28) while the seventh survived — a clean demonstration that deletion is hard even with white-box access.
- SAE. Top-k sparse autoencoder on the residual stream, decoder columns unit-norm; features interpreted by concept enrichment.