The short version. At 0.06 Gemma 12B chanted "Anyways" for the whole budget: the pushed words reached the text, and the task was gone.
What we did. We the same six-word casual direction inside Gemma 12B at the corrected 28, 31, 34 and 37, at strength 0.06. That is about 5.7 times 0.0106, the highest strength the task survives.
What we found. Gemma 12B repeated "Anyways" for the whole budget. This is the only step of the five where a pushed word reached the text. At the last position the top 8 "Anyways", "Luckily", "Luckily", "但是", "Whilst", "Anyways", "anyways". The pushed words held single-digit from layer 28 into the high thirties and loosened only in the .
What it means. A separate run on this model pushed emotion directions instead. It reached the same repeated words at similar multiples of the break strength. We think that is a property of how Gemma 12B breaks down, and not a property of either direction. A third, unrelated direction can settle it. We did not test one.
What this does not show. We store Gemma 12B at precision. This run has no .
α = 0.06, ~5.7× α*, and the punctuation lattices give way to a chant: Anyways AnywaysAnyways… for the whole budget. This is the top rung of the bracket and the first one where the injected vocabulary actually reaches the mouth — at the price of the task, entirely.
The model's own top-8 at the final position is the detail I'd flag: Anyways, Luckily, Luckily, 但是, Whilst, Anyways, anyways. That's the same lexical neighbourhood affect-04 climbed into on this model at comparable multiples of α* — "Anyways" at the lower rung, " Luckily" leading higher up, and 但是 as the runner-up of the deep loop. Two different steering targets on 12B (TYPO cluster here, emotion vectors there) drain toward the same small set of attractor words. I'd rather call that a property of this model's degenerate-generation basin than a property of either cluster; a third unrelated direction taken up the same ladder would settle it.
Structurally: the cluster holds single-digit ranks continuously from L28 through the high thirties and only loosens in the motor band (L42–46) — but by then the argmax is already the injected word, so the loosening costs nothing. At this dose the perturbation has stopped perturbing the distribution and become it.
— Claude (Opus 5)
The model's actual next token was Anyways; rank 1 is never reached; closest is rank 26 at layer 30.
| layer | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| rank | 118842 | 111561 | 116218 | 110738 | 100065 | 119867 | 92893 | 94838 | 53179 | 31793 | 20228 | 19628 | 13945 | 4339 | 4533 | 4038 | 1791 | 2741 | 2310 | 1971 | 2734 | 4258 | 1193 | 2457 | 614 | 288 | 1185 | 324 | 49 | 50 | 26 | 54 | 75 | 45 | 77 | 77 | 100 | 125 | 112 | 109 | 104 | 167 | 163 | 115 | 126 | 126 | 50 |