Why it is a question
THEORY-169, narrowed on 2026-10-19, holds that for unnormalized causal linear attention and for softmax attention the layer’s output equals a learner’s train-then-predict step on its context, and that one linear self-attention layer with constructed weights carries one gradient step of in-context linear regression. Until that date its promote_when also asked for a test of scope. At the owner’s direction, from the promotion audit’s batch 024 (ADR-047), the THEORY was narrowed and promoted on the proved identities, which were re-derived, and that part of the condition moved here unchanged.
It is open because the identities are for particular layers. Normalized linear attention, TTT-Linear as built (mini-batch updates, a learned W₀, LayerNorm) and delta-rule layers are not covered, and nothing the record holds shows that some standard layer has no such description.
What would answer it
The scope test formerly on THEORY-169, unchanged. An exact identity of this kind for a further layer class, for instance a delta-rule or mini-batch inner update, would confirm the pattern. A proof that some standard attention layer’s dependence on its context admits no description as any learner’s train-then-predict step would bound it. Restating the two known constructions, or measuring trained models’ similarity to gradient descent, does not count.