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When the induction head sees the second occurrence of A, it queries for keys which have emb(A) in the particular subspace that was written by the previous-token head. This is different from the subspace that was written to by the original embedding, and hence has a different “offset” within the residual stream. If A B only occurs once before the second A, then the only key that satisfies this constraint is B, and therefore attention will be high on B. The induction head’s OV circuit learns a high subspace score with the subspace of B that was originally written to by the embedding. Therefore it will add emb(B) to the residual stream of the query (i.e. the second A). In the 2-layer, attention-only model, the model learns an unembedding vector that dots highly at the column index of B in the unembed matrix, resulting in a high logit value that pulls up the probability of B.