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It is found that across Llama-3.1-8B and Mistral-7B, operation-span transplants causally redirect which visible state is read even when the two worlds hold identical values, revealing a routing record.
Multi-token prediction (MTP) supplies exactly the dense, forward-looking supervision the loop is missing, by softly aligning the hidden state of loop $t$ with the embedding of the token $t$ steps ahead, while a lightweight gate preserves useful information across iterations.
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