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The two factors dissociate. For learning, both routes to repeated shared access -- looped recomputation and repeated memory rereading -- cross the out-of-distribution (OOD) grokking barrier that Dense fails, so repeated shared access is the behavioral regularity, not a specific architecture. For editing, the substrates split along a different axis: applying a single localized factual edit (conditioned on direct success) and measuring 2-hop propagation on a shared pre-edit-correct set, the edit propagates strongly in both memory-bearing cells (LMC 0.78-0.92, Dense+Mem 0.71-0.96) and only weakly in the me","title":"Repeated Shared Access Enables Grokking, but Edit Propagation Depends on an Addressable Memory","url":"https://arxiv.org/abs/2606.20737","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.20737v2 Announce Type: replace \nAbstract: We study factual edit propagation in a controlled synthetic knowledge-graph QA setting using a 2x2 grid that crosses loop recurrence with shared-memory access: a dense transformer (Dense), a looped transformer (Loop), a dense backbone with shared memory (Dense+Mem), and a looped backbone with shared memory (loop-memory coupling, LMC). The two factors dissociate. For learning, both routes to repeated shared access -- looped recomputation and repeated memory rereading -- cross the out-of-distribution (OOD) grokking barrier that Dense fails, so repeated shared access is the behavioral regularity, not a specific architecture. 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