Rotate the Loop: Blockwise Conformality for Looped Transformers

arXiv:2610.14030v1 Announce Type: cross Abstract: Looped transformers reuse one shared block across many recurrent steps, so depth becomes a quantity that can be spent at runtime rather than a stack of distinct layers. Those extra steps help only if a write made on one recurrent step is still readable on later ones, and that depends on the linear map applied to the residual between recurrent steps. We show that whether the loop learns to track state is a geometric question about the form of this map, and we propose blockwise conformal injections: the residual splits into coordinate-aligned gro

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