Shared Weights, Selected Computations

How Looped Transformers Route What Each Loop Does

Jiaju Wu, Yi Hu, Muhan Zhang · 2026 · arXiv preprint · Submitted to ICLR 2027

Paper · Code and reproduction materials

We study whether successive loops with shared weights perform the same computation. In graph-walk experiments, modifying the state entering a frozen loop selects different transitions. Attention interventions test how these steering effects are routed.

The public repository links results to source code, archived evidence, and plotting commands. Its CPU reproduction path recomputes figures and statistics from saved predictions; it does not repeat all model training. The evidence is specific to the studied tasks and models.