Inside the Loop: A Mechanistic Study of Weight-Tied Transformers on Depth-Bound Algorithmic Tasks
Solving algorithmic tasks with many sequential steps typically requires scaling up transformer depth or chain-of-thought length, incurring unfavorable parameter and inference-compute costs, respectively. Looped transformers, which reuse one block of layers across many iterations, are poised to address this, since they scale effective depth without adding parameters or tokens. Yet, it remains unclear what each iteration is actually computing, or whether the loop merely simulates a deeper untied stack. Here, we study directed permutation traversal, in which a model follows $H$ hops from a starting node and reports the node it reaches, so every intermediate hop has a known ground truth. We f...
| Authors | Magnus Sesodia, Juil Sock, Philip Torr et al. |
|---|---|
| Primary category | cs.LG |
| Published | 16 October 2026 |
| Last updated at source | 16 October 2026 |
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