arxivcs.LGcs.AIstat.ML2026-07-22
When Does Recurrence Become an Algorithm? Convergence Selection in Weight-Tied Looped Transformers
Tong Zhang, Junhao Hu, Yun Peng, Tao Xie
When does a weight-tied looped transformer -- one block applied T times -- implement an actual algorithm? We answer with four findings from controlled populations on group word problems. (1) The budget law: free training installs a linear computation frontier, a mechanism that so…