IAAIConvergence Selection
When Does Recurrence Become an Algorithm? Convergence Selection in Weight-Tied Looped Transformers
Studies when a weight-tied looped transformer implements a real algorithm on group word problems. Training installs a linear computation frontier whose speed is set by the training contract, and weight tying, not expressivity, makes the model choose a serial algorithm over a parallel scan.
Inside the method
Simplified conceptual schematic. Consult the paper for the complete architecture.
- Recurrence family
- Core recurrence
- Depth control
- Principled halting rule T* = ⌈n / v⌉
- KV / state strategy
- See paper
Reading note
Frontier speed follows v ~ n_train / T_train (R² = 0.99). A5 generalizes fully while S5 stalls unless trained operator-first. Introduces a convergence-time instrument because standard probes saturate at fixed points.
Sources checked 2026-10-28. This catalog does not imply independent reproduction.
Related works
Cite this work
@misc{convergenceselection2026,
title = {When Does Recurrence Become an Algorithm? Convergence Selection in Weight-Tied Looped Transformers},
author = {Tong Zhang and Junhao Hu and Yun Peng and Tao Xie},
year = {2026},
eprint = {2607.20594},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.20594}
}