IAAIStability and Generalization
Stability and Generalization in Looped Transformers
A fixed-point framework that analyzes looped architectures along reachability, input-dependence and geometry, proving that looped networks without recall cannot achieve strong input dependence, while recall with outer normalization gives reachable, smooth, trainable fixed points.
Inside the method
[ Single layer + recall + outer norm ] × r → fixed point
Simplified conceptual schematic. Consult the paper for the complete architecture.
- Recurrence family
- Core recurrence
- Depth control
- Test-time iterations on harder problems
- KV / state strategy
- See paper
Reading note
Single-layer looped transformers on chess, Sudoku and prefix sums follow the framework's predictions; a new internal-recall placement is competitive and much better on Sudoku once outer normalization is used.
Sources checked 2026-10-28. This catalog does not imply independent reproduction.
Related works
Cite this work
@misc{loopedstabilitygeneralization2026,
title = {Stability and Generalization in Looped Transformers},
author = {Asher Labovich},
year = {2026},
eprint = {2604.15259},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2604.15259}
}