IAAIDynamical Phase Selection
Dynamical phase selection controls compute scaling in looped transformers
Shows that looped networks with the same architecture, objective and accuracy can land in different dynamical phases depending on initialization, and that the bifurcation type of each phase, such as a saddle-node fold or a Neimark–Sacker transition, sets how test-time compute scales.
Inside the method
Weight-tied map iterated → fold phase vs Neimark–Sacker phase
Simplified conceptual schematic. Consult the paper for the complete architecture.
- Recurrence family
- Core recurrence
- Depth control
- Test-time iterations governed by critical slowing down
- KV / state strategy
- See paper
Reading note
In the fold phase a normal-form reduction predicts relaxation time from local derivatives and implies a workload tail P(τ > N) ~ N⁻²; in the Neimark–Sacker phase this law disappears. Theory with small-scale experiments.
Sources checked 2026-10-28. This catalog does not imply independent reproduction.
Related works
Cite this work
@misc{dynamicalphaseselection2026,
title = {Dynamical phase selection controls compute scaling in looped transformers},
author = {Gunn Kim},
year = {2026},
eprint = {2608.26556},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.26556}
}