IAAISFPRM
Spherical Fixed-Point Reasoners: Adaptive Loop Halting on the Hypersphere
Spherical Fixed-Point Reasoners move fixed-point looped reasoning onto the unit hypersphere of normalized transformers, turning input injection, damping and halting into geodesic operations that are bounded by construction.
Inside the method
nGPT block on the hypersphere: geodesic injection → damping → halting
Simplified conceptual schematic. Consult the paper for the complete architecture.
- Recurrence family
- Adaptive depth
- Depth control
- Adaptive halting at a fixed point
- KV / state strategy
- See paper
Reading note
Proves fixed-point existence and convergence conditions. Reports 96.6% on Sudoku-Extreme, 87.9% on Maze-Hard and 59.1% on Mini-ARC, ahead of FPRM; these are puzzle benchmarks, not language modeling.
Sources checked 2026-10-28. This catalog does not imply independent reproduction.
Related works
Cite this work
@misc{sfprm2026,
title = {Spherical Fixed-Point Reasoners: Adaptive Loop Halting on the Hypersphere},
author = {Arber Zela and Artavazd Maranjyan and Pol Puigdemont and David Berghaus and Valentyn Boreiko and Volkan Cevher},
year = {2026},
eprint = {2610.25646},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25646}
}