Spherical Fixed-Point Reasoners: Adaptive Loop Halting on the Hypersphere
Looped (weight-tied) transformers enable adaptive computation by allocating more iterations to harder inputs. Fixed-Point Reasoners (FPRM) achieve this with a damped fixed-point solver, but operate in an unbounded Euclidean residual space with coupled rescaling and relative-norm halting. We introduce Spherical Fixed-Point Reasoners (SFPRM), which perform the same computation on the unit hypersphere of normalized transformers (nGPT). Input injection, damping, and halting become geodesic operations, yielding boundedness by construction and eliminating coefficient coupling. We prove fixed-point existence, local convergence under an explicit step-size condition, and global convergence under s...
| Authors | Arber Zela, Artavazd Maranjyan, Pol Puigdemont et al. |
|---|---|
| Primary category | cs.AI |
| Published | 19 October 2026 |
| Last updated at source | 19 October 2026 |
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