Spherical Fixed-Point Reasoners: bounded looped transformers that know when to stop
peter_richtarik · x · 2026-10-21
Researchers introduce Spherical Fixed-Point Reasoners (SFPRM), addressing two core problems of looped transformers: keeping the state bounded while looping, and knowing when to stop.
The method performs the loop on the unit sphere, where each iteration is an angle, and stops once the angle shrinks below a threshold — turning recursive reasoning into a fixed-point iteration on the sphere with a natural stopping criterion. Details are laid out in a 9-tweet thread.
Related event: SFPRM Teaches Looped Transformers to Know When to Stop(3 posts)→
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