Spherical Fixed-Point Reasoners: keeping looped transformers bounded and teaching them when to stop
GabGarrett · x · 2026-10-21
ZelaArber and collaborators introduce Spherical Fixed-Point Reasoners (SFPRM), addressing two core problems for looped transformers: knowing when to stop looping and keeping internal state bounded during iteration.
The trick is to loop on the unit sphere, treating each step as an angle and halting once that angle is small enough. This yields a natural stopping criterion and boundedness by construction, making it suitable for iterative-refinement reasoning. Details are laid out in a 9-part thread.
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