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Fixed-Point Reasoners: Stable and Adaptive Deep Looped Transformers

Sajad Movahedi, Vera Milovanović, Shlomo Libo Feigin, Alexander Theus, Thomas Hofmann, Valentina Boeva, T. Konstantin Rusch, Antonio Orvieto

Stabilizes repeated transformer layers and stops looping when the hidden state converges, allowing the model to spend different amounts of computation on different problems.

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arXiv:2606.18206 · Initial submission: 2026-06-16

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Recurrent reasoning — Repeat parts of the model or keep intermediate information in memory while working through a problem. Some methods also learn how many passes to run.

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