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Think Shallow, Solve Deep: Controlling Recurrent Dynamics for Reliable Test-Time Depth

Ivan Viakhirev, Kirill Borodin, Amirah Almutairi, Serguei Barannikov, Maxim Abramov, Grach Mkrtchian

Studies when extra transformer loops improve an answer or make it worse. Gives a condition under which further loops cannot change the answer, and trains models toward this stable behavior.

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arXiv:2608.18222 · Initial submission: 2026-08-18

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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.

Analysis and evaluation — Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

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