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Shared Weights, Selected Computations: How Looped Transformers Route What Each Loop Does

Jiaju Wu, Yi Hu, Muhan Zhang

Uses graph-walk tasks to study how a looped transformer performs different computations with the same weights. Tests whether changing the state entering a loop can select its computation, using steering and activation-patching experiments.

First public: · Added to this list: October 18, 2026

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ArXiv preprint

arXiv:2609.39892 · Initial submission: 2026-09-30

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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.

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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