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Right Direction, Wrong Step: Geometric Analysis of Finite-Step Failure in Looped Transformers

Zhihao Guo, Zonghan Wu, Haizhou Du, Huan Huo, Yilei Shao, Athanasios V. Vasilakos, Qingsong Wen

Studies updates that initially increase support for a reference answer but overshoot when applied in full. Uses curvature along each update to explain failures and identify smaller useful steps.

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

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arXiv:2609.16665 · Initial submission: 2026-09-15

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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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