From Growing to Looping: A Unified View of Iterative Computation in LLMs

• URL: http://arxiv.org/abs/2602.16490v1
• Date: Wed, 18 Feb 2026 14:25:16 GMT
• Title: From Growing to Looping: A Unified View of Iterative Computation in LLMs
• Authors: Ferdinand Kapl, Emmanouil Angelis, Kaitlin Maile, Johannes von Oswald, Stefan Bauer,
• Abstract summary: Looping and depth-grown models exhibit convergent depth-wise signatures.<n>Applying inference-time looping to the middle blocks of a depth-grown model improves accuracy by up to $2times$.<n> depth-grown models achieve the largest reasoning gains when using higher-quality, math-heavy mixtures.
• Score: 42.46854018848624
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Looping, reusing a block of layers across depth, and depth growing, training shallow-to-deep models by duplicating middle layers, have both been linked to stronger reasoning, but their relationship remains unclear. We provide a mechanistic unification: looped and depth-grown models exhibit convergent depth-wise signatures, including increased reliance on late layers and recurring patterns aligned with the looped or grown block. These shared signatures support the view that their gains stem from a common form of iterative computation. Building on this connection, we show that the two techniques are adaptable and composable: applying inference-time looping to the middle blocks of a depth-grown model improves accuracy on some reasoning primitives by up to $2\times$, despite the model never being trained to loop. Both approaches also adapt better than the baseline when given more in-context examples or additional supervised fine-tuning data. Additionally, depth-grown models achieve the largest reasoning gains when using higher-quality, math-heavy cooldown mixtures, which can be further boosted by adapting a middle block to loop. Overall, our results position depth growth and looping as complementary, practical methods for inducing and scaling iterative computation to improve reasoning.

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