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

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. In particular, applying inference-time looping to the middle blocks of a depth-grown model yields additional improvements in reasoning primitives accuracy, up to 2x, despite the model never being trained to loop. Building on this connection, we show that the two techniques are both adaptable and composable. Both approaches 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 looped block in the middle of the network. Overall, our results position depth growth and looping as complementary, practical methods for inducing and scaling iterative computation to improve reasoning.

• Machine intelligence