Two-Scale Latent Dynamics for Recurrent-Depth Transformers

• URL: http://arxiv.org/abs/2509.23314v1
• Date: Sat, 27 Sep 2025 14:01:40 GMT
• Title: Two-Scale Latent Dynamics for Recurrent-Depth Transformers
• Authors: Francesco Pappone, Donato Crisostomi, Emanuele Rodolà,
• Abstract summary: We study the geometry of current-depth transformers scale test-time compute by iterating latent computations before emitting tokens.<n>Across checkpoints, our measurements show that loop steps become emphsmaller and increasingly emphorthogonal to one another.<n>These dynamics motivate an early-exit mechanism based on the model's second-order difference in step-size.
• Score: 18.852161704625562
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Recurrent-depth transformers scale test-time compute by iterating latent computations before emitting tokens. We study the geometry of these iterates and argue for a simple, \emph{two-scale} operational picture: (i) within a looped block, updates act as \emph{small-scale refinements}; (ii) across consecutive blocks, states undergo a \emph{larger-scale drift}. Across checkpoints, our measurements show that loop steps become \emph{smaller} and increasingly \emph{orthogonal} to one another, indicating better local modeling of fine structure rather than merely pushing in a single direction. These dynamics motivate an early-exit mechanism based on the model's second-order difference in step-size, which we show is superior in terms of performance, stability and time-efficiency, when compared to the KL-divergence exit strategy of Geiping et al. and its naive first-order counterpart.

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