Block-Recurrent Dynamics in Vision Transformers

• URL: http://arxiv.org/abs/2512.19941v1
• Date: Tue, 23 Dec 2025 00:18:23 GMT
• Title: Block-Recurrent Dynamics in Vision Transformers
• Authors: Mozes Jacobs, Thomas Fel, Richard Hakim, Alessandra Brondetta, Demba Ba, T. Andy Keller,
• Abstract summary: We argue that trained ViTs admit a block-recurrent depth structure such that the computation of the original $L$ blocks can be accurately rewritten using only $k ll L$ distinct blocks applied recurrently.<n>We train a Raptor model to recover $96%$ of DINOv2 ImageNet-1k linear probe accuracy in only 2 blocks at equivalent computational cost.
• Score: 42.261020313952976
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: As Vision Transformers (ViTs) become standard vision backbones, a mechanistic account of their computational phenomenology is essential. Despite architectural cues that hint at dynamical structure, there is no settled framework that interprets Transformer depth as a well-characterized flow. In this work, we introduce the Block-Recurrent Hypothesis (BRH), arguing that trained ViTs admit a block-recurrent depth structure such that the computation of the original $L$ blocks can be accurately rewritten using only $k \ll L$ distinct blocks applied recurrently. Across diverse ViTs, between-layer representational similarity matrices suggest few contiguous phases. To determine whether these phases reflect genuinely reusable computation, we train block-recurrent surrogates of pretrained ViTs: Recurrent Approximations to Phase-structured TransfORmers (Raptor). In small-scale, we demonstrate that stochastic depth and training promote recurrent structure and subsequently correlate with our ability to accurately fit Raptor. We then provide an empirical existence proof for BRH by training a Raptor model to recover $96\%$ of DINOv2 ImageNet-1k linear probe accuracy in only 2 blocks at equivalent computational cost. Finally, we leverage our hypothesis to develop a program of Dynamical Interpretability. We find i) directional convergence into class-dependent angular basins with self-correcting trajectories under small perturbations, ii) token-specific dynamics, where cls executes sharp late reorientations while patch tokens exhibit strong late-stage coherence toward their mean direction, and iii) a collapse to low rank updates in late depth, consistent with convergence to low-dimensional attractors. Altogether, we find a compact recurrent program emerges along ViT depth, pointing to a low-complexity normative solution that enables these models to be studied through principled dynamical systems analysis.

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