Scale-Consistent State-Space Dynamics via Fractal of Stationary Transformations

• URL: http://arxiv.org/abs/2601.19551v1
• Date: Tue, 27 Jan 2026 12:44:20 GMT
• Title: Scale-Consistent State-Space Dynamics via Fractal of Stationary Transformations
• Authors: Geunhyeok Yu, Hyoseok Hwang,
• Abstract summary: Recent deep learning models increasingly rely on depth without structural guarantees on the validity of intermediate representations.<n>We address this limitation by formulating a structural requirement for state-space model's scale-consistent latent dynamics.<n>We empirically verify the predicted scale-consistent behavior, showing that adaptive efficiency emerges from the aligned latent geometry.
• Score: 9.983526161001997
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Recent deep learning models increasingly rely on depth without structural guarantees on the validity of intermediate representations, rendering early stopping and adaptive computation ill-posed. We address this limitation by formulating a structural requirement for state-space model's scale-consistent latent dynamics across iterative refinement, and derive Fractal of Stationary Transformations (FROST), which enforces a self-similar representation manifold through a fractal inductive bias. Under this geometry, intermediate states correspond to different resolutions of a shared representation, and we provide a geometric analysis establishing contraction and stable convergence across iterations. As a consequence of this scale-consistent structure, halting naturally admits a ranking-based formulation driven by intrinsic feature quality rather than extrinsic objectives. Controlled experiments on ImageNet-100 empirically verify the predicted scale-consistent behavior, showing that adaptive efficiency emerges from the aligned latent geometry.

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