# Scale-Consistent State-Space Dynamics via Fractal of Stationary Transformations Source: [Scale-Consistent State-Space Dynamics via Fractal of Stationary Transformations]() Collection index: [llms.txt]() Data updated: 2026-01-29T05:00:05.136Z Authors: Geunhyeok Yu, Hyoseok Hwang Published: 2026-01-27T12:44:20.000Z ## 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Model Efficiency on CIFAR-100 Image Classification](): Image Classification; CIFAR-100; GFLOPs: 24.71. ## Original sources and implementation [Original paper]() [PDF]()