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

2026-01-27

AI Summary

This work addresses the lack of structural guarantees on the validity of intermediate representations in deep neural networks, which hinders principled early stopping and adaptive computation. The authors propose FROST, a novel framework that introduces fractal inductive bias into state space models. By leveraging fractal-stationary transformations and geometric contraction analysis, FROST constructs a scale-consistent, self-similar latent dynamical manifold, enabling intermediate states at different depths to naturally correspond to multi-resolution views of the same underlying representation. This approach not only preserves alignment of the latent geometric structure throughout iterative optimization but also enables an early stopping mechanism grounded in intrinsic feature quality. Experiments on ImageNet-100 validate the model’s scale consistency and demonstrate that its adaptive efficiency stems from the aligned latent space geometry.

Technology Category

• Machine Learning: Representation Learning
• Computer Vision: Representation Learning for Vision
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Large pretrained models with web data

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.

Problem

• scale-consistent dynamics
• state-space models
• adaptive computation
• intermediate representations
• structural guarantees

Innovation

• scale-consistent dynamics
• fractal inductive bias
• state-space models
• self-similar representation
• adaptive computation