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

arXiv: https://arxiv.org/abs/2601.19551 · HTML: https://mlsanity.com/paper/2601.19551/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 33 references that are in the map.
- First posted on arXiv 27 Jan 2026.

## Builds on (most cited first, 27 of 27)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [An Empirical Study of Training Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.02057/) (2021)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [Perceiver: General Perception with Iterative Attention](https://mlsanity.com/paper/2103.03206/) (2021)
- [Vision Mamba: Efficient Visual Representation Learning with Bidirectional State Space Model](https://mlsanity.com/paper/2401.09417/) (2024)
- [VMamba: Visual State Space Model](https://mlsanity.com/paper/2401.10166/) (2024)
- [Universal Transformers](https://mlsanity.com/paper/1807.03819/) (2018)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [BranchyNet: Fast Inference via Early Exiting from Deep Neural Networks](https://mlsanity.com/paper/1709.01686/) (2017)
- [Do Better ImageNet Models Transfer Better?](https://mlsanity.com/paper/1805.08974/) (2018)
- [Adaptive Computation Time for Recurrent Neural Networks](https://mlsanity.com/paper/1603.08983/) (2016)
- [Hungry Hungry Hippos: Towards Language Modeling with State Space Models](https://mlsanity.com/paper/2212.14052/) (2022)
- [Hyena Hierarchy: Towards Larger Convolutional Language Models](https://mlsanity.com/paper/2302.10866/) (2023)
- [Recurrent Models of Visual Attention](https://mlsanity.com/paper/1406.6247/) (2014)
- [SkipNet: Learning Dynamic Routing in Convolutional Networks](https://mlsanity.com/paper/1711.09485/) (2017)
- [LayerSkip: Enabling Early Exit Inference and Self-Speculative Decoding](https://mlsanity.com/paper/2404.16710/) (2024)
- [Mixture-of-Depths: Dynamically allocating compute in transformer-based language models](https://mlsanity.com/paper/2404.02258/) (2024)
- [PonderNet: Learning to Ponder](https://mlsanity.com/paper/2107.05407/) (2021)
- [ReNet: A Recurrent Neural Network Based Alternative to Convolutional Networks](https://mlsanity.com/paper/1505.00393/) (2015)

## Abstract (arXiv)

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.