Dynamic Fractal Mamba: A neural renormalization group flow for scale-invariant sequence modeling

Fang, Shenglei, Sun, Xianfang ORCID: https://orcid.org/0000-0002-6114-0766 and Zhou, You ORCID: https://orcid.org/0000-0002-1743-1291 2026. Dynamic Fractal Mamba: A neural renormalization group flow for scale-invariant sequence modeling. Presented at: ICML 2026, Seoul, South Korea, 6-11 July 2026. Proceedings of Machine Learning Research.

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Abstract

Sequence models typically operate at a fixed temporal or spatial scale and struggle to generalize to substantially longer horizons or higher resolutions without retraining. Existing hierarchical architectures expand receptive fields but rely on scalespecific parameters and lack mechanisms to enforce consistent dynamics across scales. We propose Dynamic Fractal Mamba (DF-Mamba), a recursive state-space model that applies a single shared operator across multiple scales. By sharing parameters across recursion depths and exponentially scaling the effective time step, DF-Mamba achieves an exponentially expanding receptive field while preserving linear computational complexity. A learned content-aware coarse-graining module aggregates representations across scales. Auxiliary reconstruction and cross-scale consistency objectives stabilize recursive training. We evaluate DF-Mamba on long-range time-series forecasting, spatial transcriptomics, and computational pathology. Across all tasks, DF-Mamba consistently outperforms Transformers and flat Mamba baselines while using fewer parameters and maintaining linear-time scalability. Importantly, models trained on short sequences or lowresolution inputs generalize in a zero-shot manner to substantially larger temporal and spatial scales unseen during training. These results demonstrate that recursive parameter sharing provides an effective inductive bias for learning scaleconsistent and efficient sequence representations. Our code is available at: https://github. com/yzlab1/Dynamic-Fractal-Mamba

Item Type:	Conference or Workshop Item - published (Paper)
Status:	In Press
Schools:	Schools > Medicine Schools > Computer Science & Informatics
ISSN:	1938-7228
Date of First Compliant Deposit:	21 July 2026
Last Modified:	21 Jul 2026 11:53
URI:	https://orca.cardiff.ac.uk/id/eprint/188359

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