# FractalMamba++: Scaling Vision Mamba Across Resolutions via Hilbert Fractal Geometry

arXiv: https://arxiv.org/abs/2505.14062 · HTML: https://mlsanity.com/paper/2505.14062/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Vision Mamba backbones, one of 10 directions in State-space sequence models (S4, Mamba).
- Builds on 50 of its 57 references that are in the map.
- First posted on arXiv 20 May 2025.

## Placed in

- State-space sequence models (S4, Mamba) / [Vision Mamba backbones](https://mlsanity.com/ssm/vision-mamba-backbones/)

## Builds on (most cited first, 30 of 50)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [BLIP-2: Bootstrapping Language-Image Pre-training with Frozen Image Encoders and Large Language Models](https://mlsanity.com/paper/2301.12597/) (2023)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [BLIP: Bootstrapping Language-Image Pre-training for Unified Vision-Language Understanding and Generation](https://mlsanity.com/paper/2201.12086/) (2022)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [SAM 2: Segment Anything in Images and Videos](https://mlsanity.com/paper/2408.00714/) (2024)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [MMDetection: Open MMLab Detection Toolbox and Benchmark](https://mlsanity.com/paper/1906.07155/) (2019)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [Unified Perceptual Parsing for Scene Understanding](https://mlsanity.com/paper/1807.10221/) (2018)
- [Semantic Understanding of Scenes through the ADE20K Dataset](https://mlsanity.com/paper/1608.05442/) (2016)
- [Vision Mamba: Efficient Visual Representation Learning with Bidirectional State Space Model](https://mlsanity.com/paper/2401.09417/) (2024)
- [How Far Are We to GPT-4V? Closing the Gap to Commercial Multimodal Models with Open-Source Suites](https://mlsanity.com/paper/2404.16821/) (2024)
- [VMamba: Visual State Space Model](https://mlsanity.com/paper/2401.10166/) (2024)
- [Designing Network Design Spaces](https://mlsanity.com/paper/2003.13678/) (2020)
- [LISA: Reasoning Segmentation via Large Language Model](https://mlsanity.com/paper/2308.00692/) (2023)

## Built on by (most cited first, 1 of 1)

- [MambaEye: A Size-Agnostic Visual Encoder with Causal Sequential Processing](https://mlsanity.com/paper/2511.19963/) (2025)

## Abstract (arXiv)

Vision Mamba offers linear complexity for long visual sequences, yet its performance depends critically on how a two-dimensional patch grid is serialized into a one-dimensional state-space recurrence. Raster-style scans disrupt spatial continuity, and the mismatch between 2D locality and 1D state propagation becomes increasingly severe when the inference resolution grows beyond the training grid. This paper presents FractalMamba++, a resolution-scalable vision backbone organized around a single geometric principle: the recursive self-similar structure of the Hilbert curve determines how patches are serialized, where long-range state shortcuts are inserted, and how positional relations are encoded. First, Hilbert-curve-based Fractal Serialization preserves local 2D neighborhoods more faithfully than linear scans and provides consistent neighborhood statistics across resolutions. Second, the Fractal Hierarchy Skip Connection (FHSC) derives a compact set of deterministic state-injection routes from Hilbert recursion levels, mitigating long-sequence information fading without runtime search, hand-derived gradients, or dedicated CUDA kernels. Third, Fractal-Aware 2D Rotary Position Encoding (FA-RoPE) combines normalized 2D coordinates with a fractal hierarchy level so that feature interactions depend on actual spatial proximity and recursive structural role rather than serialized 1D distance. Extensive experiments on ImageNet-1K classification, COCO detection and instance segmentation, ADE20K semantic segmentation, and LEVIR-CD+ remote sensing change detection show that FractalMamba++ improves over existing Mamba-based vision backbones, especially under high-resolution inputs.