# QuadMamba: Learning Quadtree-based Selective Scan for Visual State Space Model

arXiv: https://arxiv.org/abs/2410.06806 · HTML: https://mlsanity.com/paper/2410.06806/

## Key facts

- Cited by 18 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 67 of its 79 references that are in the map.
- First posted on arXiv 9 Oct 2024.

## 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 67)

- [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)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [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)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Feature Pyramid Networks for Object Detection](https://mlsanity.com/paper/1612.03144/) (2016)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [SegFormer: Simple and Efficient Design for Semantic Segmentation with Transformers](https://mlsanity.com/paper/2105.15203/) (2021)
- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Pyramid Vision Transformer: A Versatile Backbone for Dense Prediction without Convolutions](https://mlsanity.com/paper/2102.12122/) (2021)
- [DARTS: Differentiable Architecture Search](https://mlsanity.com/paper/1806.09055/) (2018)
- [ViViT: A Video Vision Transformer](https://mlsanity.com/paper/2103.15691/) (2021)
- [Deformable Convolutional Networks](https://mlsanity.com/paper/1703.06211/) (2017)
- [VoxelNet: End-to-End Learning for Point Cloud Based 3D Object Detection](https://mlsanity.com/paper/1711.06396/) (2017)
- [Unified Perceptual Parsing for Scene Understanding](https://mlsanity.com/paper/1807.10221/) (2018)

## Built on by (most cited first, 18 of 18)

- [DefMamba: Deformable Visual State Space Model](https://mlsanity.com/paper/2504.05794/) (2025)
- [TinyViM: Frequency Decoupling for Tiny Hybrid Vision Mamba](https://mlsanity.com/paper/2411.17473/) (2024)
- [DRBD-Mamba for Robust and Efficient Brain Tumor Segmentation with Analytical Insights](https://mlsanity.com/paper/2510.14383/) (2025)
- [GeoMaNO: Geometric Mamba Neural Operator for Partial Differential Equations](https://mlsanity.com/paper/2505.12020/) (2025)
- [BSMamba: Brightness and Semantic Modeling for Long-Range Interaction in Low-Light Image Enhancement](https://mlsanity.com/paper/2506.18346/) (2025)
- [A2Mamba: Attention-augmented State Space Models for Visual Recognition](https://mlsanity.com/paper/2507.16624/) (2025)
- [Partial Ring Scan: Revisiting Scan Order in Vision State Space Models](https://mlsanity.com/paper/2602.04170/) (2026)
- [Towards Remote Sensing Change Detection with Neural Memory](https://mlsanity.com/paper/2602.10491/) (2026)
- [Efficiency Follows Global-Local Decoupling](https://mlsanity.com/paper/2603.19567/) (2026)
- [InceptionMamba: An Efficient Hybrid Network with Large Band Convolution and Bottleneck Mamba](https://mlsanity.com/paper/2506.08735/) (2025)
- [Keyword Mamba: Spoken Keyword Spotting with State Space Models](https://mlsanity.com/paper/2508.07363/) (2025)
- [Human-inspired Global-to-Parallel Multi-scale Encoding for Lightweight Vision Models](https://mlsanity.com/paper/2601.08190/) (2026)
- [PestVL-Net: Enabling Multimodal Pest Learning via Fine-grained Vision-Language Interaction](https://mlsanity.com/paper/2604.17278/) (2026)
- [Can Graphs Help Vision SSMs See Better?](https://mlsanity.com/paper/2605.11300/) (2026)
- [TCP-SSM: Efficient Vision State Space Models with Token-Conditioned Poles](https://mlsanity.com/paper/2605.11563/) (2026)
- [Variable-Granularity Tokenization for High-Resolution Object Detection](https://mlsanity.com/paper/2608.28706/) (2026)
- [ScopeMamba-YOLO: Widening the Perceptual Scope Inward and Outward for Small Object Detection in Remote Sensing Imagery](https://mlsanity.com/paper/2609.10156/) (2026)
- [LiAuto-MindViT: A Hybrid Vision Backbone with Adaptive Bidirectional Mamba](https://mlsanity.com/paper/2609.24337/) (2026)

## Abstract (arXiv)

Recent advancements in State Space Models, notably Mamba, have demonstrated superior performance over the dominant Transformer models, particularly in reducing the computational complexity from quadratic to linear. Yet, difficulties in adapting Mamba from language to vision tasks arise due to the distinct characteristics of visual data, such as the spatial locality and adjacency within images and large variations in information granularity across visual tokens. Existing vision Mamba approaches either flatten tokens into sequences in a raster scan fashion, which breaks the local adjacency of images, or manually partition tokens into windows, which limits their long-range modeling and generalization capabilities. To address these limitations, we present a new vision Mamba model, coined QuadMamba, that effectively captures local dependencies of varying granularities via quadtree-based image partition and scan. Concretely, our lightweight quadtree-based scan module learns to preserve the 2D locality of spatial regions within learned window quadrants. The module estimates the locality score of each token from their features, before adaptively partitioning tokens into window quadrants. An omnidirectional window shifting scheme is also introduced to capture more intact and informative features across different local regions. To make the discretized quadtree partition end-to-end trainable, we further devise a sequence masking strategy based on Gumbel-Softmax and its straight-through gradient estimator. Extensive experiments demonstrate that QuadMamba achieves state-of-the-art performance in various vision tasks, including image classification, object detection, instance segmentation, and semantic segmentation. The code is in https://github.com/VISION-SJTU/QuadMamba.