# Mamba-ND: Selective State Space Modeling for Multi-Dimensional Data

arXiv: https://arxiv.org/abs/2402.05892 · HTML: https://mlsanity.com/paper/2402.05892/

## Key facts

- Cited by 84 papers in the map (data through 14 Oct 2026).
- Placed in Core SSM architectures for language, one of 10 directions in State-space sequence models (S4, Mamba).
- Builds on 51 of its 66 references that are in the map.
- First posted on arXiv 8 Feb 2024.

## Placed in

- State-space sequence models (S4, Mamba) / [Core SSM architectures for language](https://mlsanity.com/ssm/core-ssm-architectures-for-language/)

## Builds on (most cited first, 30 of 51)

- [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)
- [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)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Quo Vadis, Action Recognition? A New Model and the Kinetics Dataset](https://mlsanity.com/paper/1705.07750/) (2017)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Non-local Neural Networks](https://mlsanity.com/paper/1711.07971/) (2017)
- [Pyramid Vision Transformer: A Versatile Backbone for Dense Prediction without Convolutions](https://mlsanity.com/paper/2102.12122/) (2021)
- [The Kinetics Human Action Video Dataset](https://mlsanity.com/paper/1705.06950/) (2017)
- [SlowFast Networks for Video Recognition](https://mlsanity.com/paper/1812.03982/) (2018)
- [Is Space-Time Attention All You Need for Video Understanding?](https://mlsanity.com/paper/2102.05095/) (2021)
- [ViViT: A Video Vision Transformer](https://mlsanity.com/paper/2103.15691/) (2021)
- [A Closer Look at Spatiotemporal Convolutions for Action Recognition](https://mlsanity.com/paper/1711.11248/) (2017)
- [Video Swin Transformer](https://mlsanity.com/paper/2106.13230/) (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)
- [UNETR: Transformers for 3D Medical Image Segmentation](https://mlsanity.com/paper/2103.10504/) (2021)
- [Swin UNETR: Swin Transformers for Semantic Segmentation of Brain Tumors in MRI Images](https://mlsanity.com/paper/2201.01266/) (2022)
- [Pixel Recurrent Neural Networks](https://mlsanity.com/paper/1601.06759/) (2016)
- [CoAtNet: Marrying Convolution and Attention for All Data Sizes](https://mlsanity.com/paper/2106.04803/) (2021)
- [Understanding the Effective Receptive Field in Deep Convolutional Neural Networks](https://mlsanity.com/paper/1701.04128/) (2017)
- [CSWin Transformer: A General Vision Transformer Backbone with Cross-Shaped Windows](https://mlsanity.com/paper/2107.00652/) (2021)
- [MViTv2: Improved Multiscale Vision Transformers for Classification and Detection](https://mlsanity.com/paper/2112.01526/) (2021)
- [VATT: Transformers for Multimodal Self-Supervised Learning from Raw Video, Audio and Text](https://mlsanity.com/paper/2104.11178/) (2021)
- [U-Mamba: Enhancing Long-range Dependency for Biomedical Image Segmentation](https://mlsanity.com/paper/2401.04722/) (2024)

## Built on by (most cited first, 30 of 84)

- [PointMamba: A Simple State Space Model for Point Cloud Analysis](https://mlsanity.com/paper/2402.10739/) (2024)
- [MambaOut: Do We Really Need Mamba for Vision?](https://mlsanity.com/paper/2405.07992/) (2024)
- [PlainMamba: Improving Non-Hierarchical Mamba in Visual Recognition](https://mlsanity.com/paper/2403.17695/) (2024)
- [Motion Mamba: Efficient and Long Sequence Motion Generation](https://mlsanity.com/paper/2403.07487/) (2024)
- [Demystify Mamba in Vision: A Linear Attention Perspective](https://mlsanity.com/paper/2405.16605/) (2024)
- [The Hidden Attention of Mamba Models](https://mlsanity.com/paper/2403.01590/) (2024)
- [ZigMa: A DiT-style Zigzag Mamba Diffusion Model](https://mlsanity.com/paper/2403.13802/) (2024)
- [Point Cloud Mamba: Point Cloud Learning via State Space Model](https://mlsanity.com/paper/2403.00762/) (2024)
- [Mamba-360: Survey of State Space Models as Transformer Alternative for Long Sequence Modelling: Methods, Applications, and Challenges](https://mlsanity.com/paper/2404.16112/) (2024)
- [State Space Model for New-Generation Network Alternative to Transformers: A Survey](https://mlsanity.com/paper/2404.09516/) (2024)
- [Vision Mamba: A Comprehensive Survey and Taxonomy](https://mlsanity.com/paper/2405.04404/) (2024)
- [A Survey on Visual Mamba](https://mlsanity.com/paper/2404.15956/) (2024)
- [STORM: Token-Efficient Long Video Understanding for Multimodal LLMs](https://mlsanity.com/paper/2503.04130/) (2025)
- [MambaMixer: Efficient Selective State Space Models with Dual Token and Channel Selection](https://mlsanity.com/paper/2403.19888/) (2024)
- [MambaQuant: Quantizing the Mamba Family with Variance Aligned Rotation Methods](https://mlsanity.com/paper/2501.13484/) (2025)
- [VideoMamba: Spatio-Temporal Selective State Space Model](https://mlsanity.com/paper/2407.08476/) (2024)
- [Matten: Video Generation with Mamba-Attention](https://mlsanity.com/paper/2405.03025/) (2024)
- [Mamba-FETrack: Frame-Event Tracking via State Space Model](https://mlsanity.com/paper/2404.18174/) (2024)
- [Autoregressive Pretraining with Mamba in Vision](https://mlsanity.com/paper/2406.07537/) (2024)
- [Mamba in Vision: A Comprehensive Survey of Techniques and Applications](https://mlsanity.com/paper/2410.03105/) (2024)
- [QuadMamba: Learning Quadtree-based Selective Scan for Visual State Space Model](https://mlsanity.com/paper/2410.06806/) (2024)
- [ViT3: Unlocking Test-Time Training in Vision](https://mlsanity.com/paper/2512.01643/) (2025)
- [A Comprehensive Survey of Mamba Architectures for Medical Image Analysis: Classification, Segmentation, Restoration and Beyond](https://mlsanity.com/paper/2410.02362/) (2024)
- [MambaTS: Improved Selective State Space Models for Long-term Time Series Forecasting](https://mlsanity.com/paper/2405.16440/) (2024)
- [ViG: Linear-complexity Visual Sequence Learning with Gated Linear Attention](https://mlsanity.com/paper/2405.18425/) (2024)
- [GrootVL: Tree Topology is All You Need in State Space Model](https://mlsanity.com/paper/2406.02395/) (2024)
- [M4V: Multimodal Mamba for Efficient Text-to-Video Generation](https://mlsanity.com/paper/2506.10915/) (2025)
- [MambaPEFT: Exploring Parameter-Efficient Fine-Tuning for Mamba](https://mlsanity.com/paper/2411.03855/) (2024)
- [DiMSUM: Diffusion Mamba -- A Scalable and Unified Spatial-Frequency Method for Image Generation](https://mlsanity.com/paper/2411.04168/) (2024)
- [Snakes and Ladders: Two Steps Up for VideoMamba](https://mlsanity.com/paper/2406.19006/) (2024)

## Abstract (arXiv)

In recent years, Transformers have become the de-facto architecture for sequence modeling on text and a variety of multi-dimensional data, such as images and video. However, the use of self-attention layers in a Transformer incurs prohibitive compute and memory complexity that scales quadratically w.r.t. the sequence length. A recent architecture, Mamba, based on state space models has been shown to achieve comparable performance for modeling text sequences, while scaling linearly with the sequence length. In this work, we present Mamba-ND, a generalized design extending the Mamba architecture to arbitrary multi-dimensional data. Our design alternatively unravels the input data across different dimensions following row-major orderings. We provide a systematic comparison of Mamba-ND with several other alternatives, based on prior multi-dimensional extensions such as Bi-directional LSTMs and S4ND. Empirically, we show that Mamba-ND demonstrates performance competitive with the state-of-the-art on a variety of multi-dimensional benchmarks, including ImageNet-1K classification, HMDB-51 action recognition, and ERA5 weather forecasting.