# Surface Vision Mamba: Leveraging Bidirectional State Space Model for Efficient Spherical Manifold Representation

arXiv: https://arxiv.org/abs/2501.14679 · HTML: https://mlsanity.com/paper/2501.14679/

## 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 29 of its 38 references that are in the map.
- First posted on arXiv 24 Jan 2025.

## Placed in

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

## Builds on (most cited first, 29 of 29)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Linformer: Self-Attention with Linear Complexity](https://mlsanity.com/paper/2006.04768/) (2020)
- [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)
- [HiPPO: Recurrent Memory with Optimal Polynomial Projections](https://mlsanity.com/paper/2008.07669/) (2020)
- [FlashAttention-3: Fast and Accurate Attention with Asynchrony and Low-precision](https://mlsanity.com/paper/2407.08608/) (2024)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [Vision GNN: An Image is Worth Graph of Nodes](https://mlsanity.com/paper/2206.00272/) (2022)
- [Blockwise Self-Attention for Long Document Understanding](https://mlsanity.com/paper/1911.02972/) (2019)
- [MambaOut: Do We Really Need Mamba for Vision?](https://mlsanity.com/paper/2405.07992/) (2024)
- [Demystify Mamba in Vision: A Linear Attention Perspective](https://mlsanity.com/paper/2405.16605/) (2024)
- [Agent Attention: On the Integration of Softmax and Linear Attention](https://mlsanity.com/paper/2312.08874/) (2023)
- [HyperAttention: Long-context Attention in Near-Linear Time](https://mlsanity.com/paper/2310.05869/) (2023)
- [Spherical U-Net on Cortical Surfaces: Methods and Applications](https://mlsanity.com/paper/1904.00906/) (2019)
- [Surface Vision Transformers: Attention-Based Modelling applied to Cortical Analysis](https://mlsanity.com/paper/2203.16414/) (2022)
- [Autoregressive Pretraining with Mamba in Vision](https://mlsanity.com/paper/2406.07537/) (2024)
- [Geometric Deep Learning for Post-Menstrual Age Prediction based on the Neonatal White Matter Cortical Surface](https://mlsanity.com/paper/2008.06098/) (2020)

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

- [SurfAge-Net: A Hierarchical Surface-Based Network for Interpretable Fine-Grained Brain Age Prediction](https://mlsanity.com/paper/2602.06994/) (2026)

## Abstract (arXiv)

Attention-based methods have demonstrated exceptional performance in modelling long-range dependencies on spherical cortical surfaces, surpassing traditional Geometric Deep Learning (GDL) models. However, their extensive inference time and high memory demands pose challenges for application to large datasets with limited computing resources. Inspired by the state space model in computer vision, we introduce the attention-free Vision Mamba (Vim) to spherical surfaces, presenting a domain-agnostic architecture for analyzing data on spherical manifolds. Our method achieves surface patching by representing spherical data as a sequence of triangular patches derived from a subdivided icosphere. The proposed Surface Vision Mamba (SiM) is evaluated on multiple neurodevelopmental phenotype regression tasks using cortical surface metrics from neonatal brains. Experimental results demonstrate that SiM outperforms both attention- and GDL-based methods, delivering 4.8 times faster inference and achieving 91.7% lower memory consumption compared to the Surface Vision Transformer (SiT) under the Ico-4 grid partitioning. Sensitivity analysis further underscores the potential of SiM to identify subtle cognitive developmental patterns. The code is available at https://github.com/Rongzhao-He/surface-vision-mamba.