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

TL;DR

The paper addresses efficient modeling of cortical surface data, where attention-based approaches are too costly for large datasets. It introduces Surface Vision Mamba (SiM), an attention-free bidirectional state-space backbone that operates on genus-zero surfaces using icosphere-based surface patching. On neonatal brain phenotype tasks, SiM outperforms attention- and Geometric Deep Learning baselines while delivering substantial speedups and memory savings, and it provides interpretable insights into cortical regions driving age predictions. The work offers a scalable, interpretable tool for large-scale non-Euclidean brain data analysis, and code is publicly available.

Abstract

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.

Figures (5)

• Figure 1: Representative icosahedron discretized spherical surfaces with sequential subdivisions. The number of faces of each spherical surface is denoted under the surface.
• Figure 2: Overview of the proposed Surface Vision Mamba (SiM) architecture. The cortical data from the left and right hemispheres are initially mapped onto a 40-week spherical template with 32,492 vertices per hemisphere. The template is then resampled to a sixth-order icosphere containing 40,962 vertice, partitioned into triangular patches (taking Ico-2 shown as an example in the Figure \ref{['fig1']}) that fully cover the sphere. Surface patches from both hemispheres are concatenated, flattened, and linearly embedded. A learnable class token is inserted between the tokens from the left and right hemispheres, followed by the addition of positional embeddings. The processed data is then fed into the Bi-directional Mamba block.
• Figure 3: Comparison of PMA prediction performance and efficiency between SiT and our SiM.
• Figure 4: Spatial distribution of informative vertices for PMA prediction.
• Figure 5: The significant difference between predicted and chronological brain age in preterm infants.