Geo-Mamba: Dual-Path Riemannian State-Space Models for Functional Dynamics

Yuwei Cao, Tingting Dan, Yang Yang, Guorong Wu

Keywords: Brain functional connectivity, Riemannian geometry, State space model, Geometric deep learning

Abstract: Functional magnetic resonance imaging (fMRI)–derived functional connectivity (FC) is represented as graphs and as correlation/covariance matrices that live on non-Euclidean spaces—cortical graphs and the Riemannian manifold of symmetric positive-definite (SPD) matrices—so conventional Euclidean sequence models are misspecified. To this end, we introduce *Geo-Mamba*, a geometric variant of Mamba formulated on Riemannian manifolds. *Geo-Mamba* employs a dual-path selective state-space design: *a stacked path* performs hierarchical spatial modeling by aggregating pyramid multi-scale features to capture local and global dependencies, while *a embedding path* combats redundancy in high-dimensional SPD inputs via progressive, geometry-aware dimensionality reduction (operating in the appropriate manifold spaces) to produce compact states without violating Riemannian constraints. Their complementary outputs are fused through the tailored *GeoMix* operator to yield a compact, discriminative SPD representation. *Geo-Mamba* is evaluated on six public fMRI datasets—ADNI, OASIS, PPMI, Taowu, Neurocon, and Mātai—spanning Alzheimer’s and Parkinson’s cohorts as well as multi-site normative populations with diverse acquisition protocols. Across these benchmarks, it delivers consistently competitive accuracy and robustness, supporting the value of dual-path manifold modeling for neuroimaging and its potential for clinical translation.

Primary Area: applications to neuroscience & cognitive science

Submission Number: 11691