MFMSRNet: An Interpretable Multi-frequency and Multi-scale Riemannian Network for Motor Imagery Decoding

Abstract

Motor imagery (MI) electroencephalography (EEG) decoding has benefited from deep learning, yet methods operate in Euclidean space and behave as opaque black boxes, neglecting the intrinsic geometry of functional brain connectivity. EEG connectivity descriptors, such as phase synchrony and covariance matrices, naturally reside on the manifold of symmetric positive definite (SPD) matrices, where Euclidean operations are geometrically inconsistent and hinder interpretability. This work proposes the Multi-frequency and Multi-scale Riemannian Network (MFMSRNet), an interpretable end-to-end geometry-aware framework for MI EEG decoding on the SPD manifold. The method constructs kernelized phase-locking value (KPLV) functional connectivity (FC) matrices to capture nonlinear phase synchrony while ensuring positive definiteness. An attention-based Riemannian fusion mechanism adaptively integrates information across multiple frequency bands in the tangent space. Furthermore, a multi-scale Riemannian network extracts global, hemispheric, and local connectivity patterns via manifold-preserving bilinear mappings and smooth eigenvalue rectification. Extensive experiments indicate that MFMSRNet yields more expressive and interpretable representations for robust MI decoding, offering a promising solution for reliable brain–computer interface applications. The code is available at https://github.com/Raeno-Rao/MFMSRNet.