ManifoldFormer: Geometric Deep Learning for Neural Dynamics on Riemannian Manifolds

Current EEG foundation models treat neural signals as generic time series in Euclidean space, ignoring the intrinsic geometric structure of neural dynamics that constrains brain activity to low-dimensional manifolds. This fundamental mismatch between model assumptions and neural geometry limits representation quality and cross-subject generalization. ManifoldFormer addresses this limitation through a novel geometric deep learning framework that explicitly learns neural manifold representations. The architecture integrates three key innovations: RiemannianVAE for manifold embedding that preserves geometric structure, GeometricTransformer with geodesic-aware attention mechanisms that operate directly on neural manifolds, and DynamicsPredictor using Neural ODEs for manifold-constrained temporal evolution. Extensive evaluation across four public datasets demonstrates substantial improvements over state-of-the-art methods, achieving 4.6-4.8% accuracy gains and 6.2-10.2% Cohen’s Kappa improvements while maintaining robust cross-subject generalization. The geometric approach reveals meaningful neural patterns aligned with neurophysiological principles, establishing geometric constraints as essential for effective EEG foundation models.