ManifoldFormer: Geometric Deep Learning for Neural Dynamics on Riemannian Manifolds

• URL: http://arxiv.org/abs/2511.16828v1
• Date: Thu, 20 Nov 2025 22:19:53 GMT
• Title: ManifoldFormer: Geometric Deep Learning for Neural Dynamics on Riemannian Manifolds
• Authors: Yihang Fu, Lifang He, Qingyu Chen,
• Abstract summary: Existing EEG foundation models mainly treat neural signals as generic time series in Euclidean space.<n>MandelaFormer addresses this limitation through a novel geometric deep learning framework that explicitly learns neural manifold representations.
• Score: 11.275535457399625
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Existing EEG foundation models mainly 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: a Riemannian VAE for manifold embedding that preserves geometric structure, a geometric Transformer with geodesic-aware attention mechanisms operating directly on neural manifolds, and a dynamics predictor leveraging neural ODEs for manifold-constrained temporal evolution. Extensive evaluation across four public datasets demonstrates substantial improvements over state-of-the-art methods, with 4.6-4.8% higher accuracy and 6.2-10.2% higher Cohen's Kappa, while maintaining robust cross-subject generalization. The geometric approach reveals meaningful neural patterns consistent with neurophysiological principles, establishing geometric constraints as essential for effective EEG foundation models.

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