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ManifoldFormer: Geometric Deep Learning for Neural Dynamics on Riemannian Manifolds

Yihang Fu, Lifang He, Qingyu Chen

TL;DR

ManifoldFormer addresses the mismatch between EEG foundation models and the brain's intrinsic geometric structure by learning neural manifold representations. It introduces a Riemannian VAE for manifold embeddings, a Geometric Transformer with geodesic-aware attention, and a Neural ODE-based dynamics predictor, all operating on Riemannian manifolds. Across four public EEG datasets, it achieves consistent improvements in accuracy and Cohen's Kappa and demonstrates robust cross-subject generalization, highlighting the value of geometric constraints for neural representation learning. The work suggests that respecting neural geometry can yield more interpretable patterns and better transfer in brain–computer interface systems.

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.

ManifoldFormer: Geometric Deep Learning for Neural Dynamics on Riemannian Manifolds

TL;DR

ManifoldFormer addresses the mismatch between EEG foundation models and the brain's intrinsic geometric structure by learning neural manifold representations. It introduces a Riemannian VAE for manifold embeddings, a Geometric Transformer with geodesic-aware attention, and a Neural ODE-based dynamics predictor, all operating on Riemannian manifolds. Across four public EEG datasets, it achieves consistent improvements in accuracy and Cohen's Kappa and demonstrates robust cross-subject generalization, highlighting the value of geometric constraints for neural representation learning. The work suggests that respecting neural geometry can yield more interpretable patterns and better transfer in brain–computer interface systems.

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.

Paper Structure

This paper contains 14 sections, 4 equations, 2 figures, 2 tables.

Table of Contents

  1. INTRODUCTION
  2. EEG Foundation Models and Architectural Innovations
  3. Self-Supervised and Representation Learning Approaches
  4. METHODOLOGY
  5. Riemannian Variational Autoencoder
  6. Riemannian Variational Autoencoder
  7. Geometric Transformer
  8. Dynamics Predictor
  9. Multi-Scale Geometric Learning
  10. Experiments
  11. Experimental Setup
  12. Results and Ablation Study
  13. Qualitative Results
  14. CONCLUSION

Figures (2)

  • Figure 1: ManifoldFormer architecture overview showing the three-stage pipeline from EEG input to manifold learning and dynamics prediction.
  • Figure 2: EEG signal processing comparison during a motor imagery task from the SEED dataset. (a) Raw EEG signals with artifacts and noise. (b) ManifoldFormer-processed signals showing enhanced motor patterns (highlighted regions) in the sensorimotor channels C3 and C4, while preserving overall neural structure.