# Towards Robust EEG Decoding Based on Riemannian Self-Attention

arXiv: https://arxiv.org/abs/2606.25456 · HTML: https://mlsanity.com/paper/2606.25456/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 72 references that are in the map.
- First posted on arXiv 24 Jun 2026.

## Builds on (most cited first, 22 of 22)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [EEGNet: A Compact Convolutional Network for EEG-based Brain-Computer Interfaces](https://mlsanity.com/paper/1611.08024/) (2016)
- [Large Brain Model for Learning Generic Representations with Tremendous EEG Data in BCI](https://mlsanity.com/paper/2405.18765/) (2024)
- [A Riemannian Network for SPD Matrix Learning](https://mlsanity.com/paper/1608.04233/) (2016)
- [Deep learning-based electroencephalography analysis: a systematic review](https://mlsanity.com/paper/1901.05498/) (2019)
- [Geoopt: Riemannian Optimization in PyTorch](https://mlsanity.com/paper/2005.02819/) (2020)
- [Riemannian batch normalization for SPD neural networks](https://mlsanity.com/paper/1909.02414/) (2019)
- [FBCNet: A Multi-view Convolutional Neural Network for Brain-Computer Interface](https://mlsanity.com/paper/2104.01233/) (2021)
- [A neural network based on SPD manifold learning for skeleton-based hand gesture recognition](https://mlsanity.com/paper/1904.12970/) (2019)
- [MAtt: A Manifold Attention Network for EEG Decoding](https://mlsanity.com/paper/2210.01986/) (2022)
- [On Riemannian Optimization over Positive Definite Matrices with the Bures-Wasserstein Geometry](https://mlsanity.com/paper/2106.00286/) (2021)
- [Dimensionality Reduction on SPD Manifolds: The Emergence of Geometry-Aware Methods](https://mlsanity.com/paper/1605.06182/) (2016)
- [Riemannian Local Mechanism for SPD Neural Networks](https://mlsanity.com/paper/2201.10145/) (2022)
- [A Statistical Recurrent Model on the Manifold of Symmetric Positive Definite Matrices](https://mlsanity.com/paper/1805.11204/) (2018)
- [Building Neural Networks on Matrix Manifolds: A Gyrovector Space Approach](https://mlsanity.com/paper/2305.04560/) (2023)
- [Learning with symmetric positive definite matrices via generalized Bures-Wasserstein geometry](https://mlsanity.com/paper/2110.10464/) (2021)
- [Understanding Matrix Function Normalizations in Covariance Pooling through the Lens of Riemannian Geometry](https://mlsanity.com/paper/2407.10484/) (2024)
- [Learning to Normalize on the SPD Manifold under Bures-Wasserstein Geometry](https://mlsanity.com/paper/2504.00660/) (2025)
- [Spatio-Temporal Covariance Descriptors for Action and Gesture Recognition](https://mlsanity.com/paper/1303.6021/) (2013)

## Abstract (arXiv)

Brain-Computer Interface (BCI) based on electroencephalography (EEG) enables direct interaction between the brain and external environments and has significant applications in assistive technologies, medical rehabilitation, and entertainment. Recently, EEG decoding methods based on Symmetric Positive Definite (SPD) learning have demonstrated superior performance. However, these methods typically employ basic network architectures and do not explicitly capture local relationships between EEG signals. This limitation is problematic for EEG signals due to their inherently low Signal-to-Noise Ratio (SNR). Moreover, most existing Riemannian manifold-based methods are restricted to specific metrics. The most widely used is the Affine-Invariant Metric (AIM). However, it has a quadratic dependency on the SPD matrices and cannot handle ill-conditioned SPD matrices, which hinders the effectiveness of networks. In contrast, the Bures-Wasserstein Metric (BWM) exhibits linear dependence on SPD matrices and demonstrates superior performance for ill conditioning. To overcome these challenges, we propose a Riemannian self-attention network based on the BWM. Additionally, the recently introduced power-deformed generalized Bures-Wasserstein metric reveals a nonlinear relationship between SPD matrices and matrix power deformation. This metric provides a more nuanced representation of the geometric structure of the SPD manifold. Consequently, we extend our model to a learnable version. For simplicity, we refer to it as GBWAtt. Experimental results on three EEG benchmarking datasets validate the robustness and effectiveness of our proposed method. The code is available at https://github.com/jissc/GBWAtt.