# Deep Riemannian Networks for End-to-End EEG Decoding

arXiv: https://arxiv.org/abs/2212.10426 · HTML: https://mlsanity.com/paper/2212.10426/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 59 references that are in the map.
- First posted on arXiv 20 Dec 2022.

## Builds on (most cited first, 17 of 17)

- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [EEGNet: A Compact Convolutional Network for EEG-based Brain-Computer Interfaces](https://mlsanity.com/paper/1611.08024/) (2016)
- [Riemannian Adaptive Optimization Methods](https://mlsanity.com/paper/1810.00760/) (2018)
- [A Riemannian Network for SPD Matrix Learning](https://mlsanity.com/paper/1608.04233/) (2016)
- [Geoopt: Riemannian Optimization in PyTorch](https://mlsanity.com/paper/2005.02819/) (2020)
- [MOABB: Trustworthy algorithm benchmarking for BCIs](https://mlsanity.com/paper/1805.06427/) (2018)
- [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)
- [SPD domain-specific batch normalization to crack interpretable unsupervised domain adaptation in EEG](https://mlsanity.com/paper/2206.01323/) (2022)
- [Covariance Pooling For Facial Expression Recognition](https://mlsanity.com/paper/1805.04855/) (2018)
- [Tensor-CSPNet: A Novel Geometric Deep Learning Framework for Motor Imagery Classification](https://mlsanity.com/paper/2202.02472/) (2022)
- [Interpretable Convolutional Filters with SincNet](https://mlsanity.com/paper/1811.09725/) (2018)
- [ManifoldNorm: Extending normalizations on Riemannian Manifolds](https://mlsanity.com/paper/2003.13869/) (2020)
- [Second-order Convolutional Neural Networks](https://mlsanity.com/paper/1703.06817/) (2017)
- [Neural Architecture Search of SPD Manifold Networks](https://mlsanity.com/paper/2010.14535/) (2020)
- [ManifoldNet: A Deep Network Framework for Manifold-valued Data](https://mlsanity.com/paper/1809.06211/) (2018)

## Built on by (most cited first, 11 of 11)

- [Evaluating the structure of cognitive tasks with transfer learning](https://mlsanity.com/paper/2308.02408/) (2023)
- [SPD Matrix Learning for Neuroimaging Analysis: Perspectives, Methods, and Challenges](https://mlsanity.com/paper/2504.18882/) (2025)
- [A Strong and Simple Deep Learning Baseline for BCI MI Decoding](https://mlsanity.com/paper/2309.07159/) (2023)
- [Riemannian Geometry-Based EEG Approaches: A Literature Review](https://mlsanity.com/paper/2407.20250/) (2024)
- [SPD Learn: A Geometric Deep Learning Python Library for Neural Decoding Through Trivialization](https://mlsanity.com/paper/2602.22895/) (2026)
- [Quantity versus Diversity: Influence of Data on Detecting EEG Pathology with Advanced ML Models](https://mlsanity.com/paper/2411.17709/) (2024)
- [RepSPD: Enhancing SPD Manifold Representation in EEGs via Dynamic Graphs](https://mlsanity.com/paper/2602.22981/) (2026)
- [MPNet: A Robust and Efficient Manifold Pooling Network for Multi-Rhythm EEG Signal Decoding](https://mlsanity.com/paper/2605.05212/) (2026)
- [Escaping the Capacity Ceiling: Routing on the Stiefel Manifold for Bilinear SPD Layers](https://mlsanity.com/paper/2605.31043/) (2026)
- [Expressivity of congruence-based architectures for DNNs on positive-definite matrices](https://mlsanity.com/paper/2606.02490/) (2026)
- [Personalised federated learning for Riemannian and Euclidean EEG decoding](https://mlsanity.com/paper/2609.29037/) (2026)

## Abstract (arXiv)

State-of-the-art performance in electroencephalography (EEG) decoding tasks is currently often achieved with either Deep-Learning (DL) or Riemannian-Geometry-based decoders (RBDs). Recently, there is growing interest in Deep Riemannian Networks (DRNs) possibly combining the advantages of both previous classes of methods. However, there are still a range of topics where additional insight is needed to pave the way for a more widespread application of DRNs in EEG. These include architecture design questions such as network size and end-to-end ability. How these factors affect model performance has not been explored. Additionally, it is not clear how the data within these networks is transformed, and whether this would correlate with traditional EEG decoding. Our study aims to lay the groundwork in the area of these topics through the analysis of DRNs for EEG with a wide range of hyperparameters. Networks were tested on five public EEG datasets and compared with state-of-the-art ConvNets. Here we propose EE(G)-SPDNet, and we show that this wide, end-to-end DRN can outperform the ConvNets, and in doing so use physiologically plausible frequency regions. We also show that the end-to-end approach learns more complex filters than traditional band-pass filters targeting the classical alpha, beta, and gamma frequency bands of the EEG, and that performance can benefit from channel specific filtering approaches. Additionally, architectural analysis revealed areas for further improvement due to the possible under utilisation of Riemannian specific information throughout the network. Our study thus shows how to design and train DRNs to infer task-related information from the raw EEG without the need of handcrafted filterbanks and highlights the potential of end-to-end DRNs such as EE(G)-SPDNet for high-performance EEG decoding.