# SPD domain-specific batch normalization to crack interpretable unsupervised domain adaptation in EEG

arXiv: https://arxiv.org/abs/2206.01323 · HTML: https://mlsanity.com/paper/2206.01323/

## Key facts

- Cited by 53 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 108 references that are in the map.
- First posted on arXiv 2 Jun 2022.

## Builds on (most cited first, 29 of 29)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [EEGNet: A Compact Convolutional Network for EEG-based Brain-Computer Interfaces](https://mlsanity.com/paper/1611.08024/) (2016)
- [How Does Batch Normalization Help Optimization?](https://mlsanity.com/paper/1805.11604/) (2018)
- [Domain-Specific Batch Normalization for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1906.03950/) (2019)
- [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)
- [Batch Renormalization: Towards Reducing Minibatch Dependence in Batch-Normalized Models](https://mlsanity.com/paper/1702.03275/) (2017)
- [Geoopt: Riemannian Optimization in PyTorch](https://mlsanity.com/paper/2005.02819/) (2020)
- [Uncovering the structure of clinical EEG signals with self-supervised learning](https://mlsanity.com/paper/2007.16104/) (2020)
- [Pymanopt: A Python Toolbox for Optimization on Manifolds using Automatic Differentiation](https://mlsanity.com/paper/1603.03236/) (2016)
- [MOABB: Trustworthy algorithm benchmarking for BCIs](https://mlsanity.com/paper/1805.06427/) (2018)
- [Transfer Learning for Brain-Computer Interfaces: A Euclidean Space Data Alignment Approach](https://mlsanity.com/paper/1808.05464/) (2018)
- [Riemannian batch normalization for SPD neural networks](https://mlsanity.com/paper/1909.02414/) (2019)
- [Transfer Learning for EEG-Based Brain-Computer Interfaces: A Review of Progress Made Since 2016](https://mlsanity.com/paper/2004.06286/) (2020)
- [FBCNet: A Multi-view Convolutional Neural Network for Brain-Computer Interface](https://mlsanity.com/paper/2104.01233/) (2021)
- [Algorithms and Theory for Multiple-Source Adaptation](https://mlsanity.com/paper/1805.08727/) (2018)
- [Multi-source Domain Adaptation in the Deep Learning Era: A Systematic Survey](https://mlsanity.com/paper/2002.12169/) (2020)
- [Transfer Learning in Brain-Computer Interfaces](https://mlsanity.com/paper/1512.00296/) (2015)
- [Covariance Pooling For Facial Expression Recognition](https://mlsanity.com/paper/1805.04855/) (2018)
- [Machine-Learning-Based Diagnostics of EEG Pathology](https://mlsanity.com/paper/2002.05115/) (2020)
- [2021 BEETL Competition: Advancing Transfer Learning for Subject Independence & Heterogenous EEG Data Sets](https://mlsanity.com/paper/2202.12950/) (2022)
- [Tensor-CSPNet: A Novel Geometric Deep Learning Framework for Motor Imagery Classification](https://mlsanity.com/paper/2202.02472/) (2022)
- [Parallel Transport on the Cone Manifold of SPD Matrices for Domain Adaptation](https://mlsanity.com/paper/1807.10479/) (2018)
- [Manifold-regression to predict from MEG/EEG brain signals without source modeling](https://mlsanity.com/paper/1906.02687/) (2019)
- [On the interpretation of linear Riemannian tangent space model parameters in M/EEG](https://mlsanity.com/paper/2107.14398/) (2021)
- [Team Cogitat at NeurIPS 2021: Benchmarks for EEG Transfer Learning Competition](https://mlsanity.com/paper/2202.03267/) (2022)

## Built on by (most cited first, 30 of 53)

- [Decoding Natural Images from EEG for Object Recognition](https://mlsanity.com/paper/2308.13234/) (2023)
- [Visual Neural Decoding via Improved Visual-EEG Semantic Consistency](https://mlsanity.com/paper/2408.06788/) (2024)
- [emg2qwerty: A Large Dataset with Baselines for Touch Typing using Surface Electromyography](https://mlsanity.com/paper/2410.20081/) (2024)
- [Graph Neural Networks on SPD Manifolds for Motor Imagery Classification: A Perspective from the Time-Frequency Analysis](https://mlsanity.com/paper/2211.02641/) (2022)
- [Adaptive Log-Euclidean Metrics for SPD Matrix Learning](https://mlsanity.com/paper/2303.15477/) (2023)
- [Matrix Manifold Neural Networks++](https://mlsanity.com/paper/2405.19206/) (2024)
- [Riemannian Flow Matching for Brain Connectivity Matrices via Pullback Geometry](https://mlsanity.com/paper/2505.18193/) (2025)
- [SPDIM: Source-Free Unsupervised Conditional and Label Shift Adaptation in EEG](https://mlsanity.com/paper/2411.07249/) (2024)
- [Deep Riemannian Networks for End-to-End EEG Decoding](https://mlsanity.com/paper/2212.10426/) (2022)
- [Riemannian Multinomial Logistics Regression for SPD Neural Networks](https://mlsanity.com/paper/2305.11288/) (2023)
- [Geodesic Optimization for Predictive Shift Adaptation on EEG data](https://mlsanity.com/paper/2407.03878/) (2024)
- [A Lie Group Approach to Riemannian Batch Normalization](https://mlsanity.com/paper/2403.11261/) (2024)
- [RMLR: Extending Multinomial Logistic Regression into General Geometries](https://mlsanity.com/paper/2409.19433/) (2024)
- [Learning to Normalize on the SPD Manifold under Bures-Wasserstein Geometry](https://mlsanity.com/paper/2504.00660/) (2025)
- [Multi-Source and Test-Time Domain Adaptation on Multivariate Signals using Spatio-Temporal Monge Alignment](https://mlsanity.com/paper/2407.14303/) (2024)
- [SPD Matrix Learning for Neuroimaging Analysis: Perspectives, Methods, and Challenges](https://mlsanity.com/paper/2504.18882/) (2025)
- [Neural Networks on Symmetric Spaces of Noncompact Type](https://mlsanity.com/paper/2601.01097/) (2026)
- [Motor Imagery Decoding Using Ensemble Curriculum Learning and Collaborative Training](https://mlsanity.com/paper/2211.11460/) (2022)
- [A Strong and Simple Deep Learning Baseline for BCI MI Decoding](https://mlsanity.com/paper/2309.07159/) (2023)
- [Geometric Neural Network based on Phase Space for BCI-EEG decoding](https://mlsanity.com/paper/2403.05645/) (2024)
- [Transfer Learning between Motor Imagery Datasets using Deep Learning -- Validation of Framework and Comparison of Datasets](https://mlsanity.com/paper/2311.16109/) (2023)
- [Fast and Stable Riemannian Metrics on SPD Manifolds via Cholesky Product Geometry](https://mlsanity.com/paper/2407.02607/) (2024)
- [Review of Deep Representation Learning Techniques for Brain-Computer Interfaces and Recommendations](https://mlsanity.com/paper/2405.19345/) (2024)
- [Classification of Buried Objects from Ground Penetrating Radar Images by using Second Order Deep Learning Models](https://mlsanity.com/paper/2410.07117/) (2024)
- [Spatial-Functional awareness Transformer-based graph archetype contrastive learning for Decoding Visual Neural Representations from EEG](https://mlsanity.com/paper/2509.24761/) (2025)
- [Sheaf Neural Networks on SPD Manifolds: Second-Order Geometric Representation Learning](https://mlsanity.com/paper/2604.20308/) (2026)
- [Cross-Subject Generalization for EEG Decoding: A Survey of Deep Learning Methods](https://mlsanity.com/paper/2604.27033/) (2026)
- [Weakly supervised covariance matrices alignment through Stiefel matrices estimation for MEG applications](https://mlsanity.com/paper/2402.03345/) (2024)
- [EEG-MACS: Manifold Attention and Confidence Stratification for EEG-based Cross-Center Brain Disease Diagnosis under Unreliable Annotations](https://mlsanity.com/paper/2405.00734/) (2024)
- [PSDNorm: Test-Time Temporal Normalization for Deep Learning in Sleep Staging](https://mlsanity.com/paper/2503.04582/) (2025)

## Abstract (arXiv)

Electroencephalography (EEG) provides access to neuronal dynamics non-invasively with millisecond resolution, rendering it a viable method in neuroscience and healthcare. However, its utility is limited as current EEG technology does not generalize well across domains (i.e., sessions and subjects) without expensive supervised re-calibration. Contemporary methods cast this transfer learning (TL) problem as a multi-source/-target unsupervised domain adaptation (UDA) problem and address it with deep learning or shallow, Riemannian geometry aware alignment methods. Both directions have, so far, failed to consistently close the performance gap to state-of-the-art domain-specific methods based on tangent space mapping (TSM) on the symmetric positive definite (SPD) manifold. Here, we propose a theory-based machine learning framework that enables, for the first time, learning domain-invariant TSM models in an end-to-end fashion. To achieve this, we propose a new building block for geometric deep learning, which we denote SPD domain-specific momentum batch normalization (SPDDSMBN). A SPDDSMBN layer can transform domain-specific SPD inputs into domain-invariant SPD outputs, and can be readily applied to multi-source/-target and online UDA scenarios. In extensive experiments with 6 diverse EEG brain-computer interface (BCI) datasets, we obtain state-of-the-art performance in inter-session and -subject TL with a simple, intrinsically interpretable network architecture, which we denote TSMNet.