RepSPD: Enhancing SPD Manifold Representation in EEGs via Dynamic Graphs

Electroencephalography (EEG) provides a non-invasive measure of ongoing neural activity, but building general-purpose EEG models remains challenging due to the heterogeneity of subjects, devices, and electrode montages. Existing EEG foundation models predominantly rely on reconstruction-based objectives defined on the observed signal, which contains both neural and non-neural components. We introduce SPERA (Spherical Prior EEG Representation Architecture), an EEG foundation model that adopts the joint-embedding predictive architecture (JEPA) to predict in latent space. SPERA introduces a Legendre-polynomial spatial prior, incorporated into attention to encode varying scalp electrode geometries. Two further components adapt the model to EEG: factorized temporal and spatial attention interleaved with periodic full-attention blocks, and a relational spectral regularizer aligning latent similarity structure with spectral views. Pretrained on approximately 80,000 hours of EEG from 29,048 subjects across 106 datasets, SPERA achieves the highest average balanced accuracy across nine downstream tasks spanning clinical, cognitive, and BCI applications. SPERA further exhibits strong parameter efficiency under linear probing and robustness across varying recording conditions, suggesting its potential as a general-purpose backbone for diverse EEG analyses.

Implementations of symmetric positive definite (SPD) matrix-based neural networks for neural decoding remain fragmented across research codebases and Python packages. Existing implementations often employ ad hoc handling of manifold constraints and non-unified training setups, which hinders reproducibility and integration into modern deep-learning workflows. To address this gap, we introduce SPD Learn, a unified and modular Python package for geometric deep learning with SPD matrices. SPD Learn provides core SPD operators and neural-network layers, including numerically stable spectral operators, and enforces Stiefel/SPD constraints via trivialization-based parameterizations. This design enables standard backpropagation and optimization in unconstrained Euclidean spaces while producing manifold-constrained parameters by construction. The package also offers reference implementations of representative SPDNet-based models and interfaces with widely used brain computer interface/neuroimaging toolkits and modern machine-learning libraries (e.g., MOABB, Braindecode, Nilearn, and SKADA), facilitating reproducible benchmarking and practical deployment.

Electroencephalography (EEG) based brain-computer interfaces enable direct brain-to-device communication for applications such as rehabilitation and communication. However, their practical utility is often limited as the non-stationary nature of the EEG data introduces distribution shifts across domains (e.g., sessions and subjects). Adapting machine learning models to be invariant to these shifts in an unsupervised way, without using costly labeled calibration data, would drastically improve the utility of EEG data. In this work, we use a classic generative model of EEG to study distribution shifts introduced by the domain-specific forward process, which is associated with factors such as head geometry. We theoretically show that such distribution shifts can be recovered solely through linear transformations on the Symmetric Positive Definite manifold. Building on this insight, we propose SPDAlign, an interpretable framework for promoting domain-invariant EEG learning. SPDAlign first aligns the domain-specific means and corrects global rotations across domains using a recent optimal transport technique called Wasserstein Procrustes. We systematically study the proposed approach through simulations and demonstrate its competitive performance on extensive public EEG datasets. Additionally, SPDAlign is a globally linear framework and is intrinsically interpretable, so that the framework can identify frequency ranges of interest, determine the spatial patterns reflecting source-sensor relationships, and address cross-subject variability.