Symmetric Positive-Definite#

Symmetric Positive-Definite (SPD)

SPD / Riemannian methods operate on covariance (or connectivity) matrices as points on the SPD manifold, combining layers such as BiMap, ReEig, and LogEig. These models are available through the spd_learn library (20), a pure-PyTorch library for geometric deep learning on SPD matrices designed for neural decoding.

Installation#

pip install spd-learn

Available models#

Model	Description
`SPDNet`	Foundational architecture for deep learning on SPD manifolds; performs dimension reduction while preserving SPD structure using BiMap, ReEig, and LogEig layers (19).
`EEGSPDNet`	Specialized for brain-computer interface applications; combines covariance estimation with SPD network layers.
`TSMNet`	Tangent Space Mapping Network that integrates convolutional processing with Riemannian geometry.
`TensorCSPNet`	SPDNet variant incorporating Tensor Common Spatial Patterns for multi-band EEG feature extraction.
`PhaseSPDNet`	Leverages instantaneous phase information from analytic signals using Hilbert transforms.
`Green`	Gabor Riemann EEGNet combining Gabor wavelets with Riemannian geometry for robust EEG decoding.
`MAtt`	Matrix Attention network for SPD manifold learning.

Citation#

If you use the SPD models, please cite the spd_learn library:

@article{aristimunha2026spd,
  title={SPD Learn: A Geometric Deep Learning Python Library for Neural
         Decoding Through Trivialization},
  author={Aristimunha, Bruno and Ju, Ce and Collas, Antoine and
          Bouchard, Florent and Mian, Ammar and Thirion, Bertrand and
          Chevallier, Sylvain and Kobler, Reinmar},
  journal={arXiv preprint arXiv:2602.22895},
  year={2026}
}

LitMap#

../../_images/litmap_spd_learn.png — Figure: LitMap with symmetric positive-definite layers, last updated 26/08/2025. Each node is a paper; rightward means more recently published, upward more cited, and links show amount of citation with logaritm scale.#