SPD Learn: A Geometric Deep Learning Python Library for Neural Decoding Through Trivialization
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arXiv
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| Auteurs principaux: | , , , , , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911470543962112 |
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| author | Aristimunha, Bruno Ju, Ce Collas, Antoine Bouchard, Florent Mian, Ammar Thirion, Bertrand Chevallier, Sylvain Kobler, Reinmar |
| author_facet | Aristimunha, Bruno Ju, Ce Collas, Antoine Bouchard, Florent Mian, Ammar Thirion, Bertrand Chevallier, Sylvain Kobler, Reinmar |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_22895 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | SPD Learn: A Geometric Deep Learning Python Library for Neural Decoding Through Trivialization Aristimunha, Bruno Ju, Ce Collas, Antoine Bouchard, Florent Mian, Ammar Thirion, Bertrand Chevallier, Sylvain Kobler, Reinmar Neurons and Cognition Machine Learning 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. |
| title | SPD Learn: A Geometric Deep Learning Python Library for Neural Decoding Through Trivialization |
| topic | Neurons and Cognition Machine Learning |
| url | https://arxiv.org/abs/2602.22895 |