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[2602.22895] SPD Learn: A Geometric Deep Learning Python Library for Neural Decoding Through Trivialization
Summary
SPD Learn is a new Python library designed for geometric deep learning, specifically for neural decoding using symmetric positive definite matrices, enhancing reproducibility and integration in machine learning workflows.
Why It Matters
This library addresses the fragmentation in existing implementations of SPD matrix-based neural networks, offering a unified solution that promotes reproducibility and ease of use in deep learning applications, particularly in neuroscience and neuroimaging.
Key Takeaways
- Introduces SPD Learn, a modular library for geometric deep learning.
- Facilitates neural decoding through trivialization of SPD matrices.
- Enforces manifold constraints while allowing standard optimization techniques.
- Integrates with popular neuroimaging and machine learning toolkits.
- Promotes reproducibility in benchmarking and practical deployment.
Quantitative Biology > Neurons and Cognition arXiv:2602.22895 (q-bio) [Submitted on 26 Feb 2026] Title:SPD Learn: A Geometric Deep Learning Python Library for Neural Decoding Through Trivialization Authors:Bruno Aristimunha, Ce Ju, Antoine Collas, Florent Bouchard, Ammar Mian, Bertrand Thirion, Sylvain Chevallier, Reinmar Kobler View a PDF of the paper titled SPD Learn: A Geometric Deep Learning Python Library for Neural Decoding Through Trivialization, by Bruno Aristimunha and 7 other authors View PDF HTML (experimental) Abstract: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...
