SPD Learn: A Geometric Deep Learning Python Library for Neural Decoding Through Trivialization

TL;DR

SPD Learn is a comprehensive Python library that simplifies the implementation of SPD matrix-based neural networks for neural decoding, ensuring reproducibility and seamless integration with existing deep learning tools.

Contribution

It introduces a unified, modular package with stable spectral operators and trivialization-based parameterizations, addressing fragmentation and reproducibility issues in SPD neural networks.

Findings

Provides core SPD operators and neural network layers.

Enables standard backpropagation with manifold constraints.

Facilitates reproducible benchmarking and deployment.

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 used brain computer interface/neuroimaging toolkits and modern machine-learning libraries (e.g., MOABB, Braindecode, Nilearn, and SKADA), facilitating reproducible benchmarking and practical deployment.