SPD Learn统一了基于对称正定矩阵的神经解码工具，让模型训练更稳定可复现。
SPD Learn: A Geometric Deep Learning Python Library for Neural Decoding Through Trivialization
- 用平凡化参数化方法统一处理流形约束，实现标准反向传播。
- 提供数值稳定的谱算子和主流神经解码模型参考实现。
- 兼容脑机接口与神经影像工具包，适合科研与实际部署使用。
基于对称正定（SPD）矩阵的神经网络在神经解码中的实现分散于多个代码库和Python包中，现有方法常采用非系统性处理流形约束，且训练设置不统一，影响复现性与现代深度学习流程的集成。为此，我们提出SPD Learn，一个面向SPD矩阵的统一模块化几何深度学习Python库。该库提供核心SPD算子与神经网络层，包括数值稳定的谱算子，并通过基于平凡化的参数化方式强制施加Stiefel/SPD约束。此设计使优化可在无约束的欧几里得空间中进行，而输出参数自然满足流形约束。此外，库内包含代表性SPDNet模型的参考实现，并与主流脑机接口/神经影像工具包（如MOABB、Braindecode、Nilearn、SKADA）集成，支持可复现的基准测试与实际部署。
原文摘要 · Abstract (English)
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.
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