State-of-the-art performance in electroencephalography (EEG) decoding tasks is currently often achieved with either Deep-Learning or Riemannian-Geometry-based decoders. Recently, there is growing interest in Deep Riemannian Networks (DRNs) possibly combining the advantages of both previous classes of methods. However, there are still a range of topics where additional insight is needed to pave the way for a more widespread application of DRNs in EEG. These include architecture design questions such as network size and end-to-end ability as well as model training questions. How these factors affect model performance has not been explored. Additionally, it is not clear how the data within these networks is transformed, and whether this would correlate with traditional EEG decoding. Our study aims to lay the groundwork in the area of these topics through the analysis of DRNs for EEG with a wide range of hyperparameters. Networks were tested on two public EEG datasets and compared with state-of-the-art ConvNets. Here we propose end-to-end EEG SPDNet (EE(G)-SPDNet), and we show that this wide, end-to-end DRN can outperform the ConvNets, and in doing so use physiologically plausible frequency regions. We also show that the end-to-end approach learns more complex filters than traditional band-pass filters targeting the classical alpha, beta, and gamma frequency bands of the EEG, and that performance can benefit from channel specific filtering approaches. Additionally, architectural analysis revealed areas for further improvement due to the possible loss of Riemannian specific information throughout the network. Our study thus shows how to design and train DRNs to infer task-related information from the raw EEG without the need of handcrafted filterbanks and highlights the potential of end-to-end DRNs such as EE(G)-SPDNet for high-performance EEG decoding.

翻译：当前，在脑电图解码任务中，最先进的性能通常由基于深度学习或黎曼几何的解码器实现。近年来，人们日益关注深度黎曼网络，该方法有望结合前述两类方法的优势。然而，在推动深度黎曼网络更广泛应用于脑电图领域的过程中，仍有一系列课题需要深入理解，包括网络规模与端到端能力等架构设计问题，以及模型训练问题。这些因素如何影响模型性能尚未得到探索。此外，网络内部数据的变换方式及其与经典脑电解码的关联性仍不明确。本研究旨在通过分析具有超参数范围的深度黎曼网络，为上述课题奠定基础。我们在两个公开脑电数据集上测试了网络，并将其与最先进的卷积网络进行比较。我们提出端到端脑电对称正定网络（EE(G)-SPDNet），并证明这种宽深的端到端深度黎曼网络能优于卷积网络，且其性能提升利用了生理学上合理的频段。我们还发现，端到端方法学习了比传统针对脑电α、β、γ经典频段的带通滤波器更复杂的滤波器，且通道特定滤波方法可提升性能。此外，架构分析揭示了因网络中黎曼特定信息可能丢失而需进一步改进的领域。因此，本研究展示了如何设计并训练深度黎曼网络，无需手工构建滤波器组即可从原始脑电中推断任务相关信息，并凸显了以EE(G)-SPDNet为代表的端到端深度黎曼网络在高性能脑电解码中的潜力。