State-of-the-art performance in electroencephalography (EEG) decoding tasks is currently often achieved with either Deep-Learning (DL) or Riemannian-Geometry-based decoders (RBDs). 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.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，脑电图（EEG）解码任务的最先进性能通常由深度学习（DL）或基于黎曼几何的解码器（RBDs）实现。近期，结合两类方法优势的深度黎曼网络（DRNs）引起了广泛关注。然而，在推动DRNs更广泛地应用于EEG领域之前，仍有一系列需要深入理解的主题，包括网络规模与端到端能力等架构设计问题。这些因素如何影响模型性能尚未被探究。此外，网络内部的数据变换方式及其与传统脑电解码的关联性仍不明确。本研究旨在通过分析具有广泛超参数的EEG DRNs，为上述领域奠定基础。我们在两个公开EEG数据集上测试了网络，并与最先进的卷积神经网络（ConvNets）进行了比较。我们提出了端到端EEG SPDNet（EE(G)-SPDNet），证明这种宽而深的端到端DRN能够超越ConvNets，并在过程中使用了生理上合理的频率区域。我们还发现，端到端方法能学习到比传统针对EEG经典α、β和γ频带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和训练DRNs以从原始EEG中推断任务相关信息，无需手动设计滤波器组，并凸显了如EE(G)-SPDNet等端到端DRN在高性能脑电解码中的潜力。