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 five public EEG datasets and compared with state-of-the-art ConvNets. Here we propose 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 under utilisation 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：目前，脑电图（EEG）解码任务中的最先进性能通常通过深度学习（DL）或基于黎曼几何的解码器（RBDs）实现。近年来，深度黎曼网络（DRNs）日益受到关注，其可能结合了前述两类方法的优势。然而，在多个主题上仍需进一步深入理解，以推动DRNs在EEG中的更广泛应用。这些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得到探索。此外，尚不清楚这些网络内部的数据如何转换，以及这种转换是否与传统EEG解码方法相关联。本研究旨在通过分析具有广泛超参数范围的EEG专用DRNs，为这些主题领域奠定基础。我们在五个公开EEG数据集上测试了网络性能，并与最先进的卷积网络进行了比较。本文提出了EE(G)-SPDNet，并证明这种宽结构、端到端的DRN能够超越卷积网络，且在此过程中使用了生理学上合理的频段。我们还发现，端到端方法能够学习比传统针对EEG经典α、β和γ频段的带通滤波器更复杂的滤波器，且性能可能受益于通道特异性滤波方法。此外，架构分析揭示了由于网络中黎曼特异性信息可能未被充分利用而存在的进一步改进空间。因此，本研究展示了如何设计和训练DRNs以从原始EEG信号中推断任务相关信息，而无需人工设计滤波器组，并凸显了如EE(G)-SPDNet这类端到端DRNs在高性能EEG解码中的潜力。