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，结合上述两类方法优势的深度黎曼网络引起了学界广泛兴趣。然而，在推动深度黎曼网络更广泛地应用于脑电解码时，仍有一系列课题需要深入探究。这些课题包括网络规模、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充分探索。此外，网络内部的数据变换机制及其与传统脑电解码的相关性仍不明确。本研究旨在通过分析不同超参数配置下的脑电解码深度黎曼网络，为这些课题奠定研究基础。我们在两个公开脑电数据集上测试网络，并与当前最先进的卷积网络进行对比。我们提出的端到端脑电SPDNet能够优于卷积网络，并在解码过程中利用生理上合理的频率区域。研究还表明，与针对经典脑电alpha、beta和gamma频带的传统带通滤波器相比，端到端方法可学习更复杂的滤波器，且通道特定滤波方法能提升解码性能。此外，架构分析揭示了由于网络中黎曼特定信息可能丢失而存在的改进空间。本研究阐明了如何设计与训练深度黎曼网络，从原始脑电信号中直接推断任务相关信息，无需手工构建滤波器组，并凸显了EE(G)-SPDNet等端到端深度黎曼网络在高性能脑电解码中的应用潜力。