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：在脑电图解码任务中，当前最优性能通常由深度学习（DL）解码器或黎曼几何解码器（RBD）实现。近年来，能够融合两类方法优势的深度黎曼网络（DRNs）引起了广泛关注。然而，仍存在一系列关键问题需要深入探究，以推动DRNs在脑电图领域的更广泛应用，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系统研究。此外，网络内部的数据变换机制及其与传统脑电解码的关联性仍不明确。本研究通过分析不同超参数配置下的脑电DRNs，旨在为上述问题奠定研究基础。我们在两个公开脑电数据集上测试了网络性能，并与最先进的卷积神经网络（ConvNets）进行了对比。我们提出了端到端脑电SPDNet（EE(G)-SPDNet），证明这种宽型端到端DRNs能够超越ConvNets，并在此过程中利用具有生理学意义的频段区域。研究还表明，端到端方法能学习比传统带通滤波器（针对经典α、β、γ脑电频段）更复杂的滤波器，且通道特异性滤波方法可提升性能。此外，架构分析揭示了由于网络中黎曼特异性信息可能丢失而存在的改进空间。本研究展示了如何设计并训练DRNs从原始脑电信号中推断任务相关信息，无需人工构建滤波器组，同时凸显了EE(G)-SPDNet等端到端DRNs在高性能脑电解码中的潜力。