Cross-subject motor-imagery decoding remains a major challenge in EEG-based brain-computer interfaces. To mitigate strong inter-subject variability, recent work has emphasized manifold-based approaches operating on covariance representations. Yet dispersion scaling and orientation alignment remain largely unaddressed in existing methods. In this paper, we address both issues through congruence transforms and introduce three complementary geometry-aware models: (i) Discriminative Congruence Transform (DCT), (ii) Deep Linear DCT (DLDCT), and (iii) Deep DCT-UNet (DDCT-UNet). These models are evaluated both as pre-alignment modules for downstream classifiers and as end-to-end discriminative systems trained via cross-entropy backpropagation with a custom logistic-regression head. Across challenging motor-imagery benchmarks, the proposed framework improves transductive cross-subject accuracy by 2-3%, demonstrating the value of geometry-aware congruence learning.

翻译：跨被试运动想象解码仍然是基于脑电图（EEG）的脑机接口领域的一个主要挑战。为了减轻强烈的被试间变异性，近期研究强调了在协方差表示上操作的基于流形的方法。然而，现有方法在很大程度上仍未解决离散度缩放和方向对齐问题。在本文中，我们通过同余变换解决了这两个问题，并引入了三个互补的几何感知模型：(i) 判别性同余变换（DCT），(ii) 深度线性DCT（DLDCT），以及 (iii) 深度DCT-UNet（DDCT-UNet）。这些模型既作为下游分类器的预对齐模块进行评估，也作为端到端的判别性系统进行评估，后者通过带有自定义逻辑回归头的交叉熵反向传播进行训练。在具有挑战性的运动想象基准测试中，所提出的框架将转导式跨被试准确率提高了2-3%，证明了几何感知同余学习的价值。