Cross-domain EEG decoding remains challenging despite advances in Riemannian deep learning: covariance matrices from different subjects occupy systematically distinct regions of the SPD manifold, yet existing domain adaptation methods either require target-domain calibration data or learn subject-specific components that cannot generalise across domains. We propose dynamic Stiefel routing: a pool of K expert projection filters on the Stiefel manifold, each specialised for a different region of the SPD manifold, with each input covariance routed to the most appropriate filter via cross-attention, adapting the subspace projection per sample. A central finding is that this approach, implemented naively, provably collapses to ensemble averaging: when routing weights are uniform, the adaptive filter reduces exactly to an equal-contribution combination of experts, indistinguishable from a single fixed filter. Three structural properties break this degeneracy: a symmetric anchor Wbase∈St(n,k) that removes proximity bias among experts; a frozen domain-discriminative query encoder that decouples routing from task optimisation; and a decoupled key alignment loss that trains expert keys toward stable domain attractors. Together they produce the first genuinely committed and domain-structured routing on SPD manifolds, with consistent gains across three datasets: balanced accuracy improves from 0.773→0.823, 0.757→0.809, and 0.801→0.839, with the alignment strategy determined automatically by a single data-driven rule and no dataset-specific hyperparameter search.
Deep learning for cross-subject EEG decoding is hindered by high inter-subject variability, which introduces a severe domain shift between training and unseen test subjects. This survey presents a comprehensive review of deep learning methodologies specifically engineered to address this cross-subject generalization challenge. To ground this analysis, we formalize the cross-subject setting as a multi-source domain problem and delineate the rigorous, subject-independent evaluation protocols required for valid assessment. Central to this survey is a systematic taxonomy of the current literature into discrete methodological families, including feature alignment, adversarial learning, feature disentanglement, and contrastive learning. We conclude by examining three critical elements for advancing robust, real-world decoding: the theoretical limitations of current methodologies, the structural value of subject identity, and the emergence of EEG foundation models.
Cross-subject motor imagery decoding remains a fundamental challenge in EEG-based brain-computer interfaces due to substantial inter-subject variability. Recent approaches have leveraged Riemannian geometry by representing EEG signals as covariance matrices on the symmetric positive definite (SPD) manifold. However, existing methods primarily focus on manifold-based representations while largely overlooking subject-specific variations in covariance dispersion and orientation. In this work, we address these challenges through geometry-aware congruence transformations and propose three complementary models: (i) Discriminative Congruence Transform (DCT), (ii) Deep Linear DCT (DLDCT), and (iii) Deep DCT-UNet (DDCT-UNet). The proposed models are evaluated both as manifold alignment modules for downstream classifiers and as end-to-end discriminative architectures optimized via cross-entropy with a custom logistic regression head. Experiments on challenging cross-subject motor imagery benchmarks demonstrate consistent improvements in transductive decoding performance, achieving 2-3% higher accuracy than strong baselines. These results highlight the effectiveness of geometry-aware congruence learning for mitigating inter-subject variability in EEG decoding.
Electroencephalography (EEG) provides non-invasive monitoring of brain activity and is widely used in emotion recognition, motor imagery and sleep staging. Although within-subject decoding has achieved considerable progress, cross-subject generalization remains a central challenge in practical applications. EEG decoders are typically trained with Adam/AdamW under a fixed second-moment decay coefficient, even though cross-subject learning involves low signal-to-noise ratios, subject variability, and gradient nonstationarity. A fixed coefficient implicitly assumes that gradient statistics are homogeneous across layers and time, which can limit model's adaptability to cross-subject EEG signals and degrade generalization. To address these issues, we propose AFOR, a tensor-wise adaptive optimizer that converts the fixed second-moment decay coefficient into a dynamic coefficient estimated online from local gradient state. AFOR combines a Residual-Alignment Signal Scorer (RASS) and an Adaptive Forgetting Controller (AFC). RASS summarizes local gradient residuals and directional agreement into a signal-quality score, and AFC maps this score through self-referential normalization to a bounded per-step decay coefficient, with cumulative-product initialization correction maintaining consistency under time-varying decay. Under a strict cross-subject protocol on three EEG benchmarks that cover three representative fields, AFOR achieves the best average performance among the compared optimizers, improving the mean test accuracy over Adam by 3.00%, 2.07%, and 4.38%, respectively.