Representation and Geometric Collapse in Spatiotemporal EEG Classifiers: A Mathematical Diagnostic Framework

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Abstract
Spatiotemporal deep learning models, like Graph Neural Networks (GNNs), Transformers, and selective State Space Models (Mamba), have achieved impressive performance in electroencephalogram (EEG) decoding and affective computing. However, their generalization performance often degrades severely under subject-independent Leave-One-Subject-Out (LOSO) cross-validation protocols. This generalization drop is often attributed to generic domain shifts in standard Brain–Computer Interface (BCI) literature, and is tackled by parameter-heavy adaptations. In contrast, this paper proposes a unified mathematical diagnostic framework to audit and measure the underlying representation and geometric collapse in spatiotemporal brain–computer interfaces. More concretely, we formalize: (1) Topological over-smoothing under volume conduction through Graph Dirichlet Energy bounds indicating GCNs as low-pass filters that smooth localized electrode variations; (2) representation collapse through the Normalized Rank Uniformity Index (NRUI) based on the Shannon Entropy of latent covariance eigenvalues, that distinguishes between dimensional and semantic collapse; and (3) geometric manifold distortions under subject domain shifts on the Symmetric Positive Definite (SPD) Riemannian manifold under the Affine-Invariant Riemannian Metric (AIRM) projection. Auditing these diagnostic metrics on canonical models across DEAP, DREAMER, and SEED, we demonstrate why standard spatiotemporal architectures suffer from performance collapse in cross-subject configurations. We provide BCI engineers with a tangible mathematical blueprint to design robust, collapse-resistant decoders.

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