The Alignment Boundary in Cross-Subject Imagined-Speech EEG: Provable Limits of Pre-Alignment and In-Training Alignment

Imagined-speech brain–computer interfaces (BCIs) promise a non-muscular communication channel, but they must generalize across people: a decoder trained on some subjects should work on an unseen subject without recalibration. Two families of remedies dominate practice—pre-alignment (fixed transforms applied before the decoder, e.g. Euclidean Alignment and its class-conditional refinements) and in-training alignment (objectives applied during training, e.g. adversarial or correlation-based domain adaptation, and episodic meta-learning). We prove that both families are fundamentally bounded, and we characterize the boundary precisely. On the pre-alignment side, we show class-conditional Euclidean alignment (CC-EA) is not an improvement over marginal EA but a catastrophe: it whitens each class covariance to the identity, equalizing the two class covariances and erasing the between-class contrast that Common Spatial Patterns (CSP) decoders read; accuracy collapses to chance (72.3%→49.3% on BCI IV-2a, replicated on Cho2017 with 49 subjects, p < 10⁻¹¹). A gauge-invariance argument then proves the CSP decoder is unchanged by any class-agnostic linear pre-alignment, making marginal EA optimal within the linear family up to a residual per-subject rotation we rule out empirically. On the in-training side, we prove that minibatch objectives such as DANN and CORAL carry zero expected cross-subject H-divergence signal, while episodic prototype alignment is a principled H-divergence surrogate; the predicted gradient alignment is confirmed on imagined-speech EEG across 29/30 proxy–dataset pairs (p < 0.001). Finally, we show these two bounds combine on imagined speech: on a new multilingual cross-subject benchmark (Telugu, Kannada, English; consumer-grade 8-channel EEG), cross-subject decoding is near chance for every method, adaptive or not—not a method failure but the quantitative prediction of the H-divergence bound at the available signal-to-subject ratio. Motor imagery serves throughout as a signal-present control where the same theory translates into measurable accuracy structure. Our analysis converts widely assumed "better alignment" heuristics into precisely characterized boundaries and tells the field where cross-subject gains cannot come from.