Geometry-Conditioned Hyperalignment for Generalizable EEG Decoding Across Datasets and Paradigms

Electroencephalography (EEG) brain-computer interfaces (BCIs) supports promising applications, but daily use remains limited by poor cross-subject and cross-dataset generalisation. That is because EEG recordings made with different electrode montages do not even share an observation space, and each subjects's leadfield projects the same neural sources onto the scalp differently. We present hTSMNet, which combines a novel geometry-conditioned hyperalignment frontend with a Riemannian symmetric positive-definite (SPD) manifold backbone that reduces the residual cross-subject distribution shift. From electrode coordinates alone, the frontend builds a linear map from any montage onto a fixed set of scalp anchors, placing every recording in one shared space. Because this map has no subjectspecific parameters, an unseen subject, dataset, or montage is aligned from its geometry alone, so transfer is zero-shot by construction. On a leave-one-dataset-out left-/right-hand motor-imagery (MI) benchmark across three datasets (172 subjects) and eight comparators, hTSMNet matches the strongest comparator at strict zero-shot, and attains the highest accuracy on every dataset once a few calibration trials for adjusting only final-layer classifier are available. We show that it orients the binary decision the same way in every dataset, so that a single linear rule learned on the source data is already correctly oriented on a held-out one. The same frozen MI-pretrained model also transfers across paradigms: with only a re-fit final-layer classifier, hTSMNet decodes mental workload and steady-state visual evoked potentials (SSVEP) well above chance, yet remains at chance on stimulus-locked event-related potentials (ERP). This dissociation follows from the architecture: covariance pooling reads oscillatory band power and is largely insensitive to the phase-locked potentials that ERP tasks depend on. What the representation generalizes is a signal family (band-limited oscillatory activity), not the named task. Geometry-conditioned hyperalignment thus yields an inspectable representation, which is generalizable across datasets and, within the oscillatory regime, across paradigms.