Learning EEG Structure in Its Native Coordinates: Operator-Preconditioned Multi-View Pretraining

EEG foundation models are trained to learn general-purpose latent representations, but different physiological structures are not equally easy to discover in the same feature space of the signal. We study feature-space mismatch: under finite data, model capacity, optimization, and readout budgets, a structure may be present in EEG while remaining difficult for a learned representation to expose and use. A deterministic change of feature space does not add information, but can make such structure more accessible to a finite learner. Motivated by this observation, we propose operator preconditioning: explicitly compute structure-aware EEG measurements, then use self-supervision to learn their organization in the resulting feature space. A learning-free operator already reads a known physiological change more accurately than the frontends, and even the pretrained encoders, of the EEG foundation models we evaluate, highlighting the importance of the feature space before representation learning itself. We instantiate this principle as OpView, a multi-view EEG foundation model with independently pretrained waveform, spectral, cross-spectral, spatial, and dynamical views. Operators can be replaced or extended according to the structures and invariances relevant to different task families. Using operator-only, matched random-encoder, and pretrained-encoder controls, we separate the contributions of measurement, architecture, and learning. Under the EEG-FM-Compass evaluation protocol, OpView achieves strong performance across multiple EEG paradigms. These results support operator-preconditioned representation learning as an extensible approach for directing foundation-model capacity toward structures that downstream EEG decoding can effectively use.