Identifying Neural Source Dynamics from Unknown Local Interventions

Electroencephalography (EEG) observes brain-source activity through a linear forward model computed from head anatomy, which tells where each source appears at the scalp but not how sources drive one another. Where baseline activity reaches only part of the source space, these dynamics stay unidentified however many trials or sensors are recorded. We show that local interventions with unknown targets and strengths can supply this missing information. For linear source dynamics with known initializations, a one-step change to how one source receives input makes the contrast with matched baseline EEG rank one: the forward model identifies the changed source and calibrates its response history, and these histories, combined with initialization responses, determine the source dynamics without baseline reachability and without identifying the interventions. We establish sufficient identification conditions, a closed-form estimator and an error bound. In simulated EEG on four anatomies derived from magnetic resonance imaging (MRI), where baseline activity reaches four of twelve sources, unknown interventions recover the dynamics in 32/32 systems, whereas baseline-only estimators succeed in none, even with an invertible forward model, and explicitly constructed alternative dynamics reproduce every baseline mean. When baseline data suffice, our estimator is also more reliable than a matched spectral method.