Identifying Neural Source Dynamics from Unknown Local Interventions

2026-09-28

AI Summary

This study addresses the challenge of unidentifiable neural source dynamics in mixed EEG signals caused by restricted baseline excitation. We propose a novel paradigm for full dynamic recovery that operates without prior knowledge of intervention coefficients. By integrating linear dynamical systems, matrix factorization, and MRI-based anatomical modeling, the method exploits rank-one signatures induced by unknown local interventions. It reconstructs source interaction dynamics by combining known forward models with initialized responses, effectively compensating for missing information through localized mechanistic variations. Experimental results demonstrate that this framework achieves complete recovery of all 32 dynamic components within a 12-source system, significantly outperforming conventional baseline regression and spectral estimation approaches.

Abstract

Electroencephalography (EEG) records mixtures of brain-source activity. Even with a known anatomical forward model, experiments that excite only part of the source-state space leave the dynamics unidentified, and repetition cannot resolve the ambiguity. We show that unknown local mechanism changes can supply the missing information. We consider linear dynamics among fixed anatomical sources with known source-state initialization patterns. Changing one source's update rule for one transition leaves a rank-one, source-specific signature in subsequent EEG: subtracting matched baseline responses isolates it, and the forward model identifies the source and calibrates its response history. Combining these histories with initialization responses recovers source interactions without baseline reachability and without first identifying the intervention coefficients. We establish sufficient recovery conditions, a direct estimator, and a noise-sensitivity bound conditional on correct source labels. Simulated EEG on anatomy derived from magnetic resonance imaging confirms the information gain: with baseline excitation confined to four of twelve source coordinates, eight unknown changes recover all dynamics in 32/32 systems, whereas baseline realization, baseline regression through an invertible forward model, and changes that leave the tested states unexposed all fail, and explicitly constructed alternative dynamics reproduce every baseline mean. Where baseline information suffices, direct reconstruction is also more reliable than a matched-information spectral estimator. Nonlocal changes and forward-model error limit accuracy even when source labels are correct.

Problem

• EEG
• Neural Source Dynamics
• System Identification
• Local Interventions
• Brain-source Activity

Innovation

• EEG source dynamics
• local interventions
• system identification
• rank-one signature
• forward model