Neuropsychiatric symptoms (NPS) such as depression and apathy are common in Alzheimer's disease (AD) and often precede cognitive decline. NPS assessments hold promise as early detection markers due to their correlation with disease progression and their non-invasive nature. Yet current tools cannot distinguish whether NPS are part of aging or early signs of AD, limiting their utility. We present a deep learning-based normative modelling framework to identify atypical NPS burden from structural MRI. A 3D convolutional neural network was trained on cognitively stable participants from the Alzheimer's Disease Neuroimaging Initiative, learning the mapping between brain anatomy and Neuropsychiatric Inventory Questionnaire (NPIQ) scores. Deviations between predicted and observed scores defined the Divergence from NPIQ scores (DNPI). Higher DNPI was associated with future AD conversion (adjusted OR=2.5; p < 0.01) and achieved predictive accuracy comparable to cerebrospinal fluid AB42 (AUC=0.74 vs 0.75). Our approach supports scalable, non-invasive strategies for early AD detection.