Fully Hyperbolic Neural Networks: A Novel Approach to Studying Aging Trajectories

Characterizing age-related alterations in brain networks is crucial for understanding aging trajectories and identifying deviations indicative of neurodegenerative disorders, such as Alzheimer's disease. In this study, we developed a Fully Hyperbolic Neural Network (FHNN) to embed functional brain connectivity graphs derived from magnetoencephalography (MEG) data into low dimensions on a Lorentz model of hyperbolic space. Using this model, we computed hyperbolic embeddings of the MEG brain networks of 587 individuals from the Cambridge Centre for Ageing and Neuroscience (Cam-CAN) dataset. Notably, we leveraged a unique metric—the radius of the node embeddings—which effectively captures the hierarchical organization of the brain, to characterize subtle hierarchical organizational changes in various brain subnetworks attributed to the aging process. Our findings revealed that a considerable number of subnetworks exhibited a reduction in hierarchy during aging, with some showing gradual changes and others undergoing rapid transformations in the elderly. Moreover, we demonstrated that hyperbolic features outperform traditional graph-theoretic measures in capturing age-related information in brain networks. Overall, our study represents the first evaluation of hyperbolic embeddings in MEG brain networks for studying aging trajectories, shedding light on critical regions undergoing significant age-related alterations in the large cohort of the Cam-CAN dataset.