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This paper investigates longitudinal brain age gap effects in a Mild Cognitive Impairment cohort using a covariance neural network (VNN) framework. By employing Integrated Gradients, the study reveals that the eigenspectrum of the anatomical covariance matrix, particularly the leading eigenvector, explains $83.2\%$ of observed longitudinal effects in brain age gap differences between amyloid positive and negative subcohorts, significantly outperforming individual brain region attributions. This highlights that coordinated input patterns within the covariance eigenspace are crucial for understanding longitudinal brain aging trajectories.
The covariance eigenspace, not individual brain regions, captures the dominant longitudinal effects in brain age gap, explaining over 83% of variance between MCI subcohorts.
Brain age gap is a promising machine learning (ML)-driven bio\-marker of accelerated biological aging and is derived from neuroimaging data. Recent works on coVariance neural networks (VNN) for brain age gap prediction have provided an explainable and anatomically verifiable framework for brain age gap prediction. Notably, VNN outcomes are derived by filtering inputs along covariance eigenvectors, providing a mechanism for explaining their decisions in terms of latent (orthogonal) vectors. In this paper, we investigate the longitudinal brain age gap effects in a Mild Cognitive Impairment (MCI) cohort using a VNN-driven brain age gap prediction framework. Specifically, using Integrated Gradients (IG) as the attribution mechanism, our results demonstrate that the eigenspectrum of the anatomical covariance matrix explains the different longitudinal effects observed in brain age gap in amyloid positive vs amyloid negative subcohorts more prominently than individual brain regions ($83.2\%$ with the leading eigenvector versus a maximal value of $7.7\%$ for any brain region). Therefore, the covariance-based latent explanation identifies a key coordinated input pattern that carries most of the observed longitudinal effect in brain age gap.