arXiv:2510.00051v2 Announce Type: replace Abstract: Neurological diseases can cause significant cognitive impairment, yet linking brain structure to cognitive function remains challenging due to the limitations of conventional methods and the black-box nature of deep learning. We propose InfoVAE-Med3D, an adaptation of InfoVAE for three-dimensional brain MRI that learns informative latent representations by relaxing the mutual information regularization penalty between inputs and latent representations. We evaluated the method on a healthy control (HC) dataset (\(n=6{,}503\)) with age and sex information and a multiple sclerosis (MS) dataset (\(n=916\)) with age, sex, and Symbol Digit Modalities Test (SDMT) scores. Two-dimensional visualizations revealed sex-related clustering and smooth transitions in grey and white matter volumes. Removing the mutual information regularization penalty generally improved MRI reconstruction and brain age and SDMT prediction using support vector regression, outperforming other variational autoencoder variants and achieving competitive performance with deep learning predictors, particularly on the MS dataset. InfoVAE-Med3D provides informative latent representations for investigating brain-related characteristics and supports latent-space analysis and imaging biomarker discovery for cognitive impairment, particularly in MS.