Background: The release of a broad, longitudinal anatomical dataset by the Parkinson’s Progression Markers Initiative promoted a surge of machine-learning studies aimed at predicting disease onset and progression. However, the excessive number of features used in these models often conceals their relationship to the Parkinsonian symptomatology. Objectives: The aim of this study is two-fold: (i) to predict future motor and cognitive impairments up to four years from brain features acquired at baseline; and (ii) to interpret the role of pivotal brain regions responsible for different symptoms from a neurological viewpoint. Methods: We test several deep-learning neural network configurations, and report our best results obtained with an autoencoder deep-learning model, run on a 5-fold cross-validation set. Comparison with Existing Methods: Our approach improves upon results from standard regression and others. It also includes neuroimaging biomarkers as features. Results: The relative contributions of pivotal brain regions to each impairment change over time, suggesting a dynamical reordering of culprits as the disease progresses. Specifically, the Putamen is initially the most critical region accounting for the overall cognitive state, only being surpassed by the Substantia Nigra in later years. The Pallidum is the first region to influence motor scores, followed by the parahippocampal and ambient gyri, and the anterior orbital gyrus. Conclusions: While the causal link between regional brain atrophy and Parkinson symptomatology is poorly understood, our methods demonstrate that the contributions of pivotal regions to cognitive and motor impairments are more dynamical than generally appreciated.