Accurate diagnosis of Alzheimer's Disease (AD) entails clinical evaluation of multiple cognition metrics and biomarkers. Metrics such as the Alzheimer's Disease Assessment Scale - Cognitive test (ADAS-cog) comprise multiple subscores that quantify different aspects of a patient's cognitive state such as learning, memory, and language production/comprehension. Although computer-aided diagnostic techniques for classification of a patient's current disease state exist, they provide little insight into the relationship between changes in brain structure and different aspects of a patient's cognitive state that occur over time in AD. We have developed a Convolutional Neural Network architecture that can concurrently predict the trajectories of the 13 subscores comprised by a subject's ADAS-cog examination results from a current minimally preprocessed structural MRI scan up to 36 months from image acquisition time without resorting to manual feature extraction. Mean performance metrics are within range of those of existing techniques that require manual feature selection and are limited to predicting aggregate scores.