Deep learning applied to MRI for Alzheimer's classification is hypothesized to improve if the deep learning model implicates disease's pathophysiology. The challenge in testing this hypothesis is that large-scale data are required to train this type of model. Here, we overcome this challenge by using a novel data augmentation strategy and show that our MRI-based deep learning model classifies Alzheimer's dementia with high accuracy. Moreover, a class activation map was found dominated by signal from the hippocampal formation, a site where Alzheimer's pathophysiology begins. Next, we tested the model's performance in prodromal Alzheimer's when patients present with mild cognitive impairment (MCI). We retroactively dichotomized a large cohort of MCI patients who were followed for up to 10 years into those with and without prodromal Alzheimer's at baseline and used the dementia-derived model to generate individual 'deep learning MRI' scores. We compared the two groups on these scores, and on other biomarkers of amyloid pathology, tau pathology, and neurodegeneration. The deep learning MRI scores outperformed nearly all other biomarkers, including, unexpectedly, biomarkers of amyloid or tau pathology, in classifying prodromal disease and in predicting clinical progression. Providing a mechanistic explanation, the deep learning MRI scores were found to be linked to regional tau pathology, through investigations using cross-sectional, longitudinal, premortem and postmortem data. Our findings validate that a disease's known pathophysiology can improve the design and performance of deep learning models. Moreover, by showing that deep learning can extract useful biomarker information from conventional MRIs, the advantages of this model extend practically, potentially reducing patient burden, risk, and cost.