Associating brain systems with mental processes requires statistical analysis of brain activity across many cognitive processes. These analyses typically face a difficult compromise between scope—from domain-specific to system-level analysis—and accuracy. Using all the functional Magnetic Resonance Imaging (fMRI) statistical maps of the largest data repository available, we trained machine-learning models that decode the cognitive concepts probed in unseen studies. For this, we leveraged two comprehensive resources: NeuroVault—an open repository of fMRI statistical maps with unconstrained annotations—and Cognitive Atlas—an ontology of cognition. We labeled NeuroVault images with Cognitive Atlas concepts occurring in their associated metadata. We trained neural networks to predict these cognitive labels on tens of thousands of brain images. Overcoming the heterogeneity, imbalance and noise in the training data, we successfully decoded more than 50 classes of mental processes on a large test set. This success demonstrates that image-based meta-analyses can be undertaken at scale and with minimal manual data curation. It enables broad reverse inferences, that is, concluding on mental processes given the observed brain activity.