Deep learning models for MRI classification face two recurring problems: they are typically limited by low sample size, and are abstracted by their own complexity (the "black box problem"). In this paper, we train a convolutional neural network (CNN) with the largest multi-source, functional MRI (fMRI) connectomic dataset ever compiled, consisting of 43,858 datapoints. We apply this model to a cross-sectional comparison of autism spectrum disorder (ASD) versus typically developing (TD) controls that has proved difficult to characterize with inferential statistics. To contextualize these findings, we additionally perform classifications of gender and task versus rest. Employing class-balancing to build a training set, we trained [Formula: see text] modified CNNs in an ensemble model to classify fMRI connectivity matrices with overall AUROCs of 0.6774, 0.7680, and 0.9222 for ASD versus TD, gender, and task versus rest, respectively. Additionally, we aim to address the black box problem in this context using two visualization methods. First, class activation maps show which functional connections of the brain our models focus on when performing classification. Second, by analyzing maximal activations of the hidden layers, we were also able to explore how the model organizes a large and mixed-center dataset, finding that it dedicates specific areas of its hidden layers to processing different covariates of data (depending on the independent variable analyzed), and other areas to mix data from different sources. Our study finds that deep learning models that distinguish ASD from TD controls focus broadly on temporal and cerebellar connections, with a particularly high focus on the right caudate nucleus and paracentral sulcus.