We propose a unified optimization framework that combines neural networks with dictionary learning to model complex interactions between resting state functional MRI and behavioral data. The dictionary learning objective decomposes patient correlation matrices into a collection of shared basis networks and subject-specific loadings. These subject-specific features are simultaneously input into a neural network that predicts multidimensional clinical information. Our novel optimization framework combines the gradient information from the neural network with that of a conventional matrix factorization objective. This procedure collectively estimates the basis networks, subject loadings, and neural network weights most informative of clinical severity. We evaluate our combined model on a multi-score prediction task using 52 patients diagnosed with Autism Spectrum Disorder (ASD). Our integrated framework outperforms state-of-the-art methods in a ten-fold cross validated setting to predict three different measures of clinical severity.