Increasingly, cognitive scientists have demonstrated interest in applying tools from deep learning. One use for deep learning is in language acquisition where it is useful to know if a linguistic phenomenon can be learned through domain-general means. To assess whether unsupervised deep learning is appropriate, we first pose a smaller question: Can unsupervised neural networks apply linguistic rules productively, using them in novel situations? We draw from the literature on determiner/noun productivity by training an unsupervised, autoencoder network measuring its ability to combine nouns with determiners. Our simple autoencoder creates combinations it has not previously encountered and produces a degree of overlap matching adults. While this preliminary work does not provide conclusive evidence for productivity, it warrants further investigation with more complex models. Further, this work helps lay the foundations for future collaboration between the deep learning and cognitive science communities.