Brain activity in numerous perisylvian brain regions is modulated by the expectedness of linguistic stimuli. We leverage recent advances in computational parsing models to test what representations guide the processes reflected by this activity. Recurrent Neural Network Grammars (RNNGs) are generative models of (tree, string) pairs that use neural networks to drive derivational choices. Parsing with them yields a variety of incremental complexity metrics that we evaluate against a publicly available fMRI data-set recorded while participants simply listen to an audiobook story. Surprisal, which captures a word’s un-expectedness, correlates with a wide range of temporal and frontal regions when it is calculated based on word-sequence information using a top-performing LSTM neural network language model. The explicit encoding of hierarchy afforded by the RNNG additionally captures activity in left posterior temporal areas. A separate metric tracking the number of derivational steps taken between words correlates with activity in the left temporal lobe and inferior frontal gyrus. This pattern of results narrows down the kinds of linguistic representations at play during predictive processing across the brain’s language network.