Recent work in NLP shows that LSTM language models capture compositional structure in language data. For a closer look at how these representations are composed hierarchically, we present a novel measure of interdependence between word meanings in an LSTM, based on their interactions at the internal gates. To explore how compositional representations arise over training, we conduct simple experiments on synthetic data, which illustrate our measure by showing how high interdependence can hurt generalization. These synthetic experiments also illustrate a specific hypothesis about how hierarchical structures are discovered over the course of training: that parent constituents rely on effective representations of their children, rather than on learning long-range relations independently. We further support this measure with experiments on English language data, where interdependence is higher for more closely syntactically linked word pairs.