  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.
