Title: Representational correlates of hierarchical phrase structure in deep language models. Abstract: While contextual representations from Transformer-based architectures have set a new standard for many NLP tasks, there is not yet a complete accounting of their inner workings. In particular, it is not entirely clear what aspects of sentence-level syntax are captured by these representations, nor how (if at all) they are built along the stacked layers of the network. In this paper, we aim to address such questions with a general class of input perturbation-based analyses of representations from Transformer networks pretrained on self-supervised objectives. Importing from computational and cognitive neuroscience the notion of representational invariance, we perform a series of probes designed to test the sensitivity of Transformer representations to several kinds of structure in sentences. Each probe involves swapping words in a sentence and comparing the representations from perturbed sentences against the original. We experiment with three different perturbations: (1) random permutations of n-grams of varying width, to test the scale at which a representation is sensitive to word position; (2) swapping of two spans which do or do not form a syntactic phrase, to test sensitivity to global phrase structure; and (3) swapping of two adjacent words which do or do not break apart a syntactic phrase, to test sensitivity to local phrase structure. We also connect our probe results to the Transformer architecture by relating the attention mechanism to syntactic distance between two words. Results from the three probes collectively suggest that Transformers build sensitivity to larger parts of the sentence along their layers, and that hierarchical phrase structure plays a role in this process. In particular, sensitivity to local phrase structure increases along deeper layers. Based on our analysis of attention, we show that this is at least partly explained by generally larger attention weights between syntactically distant words.