NLP has a rich history of representing our prior understanding of language in the form of graphs. Recent work on analyzing contextualized text representations has focused on hand-designed probe models to understand how and to what extent do these representations encode a particular linguistic phenomenon. However, due to the inter-dependence of various phenomena and randomness of training probe models, detecting how these representations encode the rich information in these linguistic graphs remains a challenging problem. In this paper, we propose a new information-theoretic probe, Birds Eye, which is a fairly simple probe method for detecting if and how these representations encode the information in these linguistic graphs. Instead of using classifier performance, our probe takes an information-theoretic view of probing and estimates the mutual information between the linguistic graph embedded in a continuous space and the contextualized word representations. Furthermore, we also propose an approach to use our probe to investigate localized linguistic information in the linguistic graphs using perturbation analysis. We call this probing setup Worms Eye. Using these probes, we analyze BERT models on their ability to encode a syntactic and a semantic graph structure, and find that these models encode to some degree both syntactic as well as semantic information; albeit syntactic information to a greater extent.
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