  Centering theory (CT; Grosz et al., 1995) provides a linguistic analysis of
the structure of discourse. According to the theory, local coherence of
discourse arises from the manner and extent to which successive utterances make
reference to the same entities. In this paper, we investigate the connection
between centering theory and modern coreference resolution systems. We provide
an operationalization of centering and systematically investigate if neural
coreference resolvers adhere to the rules of centering theory by defining
various discourse metrics and developing a search-based methodology. Our
information-theoretic analysis reveals a positive dependence between
coreference and centering; but also shows that high-quality neural coreference
resolvers may not benefit much from explicitly modeling centering ideas. Our
analysis further shows that contextualized embeddings contain much of the
coherence information, which helps explain why CT can only provide little gains
to modern neural coreference resolvers which make use of pretrained
representations. Finally, we discuss factors that contribute to coreference
which are not modeled by CT such as world knowledge and recency bias. We
formulate a version of CT that also models recency and show that it captures
coreference information better compared to vanilla CT.
