  The success of pre-trained contextualized representations has prompted
researchers to analyze them for the presence of linguistic information. Indeed,
it is natural to assume that these pre-trained representations do encode some
level of linguistic knowledge as they have brought about large empirical
improvements on a wide variety of NLP tasks, which suggests they are learning
true linguistic generalization. In this work, we focus on intrinsic probing, an
analysis technique where the goal is not only to identify whether a
representation encodes a linguistic attribute but also to pinpoint where this
attribute is encoded. We propose a novel latent-variable formulation for
constructing intrinsic probes and derive a tractable variational approximation
to the log-likelihood. Our results show that our model is versatile and yields
tighter mutual information estimates than two intrinsic probes previously
proposed in the literature. Finally, we find empirical evidence that
pre-trained representations develop a cross-lingually entangled notion of
morphosyntax.
