  There is an ongoing debate in the NLP community whether modern language
models contain linguistic knowledge, recovered through so-called probes. In
this paper, we study whether linguistic knowledge is a necessary condition for
the good performance of modern language models, which we call the
\textit{rediscovery hypothesis}. In the first place, we show that language
models that are significantly compressed but perform well on their pretraining
objectives retain good scores when probed for linguistic structures. This
result supports the rediscovery hypothesis and leads to the second contribution
of our paper: an information-theoretic framework that relates language modeling
objectives with linguistic information. This framework also provides a metric
to measure the impact of linguistic information on the word prediction task. We
reinforce our analytical results with various experiments, both on synthetic
and on real NLP tasks in English.
