  Pre-trained language models perform well on a variety of linguistic tasks
that require symbolic reasoning, raising the question of whether such models
implicitly represent abstract symbols and rules. We investigate this question
using the case study of BERT's performance on English subject-verb agreement.
Unlike prior work, we train multiple instances of BERT from scratch, allowing
us to perform a series of controlled interventions at pre-training time. We
show that BERT often generalizes well to subject-verb pairs that never occurred
in training, suggesting a degree of rule-governed behavior. We also find,
however, that performance is heavily influenced by word frequency, with
experiments showing that both the absolute frequency of a verb form, as well as
the frequency relative to the alternate inflection, are causally implicated in
the predictions BERT makes at inference time. Closer analysis of these
frequency effects reveals that BERT's behavior is consistent with a system that
correctly applies the SVA rule in general but struggles to overcome strong
training priors and to estimate agreement features (singular vs. plural) on
infrequent lexical items.
