  In this paper, we seek to measure how much information a component in a
neural network could extract from the representations fed into it. Our work
stands in contrast to prior probing work, most of which investigates how much
information a model's representations contain. This shift in perspective leads
us to propose a new principle for probing, the architectural bottleneck
principle: In order to estimate how much information a given component could
extract, a probe should look exactly like the component. Relying on this
principle, we estimate how much syntactic information is available to
transformers through our attentional probe, a probe that exactly resembles a
transformer's self-attention head. Experimentally, we find that, in three
models (BERT, ALBERT, and RoBERTa), a sentence's syntax tree is mostly
extractable by our probe, suggesting these models have access to syntactic
information while composing their contextual representations. Whether this
information is actually used by these models, however, remains an open
question.
