  Making an informed choice of pre-trained language model (LM) is critical for
performance, yet environmentally costly, and as such widely underexplored. The
field of Computer Vision has begun to tackle encoder ranking, with promising
forays into Natural Language Processing, however they lack coverage of
linguistic tasks such as structured prediction. We propose probing to rank LMs,
specifically for parsing dependencies in a given language, by measuring the
degree to which labeled trees are recoverable from an LM's contextualized
embeddings. Across 46 typologically and architecturally diverse LM-language
pairs, our probing approach predicts the best LM choice 79% of the time using
orders of magnitude less compute than training a full parser. Within this
study, we identify and analyze one recently proposed decoupled LM - RemBERT -
and find it strikingly contains less inherent dependency information, but often
yields the best parser after full fine-tuning. Without this outlier our
approach identifies the best LM in 89% of cases.
