  Understanding how linguistic structures are encoded in contextualized
embedding could help explain their impressive performance across NLP@. Existing
approaches for probing them usually call for training classifiers and use the
accuracy, mutual information, or complexity as a proxy for the representation's
goodness. In this work, we argue that doing so can be unreliable because
different representations may need different classifiers. We develop a
heuristic, DirectProbe, that directly studies the geometry of a representation
by building upon the notion of a version space for a task. Experiments with
several linguistic tasks and contextualized embeddings show that, even without
training classifiers, DirectProbe can shine light into how an embedding space
represents labels, and also anticipate classifier performance for the
representation.
