  Vector-space representations provide geometric tools for reasoning about the
similarity of a set of objects and their relationships. Recent machine learning
methods for deriving vector-space embeddings of words (e.g., word2vec) have
achieved considerable success in natural language processing. These vector
spaces have also been shown to exhibit a surprising capacity to capture verbal
analogies, with similar results for natural images, giving new life to a
classic model of analogies as parallelograms that was first proposed by
cognitive scientists. We evaluate the parallelogram model of analogy as applied
to modern word embeddings, providing a detailed analysis of the extent to which
this approach captures human relational similarity judgments in a large
benchmark dataset. We find that that some semantic relationships are better
captured than others. We then provide evidence for deeper limitations of the
parallelogram model based on the intrinsic geometric constraints of vector
spaces, paralleling classic results for first-order similarity.
