  Analysis of word embedding properties to inform their use in downstream NLP
tasks has largely been studied by assessing nearest neighbors. However,
geometric properties of the continuous feature space contribute directly to the
use of embedding features in downstream models, and are largely unexplored. We
consider four properties of word embedding geometry, namely: position relative
to the origin, distribution of features in the vector space, global pairwise
distances, and local pairwise distances. We define a sequence of
transformations to generate new embeddings that expose subsets of these
properties to downstream models and evaluate change in task performance to
understand the contribution of each property to NLP models. We transform
publicly available pretrained embeddings from three popular toolkits (word2vec,
GloVe, and FastText) and evaluate on a variety of intrinsic tasks, which model
linguistic information in the vector space, and extrinsic tasks, which use
vectors as input to machine learning models. We find that intrinsic evaluations
are highly sensitive to absolute position, while extrinsic tasks rely primarily
on local similarity. Our findings suggest that future embedding models and
post-processing techniques should focus primarily on similarity to nearby
points in vector space.
