  We describe a method for learning word embeddings with data-dependent
dimensionality. Our Stochastic Dimensionality Skip-Gram (SD-SG) and Stochastic
Dimensionality Continuous Bag-of-Words (SD-CBOW) are nonparametric analogs of
Mikolov et al.'s (2013) well-known 'word2vec' models. Vector dimensionality is
made dynamic by employing techniques used by Cote & Larochelle (2016) to define
an RBM with an infinite number of hidden units. We show qualitatively and
quantitatively that SD-SG and SD-CBOW are competitive with their
fixed-dimension counterparts while providing a distribution over embedding
dimensionalities, which offers a window into how semantics distribute across
dimensions.
