Representing Sentences as Low-Rank Subspaces

Sentences are important semantic units of natural language. A generic, distributional representation of sentences that can capture the latent semantics is beneficial to multiple downstream applications. We observe a simple geometry of sentences -- the word representations of a given sentence (on average 10.23 words in all SemEval datasets with a standard deviation 4.84) roughly lie in a low-rank subspace (roughly, rank 4). Motivated by this observation, we represent a sentence by the low-rank subspace spanned by its word vectors. Such an unsupervised representation is empirically validated via semantic textual similarity tasks on 19 different datasets, where it outperforms the sophisticated neural network models, including skip-thought vectors, by 15% on average.