Anchor & Transform: Learning Sparse Representations of Discrete Objects

Learning continuous representations of discrete objects such as text, users, and URLs lies at the heart of many applications including language and user modeling. When using discrete objects as input to neural networks, we often ignore the underlying structures (e.g. natural groupings and similarities) and embed the objects independently into individual vectors. As a result, existing methods do not scale to large vocabulary sizes. In this paper, we design a Bayesian nonparametric prior for embeddings that encourages sparsity and leverages natural groupings among objects. We derive an approximate inference algorithm based on Small Variance Asymptotics which yields a simple and natural algorithm for learning a small set of anchor embeddings and a sparse transformation matrix. We call our method Anchor & Transform (ANT) as the embeddings of discrete objects are a sparse linear combination of the anchors, weighted according to the transformation matrix. ANT is scalable, flexible, end-to-end trainable, and allows the user to incorporate domain knowledge about object relationships. On text classification and language modeling benchmarks, ANT demonstrates stronger performance with fewer parameters as compared to existing compression baselines.