Abstract
Many tasks in natural language processing require
the alignment of word embeddings. Embedding
alignment relies on the geometric properties of the
manifold of word vectors. This paper focuses on
supervised linear alignment and studies the relationship between the shape of the target embedding. We
assess the performance of aligned word vectors on
semantic similarity tasks and find that the isotropy
of the target embedding is critical to the alignment.
Furthermore, aligning with an isotropic noise can
deliver satisfactory results. We provide a theoretical
framework and guarantees which aid in the understanding of empirical results.