  Due to widespread interest in machine translation and transfer learning,
there are numerous algorithms for mapping multiple embeddings to a shared
representation space. Recently, these algorithms have been studied in the
setting of bilingual dictionary induction where one seeks to align the
embeddings of a source and a target language such that translated word pairs
lie close to one another in a common representation space. In this paper, we
propose a method, Filtered Inner Product Projection (FIPP), for mapping
embeddings to a common representation space and evaluate FIPP in the context of
bilingual dictionary induction. As semantic shifts are pervasive across
languages and domains, FIPP first identifies the common geometric structure in
both embeddings and then, only on the common structure, aligns the Gram
matrices of these embeddings. Unlike previous approaches, FIPP is applicable
even when the source and target embeddings are of differing dimensionalities.
We show that our approach outperforms existing methods on the MUSE dataset for
various language pairs. Furthermore, FIPP provides computational benefits both
in ease of implementation and scalability.

Computation and Language;Machine Learning