  Most of the successful and predominant methods for bilingual lexicon
induction (BLI) are mapping-based, where a linear mapping function is learned
with the assumption that the word embedding spaces of different languages
exhibit similar geometric structures (i.e., approximately isomorphic). However,
several recent studies have criticized this simplified assumption showing that
it does not hold in general even for closely related languages. In this work,
we propose a novel semi-supervised method to learn cross-lingual word
embeddings for BLI. Our model is independent of the isomorphic assumption and
uses nonlinear mapping in the latent space of two independently trained
auto-encoders. Through extensive experiments on fifteen (15) different language
pairs (in both directions) comprising resource-rich and low-resource languages
from two different datasets, we demonstrate that our method outperforms
existing models by a good margin. Ablation studies show the importance of
different model components and the necessity of non-linear mapping.
