Cross-Lingual Word Embeddings (CLWEs) encode words from two or more languages
in a shared high-dimensional space in which vectors representing words with
similar meaning (regardless of language) are closely located. Existing methods
for building high-quality CLWEs learn mappings that minimise the $\ell_{2}$
norm loss function. However, this optimisation objective has been demonstrated
to be sensitive to outliers. Based on the more robust Manhattan norm (aka.
$\ell_{1}$ norm) goodness-of-fit criterion, this paper proposes a simple
post-processing step to improve CLWEs. An advantage of this approach is that it
is fully agnostic to the training process of the original CLWEs and can
therefore be applied widely. Extensive experiments are performed involving ten
diverse languages and embeddings trained on different corpora. Evaluation
results based on bilingual lexicon induction and cross-lingual transfer for
natural language inference tasks show that the $\ell_{1}$ refinement
substantially outperforms four state-of-the-art baselines in both supervised
and unsupervised settings. It is therefore recommended that this strategy be
adopted as a standard for CLWE methods.

本文提出了一种基于曼哈顿距离的后处理方法来提高跨语言词向量的质量，并在十种不同的语言和语料库上进行了广泛的实验证明该方法可以提高词向量在双语词典归纳和自然语言推理任务中的性能。