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.

本文提出了一种方法 -“过滤内积投影（FIPP）”，用于在双语字典诱导的上下文中将嵌入映射到共同的表示空间，并评估了 FIPP 的性能。不同于之前的方法，FIPP 在两个嵌入中识别共同的几何结构，然后仅在该几何结构上对这些嵌入的格拉姆矩阵进行对齐，且具有易于实现和可伸缩的计算优势。在各种语言对的 MUSE 数据集上，FIPP 的结果优于现有方法。

跨语言嵌入对齐的内积投影过滤

Filtered Inner Product Projection for Crosslingual Embedding Alignment

Recent work on bilingual lexicon induction (BLI) has frequently depended
either on aligned bilingual lexicons or on distribution matching, often with an
assumption about the isometry of the two spaces. We propose a technique to
quantitatively estimate this assumption of the isometry between two embedding
spaces and empirically show that this assumption weakens as the languages in
question become increasingly etymologically distant. We then propose Bilingual
Lexicon Induction with Semi-Supervision (BLISS) --- a semi-supervised approach
that relaxes the isometric assumption while leveraging both limited aligned
bilingual lexicons and a larger set of unaligned word embeddings, as well as a
novel hubness filtering technique. Our proposed method obtains state of the art
results on 15 of 18 language pairs on the MUSE dataset, and does particularly
well when the embedding spaces don't appear to be isometric. In addition, we
also show that adding supervision stabilizes the learning procedure, and is
effective even with minimal supervision.

该论文提出了一种半监督的双语词汇识别方法（BLISS），该方法使用了一个新的中枢过滤技术，可以放松两个嵌入空间同构假设，利用有限的对齐双语词汇表和更大的未对齐词汇表，实现了令人瞩目的效果。