Offline bilingual word vectors, orthogonal transformations and the inverted softmax

TL;DR

This paper demonstrates that orthogonal transformations improve offline bilingual word vector alignment, introduces an inverted softmax for better translation accuracy, and shows robustness using pseudo-dictionaries, achieving high translation precision.

Contribution

It proves the orthogonality of the transformation, introduces the inverted softmax, and develops a noise-robust method using pseudo-dictionaries for bilingual embedding alignment.

Findings

Improved translation precision from 34% to 43% with the inverted softmax.

Achieved 40% precision using pseudo-dictionaries without expert bilingual signals.

Attained 68% precision in translating English sentences from Italian corpus.

Abstract

Usually bilingual word vectors are trained "online". Mikolov et al. showed they can also be found "offline", whereby two pre-trained embeddings are aligned with a linear transformation, using dictionaries compiled from expert knowledge. In this work, we prove that the linear transformation between two spaces should be orthogonal. This transformation can be obtained using the singular value decomposition. We introduce a novel "inverted softmax" for identifying translation pairs, with which we improve the precision @1 of Mikolov's original mapping from 34% to 43%, when translating a test set composed of both common and rare English words into Italian. Orthogonal transformations are more robust to noise, enabling us to learn the transformation without expert bilingual signal by constructing a "pseudo-dictionary" from the identical character strings which appear in both languages, achieving 40% precision on the same test set. Finally, we extend our method to retrieve the true translations of English sentences from a corpus of 200k Italian sentences with a precision @1 of 68%.