You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Cross-lingual word embeddings are becoming increasingly important in multilingual NLP. Recently, it has been shown that these embeddings can be effectively learned by aligning two disjoint monolingual vector spaces through linear transformations, using no more than a small bilingual dictionary as supervision. In this work, we propose to apply an additional transformation after the initial alignment step, which moves cross-lingual synonyms towards a middle point between them. By applying this transformation our aim is to obtain a better cross-lingual integration of the vector spaces. In addition, and perhaps surprisingly, the monolingual spaces also improve by this transformation. This is in contrast to the original alignment, which is typically learned such that the structure of the monolingual spaces is preserved. Our experiments confirm that the resulting cross-lingual embeddings outperform state-of-the-art models in both monolingual and cross-lingual evaluation tasks.

Cited Abstract(s):
[1]: We introduce new methods for estimating and evaluating embeddings of words in more than fifty languages in a single shared embedding space. Our estimation methods, multiCluster and multiCCA, use dictionaries and monolingual data; they do not require parallel data. Our new evaluation method, multiQVEC-CCA, is shown to correlate better than previous ones with two downstream tasks (text categorization and parsing). We also describe a web portal for evaluation that will facilitate further research in this area, along with open-source releases of all our methods.

[2]: 

[3]: Dictionaries and phrase tables are the basis of modern statistical machine translation systems. This paper develops a method that can automate the process of generating and extending dictionaries and phrase tables. Our method can translate missing word and phrase entries by learning language structures based on large monolingual data and mapping between languages from small bilingual data. It uses distributed representation of words and learns a linear mapping between vector spaces of languages. Despite its simplicity, our method is surprisingly effective: we can achieve almost 90 precision@5 for translation of words between English and Spanish. This method makes little assumption about the languages, so it can be used to extend and refine dictionaries and translation tables for any language pairs.

[4]: The distributional hypothesis of Harris (1954), according to which the meaning of words is evidenced by the contexts they occur in, has motivated several effective techniques for obtaining vector space semantic representations of words using unannotated text corpora. This paper argues that lexico-semantic content should additionally be invariant across languages and proposes a simple technique based on canonical correlation analysis (CCA) for incorporating multilingual evidence into vectors generated monolingually. We evaluate the resulting word representations on standard lexical semantic evaluation tasks and show that our method produces substantially better semantic representations than monolingual techniques.
Another branch of research exploits pre-trained monolingual embeddings with weak signals such as bilingual lexicons for learning bilingual embeddings [3] [4] [1] [2] . was one of the first attempts into this line of research, applying a linear transformation in order to map the embeddings from one monolingual space into another. They also noted that more sophisticated approaches, such as using multilayer perceptrons, do not improve with respect to their linear counterparts. built upon this work by normalizing word embeddings during training and adding an orthogonality constraint. In a complementary direction, put forward a technique based on canonical correlation analysis to obtain linear mappings for both monolingual embedding spaces into a new shared space. proposed a similar linear mapping to , generalizing it and providing theoretical justifications which also served to reinterpret the methods of and . further showed how orthogonality was required to improve the consistency of bilingual mappings, making them more robust to noise. Finally, a more complete generalization providing further insights on the linear transformations used in all these models can be found in .