Gromov-Wasserstein Alignment of Word Embedding Spaces (1809.00013v1)

Abstract: Cross-lingual or cross-domain correspondences play key roles in tasks ranging from machine translation to transfer learning. Recently, purely unsupervised methods operating on monolingual embeddings have become effective alignment tools. Current state-of-the-art methods, however, involve multiple steps, including heuristic post-hoc refinement strategies. In this paper, we cast the correspondence problem directly as an optimal transport (OT) problem, building on the idea that word embeddings arise from metric recovery algorithms. Indeed, we exploit the Gromov-Wasserstein distance that measures how similarities between pairs of words relate across languages. We show that our OT objective can be estimated efficiently, requires little or no tuning, and results in performance comparable with the state-of-the-art in various unsupervised word translation tasks.

An Evaluation of Gromov-Wasserstein Alignment for Word Embeddings

This paper introduces an innovative approach for aligning word embeddings across languages using the concept of Gromov-Wasserstein distance. The core idea is to formulate the cross-lingual alignment task as an optimal transport (OT) problem, thereby facilitating unsupervised bilingual lexical induction with minimal computational overhead. The proposed approach exhibits competitive performance compared to contemporary methods, highlighting its theoretical and practical potential.

Key Contributions

The paper makes several salient contributions:

1. Novel Alignment Method: The authors propose using the Gromov-Wasserstein distance to align word embeddings. This metric allows for the evaluation of relational metrics across languages by considering the similarity or distance between pairs of words, thus capturing deeper semantic correspondences.
2. Efficiency and Simplicity: The method requires little hyper-parameter tuning and can be solved efficiently with first-order methods. This marks a notable contrast to adversarial training approaches which often involve complex, multi-step processing pipelines.
3. Scalability: To scale the method to large vocabularies, the approach combines initial Gromov-Wasserstein alignment with Procrustes analysis to extend mappings. This two-step process demonstrates the method's adaptability to real-world data scale requirements.
4. Empirical Evaluation: Extensive experiments are conducted across several language pairs, demonstrating performance on par or superior to state-of-the-art methods in unsupervised word translation tasks. The method also incurs lower computational costs, both in terms of runtime and resources.

Theoretical Underpinnings

The utilization of the Gromov-Wasserstein distance stems from its capacity to align metric spaces based on relational structures rather than point-wise correspondences. This property is beneficial in the setting of monolingual word embeddings, where absolute geometric positioning is often non-robust or arbitrary due to the embeddings' learning processes. The authors effectively exploit this characteristic to facilitate robust translation alignment without requiring copious amounts of parallel data or onerous pre-processing steps.

Implications and Future Directions

Practical Implications: The ability to efficiently align embeddings in a fully unsupervised manner has significant ramifications for multilingual natural language processing applications, including machine translation and cross-lingual information retrieval. The reduced dependency on parallel corpora broadens applicability to low-resource languages, substantially impacting global digital inclusivity.

Theoretical Implications: By advancing the application of optimal transport theory in the area of word embeddings, the paper opens new pathways for exploration within both computational linguistics and the broader machine learning community. The extension of these concepts to other forms of embeddings or discrete representations could yield further advances in multi-modal or multi-domain alignment tasks.

Future Developments: Future research may focus on enhancing the scalability of the Gromov-Wasserstein-based methods, perhaps through integrating stochastic optimization techniques or more sophisticated approximation algorithms. Another line of inquiry could involve expanding the method to include contextualized word representations, thereby aligning sentence or paragraph-level embeddings as similarly demonstrated for word vectors.

In summary, this research enriches the toolkit for unsupervised cross-lingual word alignment by leveraging the mathematical foundation of optimal transport through Gromov-Wasserstein distance. The combination of theoretical elegance and empirical efficacy marks it as a promising direction in the field of computational linguistics.