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.

We interpret the predictions of any black-box structured input-structured output model around a specific input-output pair. Our method returns an “explanation” consisting of groups of input-output tokens that are causally related. These dependencies are inferred by querying the model with perturbed inputs, generating a graph over tokens from the responses, and solving a partitioning problem to select the most relevant components. We focus the general approach on sequence-to-sequence problems, adopting a variational autoencoder to yield meaningful input perturbations. We test our method across several NLP sequence generation tasks.

Continuous word representations have been remarkably useful across NLP tasks but remain poorly understood. We ground word embeddings in semantic spaces studied in the cognitive-psychometric literature, taking these spaces as the primary objects to recover. To this end, we relate log co-occurrences of words in large corpora to semantic similarity assessments and show that co-occurrences are indeed consistent with an Euclidean semantic space hypothesis. Framing word embedding as metric recovery of a semantic space unifies existing word embedding algorithms, ties them to manifold learning, and demonstrates that existing algorithms are consistent metric recovery methods given co-occurrence counts from random walks. Furthermore, we propose a simple, principled, direct metric recovery algorithm that performs on par with the state-of-the-art word embedding and manifold learning methods. Finally, we complement recent focus on analogies by constructing two new inductive reasoning datasets—series completion and classification—and demonstrate that word embeddings can be used to solve them as well.