Poincaré GloVe: Hyperbolic Word Embeddings (1810.06546v2)

Abstract: Words are not created equal. In fact, they form an aristocratic graph with a latent hierarchical structure that the next generation of unsupervised learned word embeddings should reveal. In this paper, justified by the notion of delta-hyperbolicity or tree-likeliness of a space, we propose to embed words in a Cartesian product of hyperbolic spaces which we theoretically connect to the Gaussian word embeddings and their Fisher geometry. This connection allows us to introduce a novel principled hypernymy score for word embeddings. Moreover, we adapt the well-known Glove algorithm to learn unsupervised word embeddings in this type of Riemannian manifolds. We further explain how to solve the analogy task using the Riemannian parallel transport that generalizes vector arithmetics to this new type of geometry. Empirically, based on extensive experiments, we prove that our embeddings, trained unsupervised, are the first to simultaneously outperform strong and popular baselines on the tasks of similarity, analogy and hypernymy detection. In particular, for word hypernymy, we obtain new state-of-the-art on fully unsupervised WBLESS classification accuracy.

• The paper introduces a novel adaptation of the GloVe algorithm to hyperbolic spaces to capture inherent hierarchical structures in language.
• It develops a new loss function based on hyperbolic metrics, enabling superior performance in tasks like unsupervised word hypernymy detection.
• Empirical results demonstrate state-of-the-art performance, highlighting the potential of hyperbolic embeddings to model asymmetric relationships effectively.

An Expert Overview of "Poincaré GloVe: Hyperbolic Word Embeddings"

The paper "Poincaré GloVe: Hyperbolic Word Embeddings" presents an innovative approach to word embeddings by integrating hyperbolic geometry into the modeling process traditionally dominated by Euclidean spaces. The core motivation is the acknowledgment of latent hierarchical structures within natural language, which hyperbolic spaces theoretically model more effectively due to their natural suitability for representing hierarchical data. This paper approaches the task of capturing asymmetric word relations and hierarchical features — areas wherein conventional word embedding methodologies, such as GloVe, Word2Vec, and FastText, have been found wanting.

Conceptual Foundation

At the conceptual level, this research proposes embedding words in a Cartesian product of hyperbolic spaces, leveraging their mathematical alignment with hierarchical structures. The paper draws a theoretical linkage between these embeddings and Gaussian distribution-based embeddings, emphasizing the multifaceted potential of hyperbolic spaces. An intrinsic motivation is the space's negative curvature, ideal for modeling "aristocratic" graphs—a reference to networks where a few nodes exert significantly more influence than others.

Methodological Advances

The primary methodological contribution is the adaptation of the GloVe algorithm for hyperbolic spaces. The paper achieves this by introducing a novel loss function based on hyperbolic metrics rather than Euclidean inner products. This adaptation aligns with recent advancements in statistical manifold theory and hyperbolic geometry, allowing for parallel transport operations and supporting analogy tasks within this non-Euclidean framework.

Empirical Results

Empirically, the word embeddings derived from this approach demonstrate superior performance across several word embedding evaluation tasks. The paper reports state-of-the-art results in unsupervised word hypernymy detection on the WBLESS dataset, illustrating the potential of hyperbolic embeddings to outclass traditional methods not just in capturing similarity but also in addressing analogy and hierarchical relationships. The ability to capture these complex structures is a significant accomplishment, reflecting the efficacy of hyperbolic geometric representations in natural language processing.

Theoretical and Practical Implications

Theoretically, this research interconnects the geometric properties of hyperbolic spaces with practical word embedding tasks, offering insights into the geometric underpinnings of language. Practically, the authors propose a principled score for entailment detection based on the Fisher distance metric, redefining how computational models might approach the encoding of semantic hierarchies in natural language.

Future Directions

Looking ahead, this research opens up several avenues for further exploration, such as investigating the scalability of hyperbolic embeddings to more extensive and diverse datasets, as well as optimizing for multilingual datasets. Additionally, exploring the integration of hyperbolic geometries with other deep learning architectures could broaden the applicability and performance of natural LLMs across different domains and languages.

In summary, "Poincaré GloVe: Hyperbolic Word Embeddings" offers significant contributions to the field of natural language processing by seamlessly marrying hyperbolic geometry with word embedding methodologies to address entrenched limitations in recognizing hierarchical and asymmetric language features. As computational linguistics continues to evolve, such innovative methodological adaptations play a crucial role in pushing the boundaries of what is feasible with word embeddings.