Word Representations via Gaussian Embedding (1412.6623v4)

Abstract: Current work in lexical distributed representations maps each word to a point vector in low-dimensional space. Mapping instead to a density provides many interesting advantages, including better capturing uncertainty about a representation and its relationships, expressing asymmetries more naturally than dot product or cosine similarity, and enabling more expressive parameterization of decision boundaries. This paper advocates for density-based distributed embeddings and presents a method for learning representations in the space of Gaussian distributions. We compare performance on various word embedding benchmarks, investigate the ability of these embeddings to model entailment and other asymmetric relationships, and explore novel properties of the representation.

• The paper introduces a density-based embedding technique that represents words as Gaussian distributions to capture semantic uncertainty.
• It employs a probability product kernel and KL-divergence energy functions to model both symmetric and asymmetric word similarities.
• Experimental results demonstrate competitive performance on word similarity and entailment tasks, underscoring its practical impact.

Overview of "Word Representations via Gaussian Embedding"

The paper "Word Representations via Gaussian Embedding" by Luke Vilnis and Andrew McCallum introduces a novel approach to word embeddings by mapping words into a space of Gaussian distributions instead of the conventional point vectors. This method provides a richer semantic representation that captures uncertainty and naturally handles asymmetric relationships, such as entailment, using probability density functions.

Core Contributions

The paper's primary contributions are:

1. Density-based Embeddings: Unlike traditional embeddings that map words to fixed points, this approach utilizes Gaussian distributions (with diagonal covariance matrices), allowing for the representation of concepts' uncertainties.
2. Asymmetric and Symmetric Similarity Measures: Two energy functions are proposed for learning these embeddings: a probability product kernel for symmetric similarity and KL-divergence for asymmetric similarity. Both provide closed-form gradients to facilitate learning.
3. Model Capabilities: The Gaussian representation allows modeling relationships such as entailment and inclusion and provides a mechanism for expressing uncertainty about embeddings.
4. Experimental Evaluation: The proposed model is tested against established word similarity benchmarks and is shown to be competitive with traditional methods, while also enabling the natural modeling of entailment relationships.

Experimental Findings

The experiments conducted illustrate the model's efficacy in both standard word similarity tasks and more complex semantic entailment tasks:

• The Gaussian embeddings outperform baseline methods on several word similarity datasets. Notably, they match or exceed performance seen with comparable-dimensionality Skip-Gram vectors.
• The model demonstrates its ability to capture entailment relationships unsupervised, achieving higher performance on entailment datasets compared to empirical covariances and some count-based baselines.
• Experiments show that more specific and polysemous concepts can be represented with smaller variance, suggesting an intuitive correlation between a word's semantic specificity and its probabilistic representation in latent space.

Implications and Future Directions

The paper's findings open numerous avenues for further research and practical application. By representing words as distributions, this method allows incorporating uncertainty and asymmetry into NLP models. It sets the stage for representation learning approaches in domains that require handling polysemy and hierarchical structures naturally.

Potential directions for future exploration include:

• Enhanced Covariance Structure: Extending beyond diagonal covariances to richer structures, such as low-rank plus diagonal, could enhance the expressiveness of the embeddings without significant computational overhead.
• Optimization Techniques: Improvements in optimization strategies, particularly for training supervised hierarchies with KL-divergence, could lead to more robust embeddings.
• Broader Application Areas: Beyond word-level semantics, applying these representation techniques to sentence embeddings, relational learning, and tasks requiring context-sensitive word similarity could be transformative.

Conclusion

The paper presents a compelling argument and methodology for transitioning from traditional point-based word embeddings to more nuanced, density-based representations. This approach holds significant promise for advancing computational models of semantics by integrating uncertainty, hierarchical representation, and asymmetric relationships into the core of representation learning. With its robust theoretical foundation and empirical validation, this work marks a significant step toward more sophisticated NLP systems capable of handling the complexities inherent in human language.