Analogical Inference for Multi-Relational Embeddings (1705.02426v2)

Abstract: Large-scale multi-relational embedding refers to the task of learning the latent representations for entities and relations in large knowledge graphs. An effective and scalable solution for this problem is crucial for the true success of knowledge-based inference in a broad range of applications. This paper proposes a novel framework for optimizing the latent representations with respect to the \textit{analogical} properties of the embedded entities and relations. By formulating the learning objective in a differentiable fashion, our model enjoys both theoretical power and computational scalability, and significantly outperformed a large number of representative baseline methods on benchmark datasets. Furthermore, the model offers an elegant unification of several well-known methods in multi-relational embedding, which can be proven to be special instantiations of our framework.

• The paper introduces a framework that leverages analogical inference to unify embedding methods and enhance knowledge graph completion.
• It models analogical structures by enforcing commutative constraints, reformulating embeddings as normal matrices for more coherent relational representation.
• Empirical results on FB15K and WN18 demonstrate significant performance gains over baselines like TransE, DistMult, and ComplEx.

Analogical Inference for Multi-relational Embeddings

The paper entitled "Analogical Inference for Multi-relational Embeddings" presents a comprehensive approach toward optimizing the latent representations of entities and relations in knowledge graphs using analogical inference. The authors, Liu, Wu, and Yang from Carnegie Mellon University, introduce a framework that incorporates analogical properties within embeddings to significantly outperform existing baseline models on standard datasets.

Framework Overview

The problem of multi-relational embedding involves learning latent representations for entities and relations to enhance inference over knowledge graphs. This task has become pivotal due to the expansive applications of knowledge bases such as Freebase, DBpedia, and Google's Knowledge Graph. Existing methods primarily focus on representation by either factorization or translation models. However, the proposed framework leverages analogical inference, a concept largely overlooked in previous works, to unify existing methodologies and extend relational embeddings' capacities.

Methodology: Emphasizing Analogical Structures

The core insight of the framework is the explicit modeling of analogical structures crucial for meaningful embedding. This involves ensuring that embeddings possess desirable analogical properties defined rigorously through commutative diagrams, leading to the formulation of commutative constraints for relations in knowledge graphs. These constraints necessitate that the relations form a commuting family of normal matrices, effectively ensuring that multiple relations can simultaneously exist in a coherent analogy.

The optimization objective is designed to enforce these constraints through scalable induction processes. Converting traditional representations into commutative families of normal matrices restricts the embeddings to mimic the desired analogical properties, ultimately enabling improved accuracy in knowledge base completion.

Numerical Results and Performance

On datasets such as FB15K and WN18, the framework shows substantive improvements compared to established methods like TransE, DistMult, and ComplEx. The results indicate that the algorithmic approach of ANalogy leveraged with these constraints offers a more comprehensive and unified view than translation-based methods or those relying on simpler multiplicative interactions.

Implications and Future Work

This research contributes significantly to embedding methodologies by offering a coherent framework that not only provides superior predictive capabilities but also integrates and explains the performance of several existing models. With its theoretical underpinning about normal matrices and algorithmic scalability, this work sets a stage for future developments in multi-relational embeddings.

However, the scope of this framework is not limited to knowledge graphs. The authors hint at possibly extending these insights to other machine learning domains like machine translation and image captioning, where cross-domain analogies play instrumental roles. Such extensions suggest promising practical implementations beyond academic benchmarks.

Conclusion

The paper introduced a novel perspective on embedding knowledge graphs, promoting theoretical generality and empirical potency. By exploring paths traditionally ignored, particularly emphasizing analogies, the authors provide a robust paradigm that achieves significant improvements, paving the way for both academic exploration and application across various domains. Future research will likely expand upon these ideas, exploring further intersections of analogical reasoning and learning systems.