Binder: Hierarchical Concept Representation through Order Embedding of Binary Vectors

For natural language understanding and generation, embedding concepts using an order-based representation is an essential task. Unlike traditional point vector based representation, an order-based representation imposes geometric constraints on the representation vectors for explicitly capturing various semantic relationships that may exist between a pair of concepts. In existing literature, several approaches on order-based embedding have been proposed, mostly focusing on capturing hierarchical relationships; examples include vectors in Euclidean space, complex, Hyperbolic, order, and Box Embedding. Box embedding creates region-based rich representation of concepts, but along the process it sacrifices simplicity, requiring a custom-made optimization scheme for learning the representation. Hyperbolic embedding improves embedding quality by exploiting the ever-expanding property of Hyperbolic space, but it also suffers from the same fate as box embedding as gradient descent like optimization is not simple in the Hyperbolic space. In this work, we propose Binder, a novel approach for order-based representation. Binder uses binary vectors for embedding, so the embedding vectors are compact with an order of magnitude smaller footprint than other methods. Binder uses a simple and efficient optimization scheme for learning representation vectors with a linear time complexity. Our comprehensive experimental results show that Binder is very accurate, yielding competitive results on the representation task. But Binder stands out from its competitors on the transitive closure link prediction task as it can learn concept embeddings just from the direct edges, whereas all existing order-based approaches rely on the indirect edges. In particular, Binder achieves a whopping 70% higher F1-score than the second best method (98.6% vs 29%) in our largest dataset, WordNet Nouns (743,241 edges), when using only direct edges during training.