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.

Binder 是一种新的基于顺序的表示方法，通过使用二进制向量进行嵌入，具有比其他方法小一个数量级的紧凑嵌入向量，并且使用线性时间复杂度的简单有效的优化方案进行向量学习，具有在表示任务中具有竞争力的准确性，而在传递闭包链接预测任务中，与其他基于顺序的方法相比，Binder 可以仅通过直接边学习概念嵌入。