**Learning Distributed Representations of
Concepts Using Linear Relational Embedding**

Alberto Paccanaro and Geoffrey Hinton

Gatsby Computational Neuroscience Unit

University College London

Submitted to *IEEE Trans. on Knowledge and Data Engineering -
Special Issue on 'Connectionists Models for learning in Structured Domains*

In this paper we introduce Linear Relational Embedding as a means of
learning a distributed representation of concepts from data consisting of binary relations
between concepts. The key idea is to represent concepts as vectors, binary relations as
matrices, and the operation of applying a relation to a concept as a matrix-vector
multiplication that produces an approximation to the related concept. A
repesentation for concepts and relations is learned by maximizing an appropriate
discriminative goodness function using gradient ascent. On a task involving family
relationships, learning is fast and leads to good generalization.

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