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Using matrices to model symbolic relationship
Ilya Sutskever · Geoffrey E Hinton

Wed Dec 10 11:59 AM -- 12:00 PM (PST) @ None
We describe a way of learning matrix representations of objects and relationships. The goal of learning is to allow multiplication of matrices to represent symbolic relationships between objects and symbolic relationships between relationships, which is the main novelty of the method. We demonstrate that this leads to excellent generalization in two different domains: modular arithmetic and family relationships. We show that the same system can learn first-order propositions such as $(2, 5) \member +\!3$ or $(Christopher, Penelope)\member has\_wife$, and higher-order propositions such as $(3, +\!3) \member plus$ and $(+\!3, -\!3) \member inverse$ or $(has\_husband, has\_wife)\in higher\_oppsex$. We further demonstrate that the system understands how higher-order propositions are related to first-order ones by showing that it can correctly answer questions about first-order propositions involving the relations $+\!3$ or $has\_wife$ even though it has not been trained on any first-order examples involving these relations.

Author Information

Ilya Sutskever (OpenAI)
Geoffrey E Hinton (Google & University of Toronto)

Geoffrey Hinton received his PhD in Artificial Intelligence from Edinburgh in 1978 and spent five years as a faculty member at Carnegie-Mellon where he pioneered back-propagation, Boltzmann machines and distributed representations of words. In 1987 he became a fellow of the Canadian Institute for Advanced Research and moved to the University of Toronto. In 1998 he founded the Gatsby Computational Neuroscience Unit at University College London, returning to the University of Toronto in 2001. His group at the University of Toronto then used deep learning to change the way speech recognition and object recognition are done. He currently splits his time between the University of Toronto and Google. In 2010 he received the NSERC Herzberg Gold Medal, Canada's top award in Science and Engineering.

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