Learning of human-like algebraic reasoning using deep feedforward neural networks

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Author(s)
Cai, Cheng-Hao
Xu, Yanyan
Ke, Dengfeng
Su, Kaile
Griffith University Author(s)
Year published
2018
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Human-like rewriting, which is an algebraic reasoning system imitating human intelligence of problem solving, is proposed in this work. In order to imitate both learning and reasoning aspects of human cognition, a deep feedforward neural network learns from algebraic reasoning examples produced by humans and then uses learnt experiences to guide other reasoning processes. This work shows that the neural network can learn human’s behaviours of solving mathematical problems, and it can indicate suitable directions of reasoning, so that intelligent and heuristic reasoning can be performed. Moreover, human-like rewriting bridges ...
View more >Human-like rewriting, which is an algebraic reasoning system imitating human intelligence of problem solving, is proposed in this work. In order to imitate both learning and reasoning aspects of human cognition, a deep feedforward neural network learns from algebraic reasoning examples produced by humans and then uses learnt experiences to guide other reasoning processes. This work shows that the neural network can learn human’s behaviours of solving mathematical problems, and it can indicate suitable directions of reasoning, so that intelligent and heuristic reasoning can be performed. Moreover, human-like rewriting bridges the gap between symbolic reasoning and biologically inspired machine learning. To enable the neural network to recognise patterns of symbolic expressions with non-deterministic sizes, the expressions are reduced to partial tree representations and then vectorised as numeric features. Further, the centralisation method, symbolic association vectors and rule application records are used to improve the vectorised features. With these approaches, human-like rewriting shows satisfactory performance on the tasks of solving linear equations and computing derivations and indefinite integrals.
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View more >Human-like rewriting, which is an algebraic reasoning system imitating human intelligence of problem solving, is proposed in this work. In order to imitate both learning and reasoning aspects of human cognition, a deep feedforward neural network learns from algebraic reasoning examples produced by humans and then uses learnt experiences to guide other reasoning processes. This work shows that the neural network can learn human’s behaviours of solving mathematical problems, and it can indicate suitable directions of reasoning, so that intelligent and heuristic reasoning can be performed. Moreover, human-like rewriting bridges the gap between symbolic reasoning and biologically inspired machine learning. To enable the neural network to recognise patterns of symbolic expressions with non-deterministic sizes, the expressions are reduced to partial tree representations and then vectorised as numeric features. Further, the centralisation method, symbolic association vectors and rule application records are used to improve the vectorised features. With these approaches, human-like rewriting shows satisfactory performance on the tasks of solving linear equations and computing derivations and indefinite integrals.
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Journal Title
Biologically Inspired Cognitive Architectures
Volume
25
Copyright Statement
© The Author(s) 2018. This is an Open Access article distributed under the terms of the Creative Commons Attribution 4.0 International (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Subject
Medical microbiology not elsewhere classified