There is a wide gap between symbolic reasoning and deep learning. In this
research, we explore the possibility of using deep learning to improve symbolic
reasoning. Briefly, in a reasoning system, a deep feedforward neural network is
used to guide rewriting processes after learning from algebraic reasoning
examples produced by humans. To enable the neural network to recognise patterns
of algebraic expressions with non-deterministic sizes, reduced partial trees
are used to represent the expressions. Also, to represent both top-down and
bottom-up information of the expressions, a centralisation technique is used to
improve the reduced partial trees. Besides, symbolic association vectors and
rule application records are used to improve the rewriting processes.
Experimental results reveal that the algebraic reasoning examples can be
accurately learnt only if the feedforward neural network has enough hidden
layers. Also, the centralisation technique, the symbolic association vectors
and the rule application records can reduce error rates of reasoning. In
particular, the above approaches have led to 4.6% error rate of reasoning on a
dataset of linear equations, differentials and integrals.Comment: 8 pages, 7 figure
