Learning of Human-like Algebraic Reasoning Using Deep Feedforward Neural Networks
This work addresses the gap between symbolic reasoning and deep learning for researchers in AI and mathematics, though it appears incremental as it builds on existing methods with specific enhancements.
The paper tackled the problem of bridging symbolic reasoning and deep learning by using a deep feedforward neural network to guide algebraic rewriting processes, achieving a 4.6% error rate on a dataset of linear equations, differentials, and integrals.
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.