# Learning of Human-like Algebraic Reasoning Using Deep Feedforward Neural Networks

## TL;DR

This paper investigates using deep feedforward neural networks to emulate human-like algebraic reasoning, employing novel representation and learning techniques to improve accuracy in symbolic reasoning tasks.

## Contribution

It introduces a method combining reduced partial trees, centralisation, and symbolic association vectors to enable neural networks to learn algebraic reasoning with improved accuracy.

## Key findings

- Achieved a 4.6% error rate on algebraic reasoning tasks
- Deep neural networks require sufficient hidden layers for effective learning
- Centralisation and symbolic association techniques reduce reasoning errors

## Abstract

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.