Learning Division with Neural Arithmetic Logic Modules

TL;DR

This paper addresses the challenge of systematically learning division in neural networks by proposing novel modules, achieving significant improvements in success rates over existing methods through extensive experiments.

Contribution

Introduces two new neural modules, NRU and NMRU, and enhances an existing division module, significantly improving systematic division learning performance.

Findings

Proposed modules achieve up to 91.6% success rate.

Improvements over existing division modules by 15.1%.

Extensive testing across 225 training sets.

Abstract

To achieve systematic generalisation, it first makes sense to master simple tasks such as arithmetic. Of the four fundamental arithmetic operations (+,-,$\times$,$\div$), division is considered the most difficult for both humans and computers. In this paper we show that robustly learning division in a systematic manner remains a challenge even at the simplest level of dividing two numbers. We propose two novel approaches for division which we call the Neural Reciprocal Unit (NRU) and the Neural Multiplicative Reciprocal Unit (NMRU), and present improvements for an existing division module, the Real Neural Power Unit (Real NPU). Experiments in learning division with input redundancy on 225 different training sets, find that our proposed modifications to the Real NPU obtains an average success of 85.3$\%$ improving over the original by 15.1$\%$. In light of the suggestion above, our NMRU approach can further improve the success to 91.6$\%$.