Learning Division with Neural Arithmetic Logic Modules
This addresses a fundamental arithmetic problem for AI systems, with incremental improvements in neural network modules for division tasks.
The paper tackles the challenge of robustly learning division systematically, proposing novel approaches like the Neural Reciprocal Unit (NRU) and Neural Multiplicative Reciprocal Unit (NMRU), which improve an existing module to achieve up to 91.6% success in experiments.
To achieve systematic generalisation, it first makes sense to master simple tasks such as arithmetic. Of the four fundamental arithmetic operations (+,-,$\times$,$÷$), 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$\%$.