# Learning Division with Neural Arithmetic Logic Modules

arXiv: https://arxiv.org/abs/2110.05177 · HTML: https://mlsanity.com/paper/2110.05177/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 14 references that are in the map.
- First posted on arXiv 11 Oct 2021.

## Builds on (most cited first, 10 of 10)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Learning Equations for Extrapolation and Control](https://mlsanity.com/paper/1806.07259/) (2018)
- [Neural Arithmetic Logic Units](https://mlsanity.com/paper/1808.00508/) (2018)
- [Neural Arithmetic Units](https://mlsanity.com/paper/2001.05016/) (2020)
- [Neural Power Units](https://mlsanity.com/paper/2006.01681/) (2020)
- [A Primer for Neural Arithmetic Logic Modules](https://mlsanity.com/paper/2101.09530/) (2021)
- [Measuring Arithmetic Extrapolation Performance](https://mlsanity.com/paper/1910.01888/) (2019)
- [iNALU: Improved Neural Arithmetic Logic Unit](https://mlsanity.com/paper/2003.07629/) (2020)
- [Neural Status Registers](https://mlsanity.com/paper/2004.07085/) (2020)

## Abstract (arXiv)

To achieve systematic generalisation, it first makes sense to master simple tasks such as arithmetic. Of the four fundamental arithmetic operations (+,-,×,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%.