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$\%$.
翻译:为了实现系统化的概括化,首先需要掌握算术等简单任务。在四种基本算术操作(+,-,$/times$,$/div$)中,司被认为对人类和计算机都是最困难的。在本文中,我们表明,系统化地学习司即使在两个数字之间的最简单层次上仍是一项挑战。我们为司提出了两种新办法,我们称之为神经对等股(NRU)和神经倍增对等股(NMRRU),并对现有司单元“实际神经动力股(REAL NPU)”进行改进。在225套不同的培训中,用投入冗余进行学习司的实验发现,我们提议的对RENPU的修改平均取得了85.3美元的成功,比原来的增加15.1美元。根据上述建议,我们的NMRU方针可以进一步将成功提高到91.6美元。