arXiv:2509.08180cs.LG2025-09

新神经算术单元通过混合对数与线性空间,提升加减乘除泛化能力。

The Domain Mixed Unit: A New Neural Arithmetic Layer

  • 设计可学习门控机制,动态混合对数与线性表示进行计算
  • 在NALM基准上,乘除任务求解率领先所有种子实验
  • 适用于需要高精度算术泛化的神经网络系统

域混合单元(DMU)是一种新型神经算术单元,通过学习单一参数门控,在对数空间与线性空间间混合表示,完成加法(DMU add)或减法(DMU sub)。提出了两种初始化方式:一种覆盖加法与乘法,另一种覆盖减法与除法。在专为测试神经算术单元泛化能力设计的NALM基准上,DMU取得了当前最佳表现,尤其在乘法与除法任务中,对所有种子实验均达到最高求解率。代码已提交至开源NALM基准的Pull Request,并可在GitHub获取:https://github.com/marict/nalm-benchmark。

原文摘要 · Abstract (English)

The Domain Mixed Unit (DMU) is a new neural arithmetic unit that learns a single parameter gate that mixes between log-space and linear-space representations while performing either addition (DMU add) or subtraction (DMU sub). Two initializations are proposed for the DMU: one covering addition and multiplication, and another covering subtraction and division. The DMU achieves state-of-the-art performance on the NALM Benchmark, a dataset designed to test the ability of neural arithmetic units to generalize arithmetic operations, specifically performing with the highest percentage solved over all seeds on multiplication and division. The DMU will be submitted as a pull request to the open-source NALM benchmark, and its code is available on GitHub at https://github.com/marict/nalm-benchmark

神经算术门控机制泛化能力

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