Recent advancements in pretraining have demonstrated that modern Large Language Models (LLMs) possess the capability to effectively learn arithmetic operations. However, despite acknowledging the significance of digit order in arithmetic computation, current methodologies predominantly rely on sequential, step-by-step approaches for teaching LLMs arithmetic, resulting in a conclusion where obtaining better performance involves fine-grained step-by-step. Diverging from this conventional path, our work introduces a novel strategy that not only reevaluates the digit order by prioritizing output from the least significant digit but also incorporates a step-by-step methodology to substantially reduce complexity. We have developed and applied this method in a comprehensive set of experiments. Compared to the previous state-of-the-art (SOTA) method, our findings reveal an overall improvement of in accuracy while requiring only a third of the tokens typically used during training. For the purpose of facilitating replication and further research, we have made our code and dataset publicly available at \url{https://anonymous.4open.science/r/RAIT-9FB7/}.

最近的预训练研究表明，现代大型语言模型（LLMs）具备有效学习算术运算的能力。然而，尽管承认数字顺序在算术计算中的重要性，当前的方法主要依赖顺序、逐步的方法来教授LLMs算术，导致一个结论，即获得更好的性能需要细粒度的逐步操作。与传统方法不同，我们的工作引入了一种新颖的策略，不仅重新评估了数字顺序，优先考虑了最低有效位的输出，而且还采用了逐步的方法大幅减少了复杂性。我们在一系列全面的实验中开发并应用了这种方法。与先前的最先进方法相比，我们的研究结果显示了整体准确性的提升，同时在训练过程中仅使用了通常使用的三分之一的标记。为了方便复制和进一步研究，我们已公开提供了我们的代码和数据集，网址为https://anonymous.4open.science/r/RAIT-9FB7/。

逆向数字！算术学习中解码顺序的重要性