A better understanding of the emergent computation and problem-solving capabilities of recent large language models is of paramount importance to further improve them and broaden their applicability. This work investigates how a language model, trained to predict the next token, can perform arithmetic computations generalizing beyond training data. Binary addition and multiplication constitute a good testbed for this purpose, since they require a very small vocabulary and exhibit relevant input/output discontinuities making smooth input interpolation ineffective for novel data. We successfully trained a light language model to learn these tasks and ran a number of experiments to investigate the extrapolation capabilities and internal information processing. Our findings support the hypotheses that the language model works as an Encoding-Regression-Decoding machine where the computation takes place in the value space once the input token representation is mapped to an appropriate internal representation.

该研究调查了语言模型在计算预测和问题解决能力方面的应用，以及其在进行算术计算和内部信息处理方面的推广能力。通过使用二进制加法和乘法作为测试样本，该研究成功地训练了一个轻量级语言模型，并进行了一系列实验以探究其外推能力和内部信息处理过程。研究结果支持了该假设，即语言模型在适当的内部表示映射后，计算发生在数值空间中，其工作类似于一个编码-回归-解码机器。

语言模型的数值计算能力：从记忆到计算