Creating learning models that can exhibit sophisticated reasoning skills is one of the greatest challenges in deep learning research, and mathematics is rapidly becoming one of the target domains for assessing scientific progress in this direction. In the past few years there has been an explosion of neural network architectures, data sets, and benchmarks specifically designed to tackle mathematical problems, reporting notable success in disparate fields such as automated theorem proving, numerical integration, and discovery of new conjectures or matrix multiplication algorithms. However, despite these impressive achievements it is still unclear whether deep learning models possess an elementary understanding of quantities and symbolic numbers. In this survey we critically examine the recent literature, concluding that even state-of-the-art architectures often fall short when probed with relatively simple tasks designed to test basic numerical and arithmetic knowledge.

翻译：创建能够展现复杂推理能力的学习模型是深度学习研究中的最大挑战之一，而数学正迅速成为评估该方向科学进展的目标领域之一。在过去几年中，专门为处理数学问题而设计的神经网络架构、数据集和基准测试大量涌现，并在自动定理证明、数值积分、新猜想发现或矩阵乘法算法等不同领域取得了显著成功。然而，尽管取得了这些令人瞩目的成就，深度学习模型是否具备对量和符号数字的基本理解仍不明确。本综述批判性地审视了近期文献，得出结论：即使是最前沿的架构，在针对基本数值和算术知识设计的相对简单任务的测试中，也常常表现不佳。