Can Neural Networks Do Arithmetic? A Survey on the Elementary Numerical Skills of State-of-the-Art Deep Learning Models

Abstract

Creating learning models that can exhibit sophisticated reasoning abilities 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, datasets, and benchmarks specifically designed to tackle mathematical problems, reporting impressive achievements in disparate fields such as automated theorem proving, numerical integration, and the discovery of new conjectures or matrix multiplication algorithms. However, despite this notable success it is still unclear whether deep learning models possess an elementary understanding of quantities and numbers. This survey critically examines the recent literature, concluding that even state-of-the-art architectures and large language models often fall short when probed with relatively simple tasks designed to test basic numerical and arithmetic knowledge.

Keywords

• artificial intelligence
• neuro-symbolic systems
• deep learning
• large language models
• number embeddings
• numerical cognition