Can neural networks do arithmetic? A survey on the elementary numerical skills of state-of-the-art deep learning models
This is an incremental survey that highlights a critical gap in AI reasoning capabilities, relevant for researchers aiming to improve mathematical understanding in neural networks.
The survey examines whether state-of-the-art deep learning models can perform basic arithmetic and numerical tasks, concluding that they often fail on simple tests designed to assess elementary numerical skills.
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.