As a comprehensive indicator of mathematical thinking and intelligence, the number sense (Dehaene 2011) bridges the induction of symbolic concepts and the competence of problem-solving. To endow such a crucial cognitive ability to machine intelligence, we propose a dataset, Machine Number Sense (MNS), consisting of visual arithmetic problems automatically generated using a grammar model--And-Or Graph (AOG). These visual arithmetic problems are in the form of geometric figures: each problem has a set of geometric shapes as its context and embedded number symbols. Solving such problems is not trivial; the machine not only has to recognize the number, but also to interpret the number with its contexts, shapes, and relations (e.g., symmetry) together with proper operations. We benchmark the MNS dataset using four predominant neural network models as baselines in this visual reasoning task. Comprehensive experiments show that current neural-network-based models still struggle to understand number concepts and relational operations. We show that a simple brute-force search algorithm could work out some of the problems without context information. Crucially, taking geometric context into account by an additional perception module would provide a sharp performance gain with fewer search steps. Altogether, we call for attention in fusing the classic search-based algorithms with modern neural networks to discover the essential number concepts in future research.

为了将关键的认知能力赋予机器智能，本文提出一个新的数据集，即机器数理感知(MNS)，其由采用And-Or Graph(AOG)语法模型自动生成的视觉算术问题组成，提出结合经典搜索算法和现代神经网络的方法，以更好地理解数字概念和关系运算。

机器数感：一组用于抽象和关系推理的视觉算术问题数据集