@article{Zhang_Zhang_Zhu_Zhu_2020, title={Machine Number Sense: A Dataset of Visual Arithmetic Problems for Abstract and Relational Reasoning}, volume={34}, url={https://ojs.aaai.org/index.php/AAAI/article/view/5489}, DOI={10.1609/aaai.v34i02.5489}, abstractNote={<p>As a comprehensive indicator of mathematical thinking and intelligence, the <em>number sense</em> (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 <em>visual</em> arithmetic problems automatically generated using a grammar modelâ€”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 (<em>e.g.</em>, 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.</p>}, number={02}, journal={Proceedings of the AAAI Conference on Artificial Intelligence}, author={Zhang, Wenhe and Zhang, Chi and Zhu, Yixin and Zhu, Song-Chun}, year={2020}, month={Apr.}, pages={1332-1340} }