# Machine Number Sense: A Dataset of Visual Arithmetic Problems for Abstract and Relational Reasoning

arXiv: https://arxiv.org/abs/2004.12193 · HTML: https://mlsanity.com/paper/2004.12193/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Apr 2020.

## Built on by (most cited first, 18 of 18)

- [A Survey of Deep Learning for Mathematical Reasoning](https://mlsanity.com/paper/2212.10535/) (2022)
- [Abstract Spatial-Temporal Reasoning via Probabilistic Abduction and Execution](https://mlsanity.com/paper/2103.14230/) (2021)
- [Deep Learning Methods for Abstract Visual Reasoning: A Survey on Raven's Progressive Matrices](https://mlsanity.com/paper/2201.12382/) (2022)
- [A Review of Emerging Research Directions in Abstract Visual Reasoning](https://mlsanity.com/paper/2202.10284/) (2022)
- [Reasoning Abilities of Large Language Models: In-Depth Analysis on the Abstraction and Reasoning Corpus](https://mlsanity.com/paper/2403.11793/) (2024)
- [ACRE: Abstract Causal REasoning Beyond Covariation](https://mlsanity.com/paper/2103.14232/) (2021)
- [MM-IQ: Benchmarking Human-Like Abstraction and Reasoning in Multimodal Models](https://mlsanity.com/paper/2502.00698/) (2025)
- [Learning Algebraic Representation for Systematic Generalization in Abstract Reasoning](https://mlsanity.com/paper/2111.12990/) (2021)
- [Are Deep Neural Networks SMARTer than Second Graders?](https://mlsanity.com/paper/2212.09993/) (2022)
- [MEWL: Few-shot multimodal word learning with referential uncertainty](https://mlsanity.com/paper/2306.00503/) (2023)
- [Calibrating Concepts and Operations: Towards Symbolic Reasoning on Real Images](https://mlsanity.com/paper/2110.00519/) (2021)
- [ARCLE: The Abstraction and Reasoning Corpus Learning Environment for Reinforcement Learning](https://mlsanity.com/paper/2407.20806/) (2024)
- [A Minimalist Dataset for Systematic Generalization of Perception, Syntax, and Semantics](https://mlsanity.com/paper/2103.01403/) (2021)
- [FACT: Learning Governing Abstractions Behind Integer Sequences](https://mlsanity.com/paper/2209.09543/) (2022)
- [Geoclidean: Few-Shot Generalization in Euclidean Geometry](https://mlsanity.com/paper/2211.16663/) (2022)
- [COLUMBUS: Evaluating COgnitive Lateral Understanding through Multiple-choice reBUSes](https://mlsanity.com/paper/2409.04053/) (2024)
- [DETR++: Taming Your Multi-Scale Detection Transformer](https://mlsanity.com/paper/2206.02977/) (2022)
- [A-I-RAVEN and I-RAVEN-Mesh: Two New Benchmarks for Abstract Visual Reasoning](https://mlsanity.com/paper/2406.11061/) (2024)

## Abstract (arXiv)

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.