# Geoclidean: Few-Shot Generalization in Euclidean Geometry

arXiv: https://arxiv.org/abs/2211.16663 · HTML: https://mlsanity.com/paper/2211.16663/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 63 references that are in the map.
- First posted on arXiv 30 Nov 2022.

## Builds on (most cited first, 30 of 32)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Matching Networks for One Shot Learning](https://mlsanity.com/paper/1606.04080/) (2016)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [Fine-Grained Visual Classification of Aircraft](https://mlsanity.com/paper/1306.5151/) (2013)
- [PartNet: A Large-scale Benchmark for Fine-grained and Hierarchical Part-level 3D Object Understanding](https://mlsanity.com/paper/1812.02713/) (2018)
- [CLEVRER: CoLlision Events for Video REpresentation and Reasoning](https://mlsanity.com/paper/1910.01442/) (2019)
- [Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning](https://mlsanity.com/paper/2105.04165/) (2021)
- [ABC: A Big CAD Model Dataset For Geometric Deep Learning](https://mlsanity.com/paper/1812.06216/) (2018)
- [Meta-Dataset: A Dataset of Datasets for Learning to Learn from Few Examples](https://mlsanity.com/paper/1903.03096/) (2019)
- [FewRel: A Large-Scale Supervised Few-Shot Relation Classification Dataset with State-of-the-Art Evaluation](https://mlsanity.com/paper/1810.10147/) (2018)
- [ThreeDWorld: A Platform for Interactive Multi-Modal Physical Simulation](https://mlsanity.com/paper/2007.04954/) (2020)
- [RAVEN: A Dataset for Relational and Analogical Visual rEasoNing](https://mlsanity.com/paper/1903.02741/) (2019)
- [Measuring abstract reasoning in neural networks](https://mlsanity.com/paper/1807.04225/) (2018)
- [Few-NERD: A Few-Shot Named Entity Recognition Dataset](https://mlsanity.com/paper/2105.07464/) (2021)
- [CSGNet: Neural Shape Parser for Constructive Solid Geometry](https://mlsanity.com/paper/1712.08290/) (2017)
- [Learning to Infer Graphics Programs from Hand-Drawn Images](https://mlsanity.com/paper/1707.09627/) (2017)
- [SketchGraphs: A Large-Scale Dataset for Modeling Relational Geometry in Computer-Aided Design](https://mlsanity.com/paper/2007.08506/) (2020)
- [Bongard-LOGO: A New Benchmark for Human-Level Concept Learning and Reasoning](https://mlsanity.com/paper/2010.00763/) (2020)
- [Learning to Make Analogies by Contrasting Abstract Relational Structure](https://mlsanity.com/paper/1902.00120/) (2019)
- [Structured agents for physical construction](https://mlsanity.com/paper/1904.03177/) (2019)
- [ORBIT: A Real-World Few-Shot Dataset for Teachable Object Recognition](https://mlsanity.com/paper/2104.03841/) (2021)
- [Solving Bongard Problems with a Visual Language and Pragmatic Reasoning](https://mlsanity.com/paper/1804.04452/) (2018)
- [Plane Geometry Diagram Parsing](https://mlsanity.com/paper/2205.09363/) (2022)
- [Machine Number Sense: A Dataset of Visual Arithmetic Problems for Abstract and Relational Reasoning](https://mlsanity.com/paper/2004.12193/) (2020)

## Built on by (most cited first, 6 of 6)

- [Explain Before You Answer: A Survey on Compositional Visual Reasoning](https://mlsanity.com/paper/2508.17298/) (2025)
- [MEWL: Few-shot multimodal word learning with referential uncertainty](https://mlsanity.com/paper/2306.00503/) (2023)
- [Learning Geometry-aware Representations by Sketching](https://mlsanity.com/paper/2304.08204/) (2023)
- [Human-Like Geometric Abstraction in Large Pre-trained Neural Networks](https://mlsanity.com/paper/2402.04203/) (2024)
- [Visual serial processing deficits explain divergences in human and VLM reasoning](https://mlsanity.com/paper/2509.25142/) (2025)
- [Computer Vision Models Show Human-Like Sensitivity to Geometric and Topological Concepts](https://mlsanity.com/paper/2505.13281/) (2025)

## Abstract (arXiv)

Euclidean geometry is among the earliest forms of mathematical thinking. While the geometric primitives underlying its constructions, such as perfect lines and circles, do not often occur in the natural world, humans rarely struggle to perceive and reason with them. Will computer vision models trained on natural images show the same sensitivity to Euclidean geometry? Here we explore these questions by studying few-shot generalization in the universe of Euclidean geometry constructions. We introduce Geoclidean, a domain-specific language for Euclidean geometry, and use it to generate two datasets of geometric concept learning tasks for benchmarking generalization judgements of humans and machines. We find that humans are indeed sensitive to Euclidean geometry and generalize strongly from a few visual examples of a geometric concept. In contrast, low-level and high-level visual features from standard computer vision models pretrained on natural images do not support correct generalization. Thus Geoclidean represents a novel few-shot generalization benchmark for geometric concept learning, where the performance of humans and of AI models diverge. The Geoclidean framework and dataset are publicly available for download.