Bongard problem
A Bongard problem is a visual pattern recognition puzzle that shows two sets of figures and asks what concept sets them apart. The original collection of 100 problems first appeared in an appendix to Soviet computer scientist Mikhail Bongard's 1967 book on pattern recognition.[1][2] In the preface, Bongard attributes the ideas to joint work with M. N. Vaintsvaig, V. V. Maksimov, and M. S. Smirnov.[2]
Overview
[edit]Bongard problems consist of twelve images divided into two sets of six. A solver must formulate a rule or concept that distinguishes the two sets.[3] Because many rules may plausibly distinguish the sets, solving a problem requires inferring what concept the designer likely intended to communicate. Bongard originally presented the problems as a challenge for vision systems, and they have continued to be studied in artificial intelligence and cognitive science research.[4][5]
Bongard problems were popularized by Douglas Hofstadter's discussion of them in his 1979 book Gödel, Escher, Bach. He wrote that, "the skill of solving Bongard problems lies very close to the core of 'pure' intelligence, if there is such a thing."[3] Hofstadter created 56 new Bongard problems in an unpublished 1977 manuscript.[6]
In popular culture
[edit]Bongard problems influenced the design of the tabletop game Zendo.[7]
References
[edit]- ↑ Bongard, Mikhail (1967). Проблема узнавания [Pattern Recognition] (in Russian). Nauka; Glav. red. fiziko-matematicheskoĭ lit-ry.
- 1 2 Bongard, Mikhail (1970). Hawkins, Joseph (ed.). Pattern Recognition. Translated by Cheron, Theodore. New York: Spartan Books. ISBN 0-87671-118-2. LCCN 76-80435.
- 1 2 Gödel, Escher, Bach, Douglas Hofstadter, Twentieth anniversary Edition, 1999, Artificial Intelligence: Prospects
- ↑ Nie, Weili; Yu, Zhiding; Mao, Lei; Patel, Ankit B; Zhu, Yuke; Anandkumar, Anima (2020). "Bongard-LOGO: A New Benchmark for Human-Level Concept Learning and Reasoning". Advances in Neural Information Processing Systems. 33. Curran Associates, Inc.: 16468–16480.
- ↑ Depeweg, Stefan; Rothkopf, Contantin A.; Jäkel, Frank (2024). "Solving Bongard Problems With a Visual Language and Pragmatic Constraints". Cognitive Science. 48 (5) e13432. doi:10.1111/cogs.13432. ISSN 1551-6709.
- ↑ Linhares, Alexandre (August 2000). "A glimpse at the metaphysics of Bongard problems". Artificial Intelligence (journal). 121 (1–2): 251–270 – via Elsevier Science Direct.
- ↑ "Zendo—Design History | Kory Heath". Retrieved 2026-08-26.
Further reading
[edit] | This "further reading" section may need cleanup. (August 2026) |
- Maksimov, V. V. (1975). Система, обучающаяся классификации геометрических изображений (A system capable of learning to classify geometric images; as translated from the Russian by Marina Eskina), in Моделирование Обучения и Поведения (Modeling of Learning and Behavior, in Russian), M.S. Smirnov, V.V. Maksimov (eds.), Nauka, Moskva.
- Montalvo, F. S. (1985). Diagram Understanding: the Intersection of Computer Vision and Graphics. M.I.T. Artificial Intelligence Laboratory, A. I. Memo 873, November 1985.
- Saito, K., and Nakano, R. (1993) A Concept Learning Algorithm with Adaptive Search. Proceedings of Machine Intelligence 14 Workshop. Oxford University Press. See pp. 347–363.
- Hofstadter, D. R. and the Fluid Analogies Research Group (1995). Fluid Concepts and Creative Analogies: Computer Models of the Fundamental Mechanisms of Thought. New York: Basic Books.
- Hofstadter, D. R. (1995). On Seeing A’s and Seeing As. Stanford Humanities Review 4/2 pp. 109–121.
- Foundalis, H. (2006). Phaeaco: A Cognitive Architecture Inspired by Bongard’s Problems. Doctoral dissertation, Indiana University, Center for Research on Concepts and Cognition (CRCC), Bloomington, Indiana.
- Anastasiade, J., and Szalwinski, C. (2010). Building Computer-Based Tutors to Help Learners Solve Ill-Structured Problems. In Proceedings of the World Conference on Educational Multimedia, Hypermedia and Telecommunications 2010. Toronto, Ontario, Canada: Association for the Advancement of Computing in Education. pp. 3726–3732.
- Jiang, H., Ma, X. and NVIDIA Research (2022). Bongard-HOI: Benchmarking Few-Shot Visual Reasoning for Human-Object Interactions. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2022.
- Spratley, S., Ehinger, K., and Miller, T. (2023). Unicode Analogies: An Anti-Objectivist Visual Reasoning Challenge. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2023.
- Wüst, A., Tobiasch, T., Helff, L., Ibs, I., Stammer, W., Dhami, D. S., Rothkopf, C. A., and Kersting, K. (2025). Bongard in Wonderland: Visual Puzzles that Still Make AI Go Mad? Proceedings of the 42nd International Conference on Machine Learning, 2025.
- Langenfeld, C., Beger, C., Geng, G., Piriyakulkij, W. T., Hu, K., Pu, Y., and Ellis, K. (2026). Bongards at the Boundary of Perception and Reasoning: Programs or Language? arXiv:2602.03038.
External links
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