A Bongard problem is a kind of puzzle invented by the Russian

computer scientist A computer scientist is a person who is trained in the academic study of computer science. Computer scientists typically work on the theoretical side of computation, as opposed to the hardware side on which computer engineers mainly focus ( ...

Mikhail Moiseevich Bongard (Михаил Моисеевич Бонгард, 1924–1971), probably in the mid-1960s. They were published in his 1967 book on

pattern recognition Pattern recognition is the automated recognition of patterns and regularities in data. It has applications in statistical data analysis, signal processing, image analysis, information retrieval, bioinformatics, data compression, computer graphic ...

. The objective is to spot the differences between the two sides. Bongard, in the introduction of the book (which deals with a number of topics including

perceptron In machine learning, the perceptron (or McCulloch-Pitts neuron) is an algorithm for supervised classification, supervised learning of binary classification, binary classifiers. A binary classifier is a function which can decide whether or not an ...

s) credits the ideas in it to a group including

M. N. Vaintsvaig ( ; ; pl. ; ; 1512, from Middle French , literally "my lord") is an honorific title that was used to refer to or address the eldest living brother of the king in the French royal court. It has now become the customary French title of resp ...

, V. V. Maksimov, and

M. S. Smirnov ( ; ; pl. ; ; 1512, from Middle French , literally "my lord") is an honorific title that was used to refer to or address the eldest living brother of the king in the French royal court. It has now become the customary French title of respec ...

Overview

The idea of a Bongard problem is to present two sets of relatively simple diagrams, say ''A'' and ''B''. All the diagrams from set ''A'' have a common factor or attribute, which is lacking in all the diagrams of set ''B''. The problem is to find, or to formulate, convincingly, the common factor. The problems were popularised by their occurrence in the 1979 book '' Gödel, Escher, Bach'' by

Douglas Hofstadter Douglas Richard Hofstadter (born February 15, 1945) is an American scholar of cognitive science, physics, and comparative literature whose research includes concepts such as the sense of self in relation to the external world, consciousness, an ...

, himself a composer of Bongard problems. According to Hofstadter, "the skill of solving Bongard problems lies very close to the core of 'pure' intelligence, if there is such a thing". Bongard problems are also at the heart of the game Zendo.

Scientific works on Bongard problems

* Bongard, M. M. (1970). Pattern Recognition. Rochelle Park, N.J.: Hayden Book Co., Spartan Books. (Original publication: Проблема Узнавания, Nauka Press, Moscow, 1967) * 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. * Hofstadter, D. R. (1979). Gödel, Escher, Bach: an Eternal Golden Braid. New York: Basic Books. * 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. * Hofstadter, D. R. (1997). Le Ton beau de Marot. New York: Basic Books. * Linhares, A. (2000)
A glimpse at the metaphysics of Bongard problems

Artificial Intelligence Artificial intelligence (AI) is intelligence—perceiving, synthesizing, and inferring information—demonstrated by machine A machine is a physical system using Power (physics), power to apply Force, forces and control Motion, moveme ...

, Volume 121, Issue 1-2, pp. 251–270. * 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. Foundalis left the field in 2008 due to ethical concerns regarding machines that can pass as human, and restarted in 2011 having considered that human suicide bombers are already here anyway. * Anastasiade, J., and Szalwinski, C. (2010). Building Computer-Based Tutors to Help Learners Solve Ill-Structured Problems. I
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. * Nie, W. and NVIDIA Research (2020)
Bongard-LOGO: A New Benchmark for Human-Level Concept Learning and Reasoning
Advances in Neural Information Processing Systems, Volume 33, pp. 16468-16480. * 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.

References

External links

{{Wikibooks, Puzzles, Bongard problems
The On-Line Encyclopedia of Bongard Problems
Puzzles Cognitive science Cognitive psychology Computer-related introductions in 1967