# Bongard problem

A Bongard problem is a visual puzzle requiring classification of two sets of images based on a hidden rule, used to study human and machine pattern recognition and abstract reasoning.

A Bongard problem is a type of visual puzzle in which a person or machine must identify a rule that distinguishes two sets of images, typically presented side by side. Each set contains six simple diagrams, and the solver must find a binary classification criterion that separates the left set from the right set. The problems were introduced by Soviet computer scientist Mikhail Bongard in his 1970 book "Pattern Recognition," and they have since become a standard benchmark in cognitive science and artificial intelligence research.

Bongard problems are notable for their combination of perceptual and conceptual difficulty. The rules can involve geometric properties such as shape, size, orientation, number, or spatial arrangement, but they often require abstract reasoning about relationships, symmetry, or even semantic categories. Because the images are deliberately minimal, the problems isolate the core challenge of discovering a general rule from limited examples, a task that is trivial for humans in many cases but notoriously difficult for machines.

## Historical Context

Mikhail Bongard developed these problems while working at the Institute of Cybernetics in Moscow, aiming to understand the mechanisms of pattern recognition in biological and artificial systems. His 1970 monograph presented 100 problems, each designed to test different aspects of visual abstraction. The problems gained wider attention in the West through Douglas Hofstadter's 1979 book "Gödel, Escher, Bach," which discussed them as examples of the "tacit knowledge" involved in perception and analogy-making. Hofstadter later used Bongard problems in his research at the [MIT Computer Science and Artificial Intelligence Laboratory](https://www.wikiprompt.org/wiki/mit-csail), where he and his students developed computational models to solve them.

## Structure and Examples

A typical Bongard problem presents two boxes, labeled A and B, each containing six small diagrams. The solver must find a rule that all six diagrams in box A satisfy, while none of the six in box B do. For instance, one problem might have box A containing only shapes with an even number of sides, and box B containing odd-sided shapes. Another might require recognizing that all figures in box A are oriented vertically, while those in box B are horizontal. The rules can be hierarchical, such as "all shapes in A contain a small circle inside a larger triangle," or they can involve comparisons between elements, like "the number of black dots equals the number of white squares."

Some problems are deliberately ambiguous, with multiple plausible rules, which highlights the role of prior knowledge and context in interpretation. The difficulty ranges from trivial (e.g., color or size) to highly abstract (e.g., "the figures in A are all topologically equivalent to a circle").

## Role in Cognitive Science

Cognitive scientists have used Bongard problems to study human concept formation, inductive reasoning, and the nature of visual intelligence. Researchers such as [Joshua Tenenbaum](https://www.wikiprompt.org/wiki/joshua-tenenbaum) and [Brendan Lake](https://www.wikiprompt.org/wiki/brendan-lake) at [Stanford](https://www.wikiprompt.org/wiki/stanford-ai-lab) and [MIT](https://www.wikiprompt.org/wiki/mit-csail) have cited them as examples of the "fast mapping" and "one-shot learning" abilities that humans possess but machines lack. The problems require not just pattern matching but also the ability to generate and test hypotheses about abstract categories, a process that remains poorly understood. Studies have shown that human solvers often rely on verbalizable rules, suggesting a link between language and visual reasoning.

## Machine Learning and AI Benchmarks

In the field of [artificial-intelligence](https://www.wikiprompt.org/wiki/artificial-intelligence), Bongard problems have become a benchmark for evaluating visual reasoning capabilities. Early attempts in the 1970s and 1980s used symbolic AI approaches, but they struggled with the open-ended nature of the rules. With the rise of [machine-learning](https://www.wikiprompt.org/wiki/machine-learning) and [deep-learning](https://www.wikiprompt.org/wiki/deep-learning), researchers have developed new datasets based on Bongard problems, such as the Bongard-HOI dataset (2020) and the Bongard-LOGO dataset (2022), which generate large numbers of problems programmatically. These datasets are used to test [neural networks](https://www.wikiprompt.org/wiki/neural-network) and [transformer](https://www.wikiprompt.org/wiki/transformer)-based models, including [large language models](https://www.wikiprompt.org/wiki/large-language-model) when combined with visual encoders.

Current state-of-the-art systems still perform far below human accuracy on novel Bongard problems. For example, a 2023 study found that even the best models achieved only around 60% accuracy on a set of 100 problems, compared to near-perfect human performance. The difficulty lies in the need for compositional reasoning and the ability to generalize from a handful of examples, which contrasts with the data-hungry nature of most [deep-learning](https://www.wikiprompt.org/wiki/deep-learning) approaches. Researchers at [Google DeepMind](https://www.wikiprompt.org/wiki/google-deepmind) and [OpenAI](https://www.wikiprompt.org/wiki/openai) have explored using Bongard problems to probe the reasoning capabilities of their models, but no system has yet mastered them.

## Related Concepts and Future Directions

The problems are closely related to other visual reasoning tasks such as Raven's Progressive Matrices, which involve completing a pattern in a grid, and the Abstraction and Reasoning Corpus (ARC) introduced by [François Fleuret](https://www.wikiprompt.org/wiki/francois-fleuret) in 2019. ARC shares the goal of measuring general intelligence through visual puzzles, but it uses a different format. Some researchers argue that Bongard problems are more challenging because they require discovering a binary rule from positive and negative examples, whereas ARC tasks often involve transformation rules.

Future work may involve combining Bongard problems with [curriculum learning](https://www.wikiprompt.org/wiki/curriculum-learning) or [meta-learning](https://www.wikiprompt.org/wiki/meta-learning) approaches, or using them to evaluate the emergent reasoning abilities of [generative AI](https://www.wikiprompt.org/wiki/generative-ai) systems. As of the mid-2020s, no published system has achieved human-level performance on a broad set of Bongard problems, making them an active area of research in the quest for artificial general intelligence.

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Source: https://www.wikiprompt.org/wiki/bongard-problem
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Last updated: 2026-09-14T04:21:56.895945+00:00