More than 50 years ago, Bongard introduced 100 visual concept learning problems as a challenge for artificial vision systems. These problems are now known as Bongard problems. Although they are well known in cognitive science and artificial intelligence, only very little progress has been made toward building systems that can solve a substantial subset of them. In the system presented here, visual features are extracted through image processing and then translated into a symbolic visual vocabulary. We introduce a formal language that allows representing compositional visual concepts based on this vocabulary. Using this language and Bayesian inference, concepts can be induced from the examples that are provided in each problem. We find a reasonable agreement between the concepts with high posterior probability and the solutions formulated by Bongard himself for a subset of 35 problems. While this approach is far from solving Bongard problems like humans, it does considerably better than previous approaches. We discuss the issues we encountered while developing this system and their continuing relevance for understanding visual cognition. For instance, contrary to other concept learning problems, the examples are not random in Bongard problems; instead they are carefully chosen to ensure that the concept can be induced, and we found it helpful to take the resulting pragmatic constraints into account.

中文翻译：

---

用视觉语言和语用约束解决邦加德问题


50 多年前，Bongard 引入了 100 个视觉概念学习问题作为对人工视觉系统的挑战。这些问题现在被称为邦加德问题。尽管它们在认知科学和人工智能领域众所周知，但在构建能够解决其中大部分问题的系统方面只取得了很少的进展。在此介绍的系统中，通过图像处理提取视觉特征，然后将其转换为符号视觉词汇。我们引入了一种形式语言，允许基于该词汇表表示组合视觉概念。使用这种语言和贝叶斯推理，可以从每个问题中提供的示例中归纳出概念。我们发现高后验概率的概念与 Bongard 本人针对 35 个问题的子集提出的解决方案之间存在合理的一致性。虽然这种方法远不能像人类一样解决邦加德问题，但它比以前的方法要好得多。我们讨论了开发该系统时遇到的问题及其与理解视觉认知的持续相关性。例如，与其他概念学习问题相反，Bongard 问题中的示例不是随机的；相反，它们是经过精心选择的，以确保概念可以被归纳出来，我们发现考虑到由此产生的实用约束是有帮助的。