Abstract reasoning ability is fundamental to human intelligence. It enables humans to uncover relations among abstract concepts and further deduce implicit rules from the relations. As a well-known abstract visual reasoning task, Raven's Progressive Matrices (RPM) are widely used in human IQ tests. Although extensive research has been conducted on RPM solvers with machine intelligence, few studies have considered further advancing the standard answer-selection (classification) problem to a more challenging answer-painting (generating) problem, which can verify whether the model has indeed understood the implicit rules. In this paper we aim to solve the latter one by proposing a deep latent variable model, in which multiple Gaussian processes are employed as priors of latent variables to separately learn underlying abstract concepts from RPMs; thus the proposed model is interpretable in terms of concept-specific latent variables. The latent Gaussian process also provides an effective way of extrapolation for answer painting based on the learned concept-changing rules. We evaluate the proposed model on RPM-like datasets with multiple continuously-changing visual concepts. Experimental results demonstrate that our model requires only few training samples to paint high-quality answers, generate novel RPM panels, and achieve interpretability through concept-specific latent variables.

翻译：抽象推理能力是人类智能的基础，它使人类能够发现抽象概念间的关联，并进一步从这些关联中推断隐含规则。瑞文渐进矩阵作为一项著名的抽象视觉推理任务，广泛用于人类智商测试。尽管基于机器智能的RPM求解器已有大量研究，但鲜有工作将标准答案选择问题进一步推进至更具挑战性的答案绘制问题——后者能验证模型是否真正理解隐含规则。本文通过提出深度潜变量模型来解决后者：该模型采用多个高斯过程作为潜变量的先验，从RPM中分别学习底层抽象概念，因此所提模型在概念特定潜变量方面具有可解释性。基于已习得的概念变化规则，潜在高斯过程还可为答案绘制提供有效的外推方法。我们在包含多个连续变化视觉概念的类RPM数据集上评估该模型。实验结果表明，我们的模型仅需少量训练样本即可绘制高质量答案、生成新颖RPM面板，并通过概念特定潜变量实现可解释性。