Endowing machines with abstract reasoning ability has been a long-term research topic in artificial intelligence. Raven's Progressive Matrix (RPM) is widely used to probe abstract visual reasoning in machine intelligence, where models will analyze the underlying rules and select one image from candidates to complete the image matrix. Participators of RPM tests can show powerful reasoning ability by inferring and combining attribute-changing rules and imagining the missing images at arbitrary positions of a matrix. However, existing solvers can hardly manifest such an ability in realistic RPM tests. In this paper, we propose a deep latent variable model for answer generation problems through Rule AbstractIon and SElection (RAISE). RAISE can encode image attributes into latent concepts and abstract atomic rules that act on the latent concepts. When generating answers, RAISE selects one atomic rule out of the global knowledge set for each latent concept to constitute the underlying rule of an RPM. In the experiments of bottom-right and arbitrary-position answer generation, RAISE outperforms the compared solvers in most configurations of realistic RPM datasets. In the odd-one-out task and two held-out configurations, RAISE can leverage acquired latent concepts and atomic rules to find the rule-breaking image in a matrix and handle problems with unseen combinations of rules and attributes.

翻译：使机器具备抽象推理能力一直是人工智能领域的长期研究课题。瑞文推理矩阵（RPM）广泛用于探究机器智能中的抽象视觉推理，模型需分析潜在规则并从候选图像中选择一幅以补全图像矩阵。RPM测试的参与者能够通过推断并组合属性变化规则，想象矩阵中任意缺失位置的图像，展现出强大的推理能力。然而，现有求解器难以在真实RPM测试中体现这一能力。本文提出一种基于规则抽象与选择的深层潜变量模型（RAISE），用于答案生成问题。RAISE能将图像属性编码为潜在概念，并抽象出作用于潜在概念的原子规则。在生成答案时，RAISE从全局知识集中为每个潜在概念选择一条原子规则，构成RPM的潜在规则。在右下角及任意位置答案生成实验中，RAISE在大多数真实RPM数据集配置下优于对比求解器。在异常检测任务及两种保留配置中，RAISE可利用已习得的潜在概念与原子规则识别矩阵中的异常图像，并处理包含未见规则与属性组合的问题。