RI: Small: Addressing Visual Analogy Problems on the Raven's Intelligence Test

该提案旨在创建纯粹基于图像的推理方法来解决视觉类比问题，特别是所谓的Raven's Progressive Matrices （RPM）问题。该项目借鉴了人类认知、计算机科学和数学研究的最新成果。瑞文渐进矩阵完全由视觉类比问题组成，其中几何图形矩阵中有一个条目缺失，并且必须从一组答案选项中选择正确的缺失条目。最近对RPM数据的分析表明，尽管总体而言，自闭症患者在大多数智力测试中的表现明显低于正常发育的个体，但在瑞文测试中，两组的表现是相当的。这一数据与“图像思维”假说相一致，该假说被认为是自闭症的一种潜在的部分认知解释。在人工智能和心理学中，目前解决RPM问题的理论首先将视觉输入转换为语言表征，然后对语言表征进行处理。相比之下，这个项目探索了一个假设，即许多RPM问题可以只用视觉表示来解决，而不需要从输入图像中提取任何口头表示。该项目将开发和分析计算技术，仅用视觉表示来解决RPM问题。特别是，该项目将开发一种基于仿射变换的新算法来解决RPM问题，以及使用分形编码的第二种算法。通过仿射和分形这两种方法，该项目试图在RPM上实现人类水平的性能，即正确解决问题的百分比。这两种算法还将在包含数千个视觉类比问题的“奇数人出局”语料库上进行测试。该项目将正式描述仿射和分形算法适用的视觉类比问题集，分析算法的计算特性，构建对特定类别问题的正确性证明，并将两种算法所犯的错误与两组人类（典型的发展个体和自闭症个体）所犯的错误进行比较。该项目将对可视化算法进行参数化，以检测在哪些设置下，算法对RPM问题产生的错误模式最接近于两组人类的错误模式。自闭症是一个日益受到社会关注的重要问题。虽然图像思维假说长期以来一直是对自闭症认知的重要见解，而且支持该假说的经验证据——包括行为和神经影像学证据——也在不断增加，但目前还没有相应的计算模型。拟议的研究将有助于为这一假设提供一个计算形式，并可能有助于建立自闭症患者的视觉思维倾向。RPM被认为是智力的核心测试之一，尽管有一些关于RPM问题的视觉空间性质的建议，但目前解决此类视觉类比问题的所有计算模型都使用对输入图像的命题表示进行顺序处理。这个项目的算法依赖于RPM的可视化表示，可以为智能测试提供新的见解。最后，虽然分形编码已经在计算机图形学中用于生成图像，在计算机视觉中用于图像处理中的纹理分析，但本项目在智力测试中使用分形编码进行视觉类比将有助于分形计算的知识。

This proposal aims to create purely image-based reasoning methods for solving visual analogy problems, particularly so-called Raven's Progressive Matrices (RPM) problems. The project draws on recent results from the study of human cognition as well computer science and mathematics. Raven's Progressive Matrices consist wholly of visual analogy problems in which a matrix of geometric figures is presented with one entry missing, and the correct missing entry must be selected from a set of answer choices. Recent analysis of RPM data suggests that although in general the performance of individuals with autism on most intelligence tests is significantly inferior to that of typically developing individuals, on the Raven's test the performance of the two groups is comparable. This data is consistent with the "Thinking in Pictures" hypothesis that has been proposed as a potential, partial cognitive explanation of autism. In both artificial intelligence and psychology, current theories of solving RPM problems first convert the visual inputs into verbal representations and then process the verbal representations. In contrast, this project explores the hypothesis that many RPM problems can be solved using only visual representations, without extracting any verbal representations from the input images. This project will develop and analyze computational techniques for addressing RPM problems with only visual representations. In particular, this project will develop a novel algorithm based on affine transformations for addressing RPM problems as well as a second algorithm that makes use of fractal encodings. With both approaches -- affine and fractal -- the project seeks to achieve human-level performance on RPM in terms of percentages of problems solved correctly. The two algorithms will also be tested on the "odd-man-out" corpus that contains thousands of visual analogy problems. The project will formally characterize the set of visual analogy problems for which the affine and fractal algorithms are applicable, analyze the computational properties of the algorithms, construct proofs of their correctness for specific classes of problems, and compare the errors made by the two algorithms with those made by two groups of humans -- typically developing individuals and individuals with autism. The project will parameterize the visual algorithms to detect the settings under which the patterns of errors made by an algorithm on RPM problems most closely match the error patterns of the two human groupings. Autism is an important problem of growing social concern. While the thinking-in-pictures hypothesis has long been a significant insight into cognition in autism, and empirical evidence -- both behavioral and neuroimaging -- in its favor is increasing, there have been no computational models for it. The proposed research would help provide a computational form to this hypothesis and may help establish a disposition towards visual thinking with autism. RPM is considered one of the core tests of intelligence, and although there have been several suggestions about the visuospatial nature of RPM problems, all current computational models addressing such visual analogy problems use sequential processing on propositional representations of the input images. The algorithms from this project that rely on visual representations for RPM could provide new insights into intelligence testing. Lastly, while fractal encodings have been used in computer graphics for generating images and in computer vision for texture analysis in image processing, this project's use of fractal encodings for visual analogies on intelligence tests will contribute to knowledge of fractal computing.