Visual problem solving in autism, psychometrics, and AI: the case of the Raven's Progressive Matrices intelligence test
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Much of cognitive science research and almost all of AI research into problem solving has focused on the use of verbal or propositional representations. However, there is significant evidence that humans solve problems using different representational modalities, including visual or iconic ones. In this dissertation, I investigate visual problem solving from the perspectives of autism, psychometrics, and AI. Studies of individuals on the autism spectrum show that they often use atypical patterns of cognition, and anecdotal reports have frequently mentioned a tendency to "think visually." I examined one precise characterization of visual thinking in terms of iconic representations. I then conducted a comprehensive review of data on several cognitive tasks from the autism literature and found numerous instances indicating that some individuals with autism may have a disposition towards visual thinking. One task, the Raven's Progressive Matrices test, is of particular interest to the field of psychometrics, as it represents one of the single best measures of general intelligence that has yet been developed. Typically developing individuals are thought to solve the Raven's test using largely verbal strategies, especially on the more difficult subsets of test problems. In line with this view, computational models of information processing on the Raven's test have focused exclusively on propositional representations. However, behavioral and fMRI studies of individuals with autism suggest that these individuals may use instead a predominantly visual strategy across most or all test problems. To examine visual problem solving on the Raven's test, I first constructed a computational model, called the Affine and Set Transformation Induction (ASTI) model, which uses a combination of affine transformations and set operations to solve Raven's problems using purely pixel-based representations of problem inputs, without any propositional encoding. I then performed four analyses using this model. First, I tested the model against three versions of the Raven's test, to determine the sufficiency of visual representations for solving this type of problem. The ASTI model successfully solves 50 of the 60 problems on the Standard Progressive Matrices (SPM) test, comparable in performance to the best computational models that use propositional representations. Second, I evaluated model robustness in the face of changes to the representation of pixels and visual similarity. I found that varying these low-level representational commitments causes only small changes in overall performance. Third, I performed successive ablations of the model to create a new classification of problem types, based on which transformations are necessary and sufficient for finding the correct answer. Fourth, I examined if patterns of errors made on the SPM can provide a window into whether a visual or verbal strategy is being used. While many of the observed error patterns were predicted by considering aspects of the model and of human behavior, I found that overall error patterns do not seem to provide a clear indicator of strategy type. The main contributions of this dissertation include: (1) a rigorous definition and examination of a disposition towards visual thinking in autism; (2) a sufficiency proof, through the construction of a novel computational model, that visual representations can successfully solve many Raven's problems; (3) a new, data-based classification of problem types on the SPM; (4) a new classification of conceptual error types on the SPM; and (5) a methodology for analyzing, and an analysis of, error patterns made by humans and computational models on the SPM. More broadly, this dissertation contributes significantly to our understanding of visual problem solving.