Fractally Finding the Odd One Out: An Analogical Strategy For Noticing Novelty

The Odd One Out test of intelligence consists of 3x3 matrix reasoning problems organized in 20 levels of difficulty. Addressing problems on this test appears to require integration of multiple cognitive abilities usually associated with creativity, including visual encoding, similarity assessment, pattern detection, and analogical transfer. We describe a novel fractal strategy for addressing visual analogy problems on the Odd One Out test. In our strategy, the relationship between images is encoded fractally, capturing important aspects of similarity as well as inherent self-similarity. The strategy starts with fractal representations encoded at a high level of resolution, but, if that is not sufficient to resolve ambiguity, it automatically adjusts itself to the right level of resolution for addressing a given problem. Similarly, the strategy starts with searching for fractally-derived similarity between simpler relationships, but, if that is not sufficient to resolve ambiguity, it automatically shifts to search for such similarity between higher-order relationships. We present preliminary results and initial analysis from applying the fractal technique on nearly 3,000 problems from the Odd One Out test. Computational Psychometrics Psychometrics entails the theory and technique of quantitative measurement of intelligence, including factors such as personality, aptitude, knowledge, creativity, and academic achievement. AI research on "computational psychometrics" dates at least as far back as Evan’s (1968) Analogy program, which addressed geometric analogy problems on the Miller Geometric Analogies test. Recently, Bringsjord & Schimanski (2003) have proposed psychometric AI, i.e., AI that can pass psychometric tests of intelligence, as a possible mechanism for measuring and comparing AI. Copyright © 2011, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. Visual analogies are common on standardized intelligence tests that measure personality, aptitude, knowledge, creativity, and academic achievement, such as the Miller’s Geometric Analogies test, the Wechsler’s intelligence test (Wechsler 1939), and the Raven’s Progressive Matrices test (Raven et al. 1998). Some tests of intelligence, such as the Wechsler’s, contain a mix of verbal and visual questions. Others, such as the Raven’s Progressive Matrices test, consist of purely visual analogy problems. There is general agreement that addressing the matrix reasoning problems on tests such as Raven’s requires integration of multiple abilities including visual encoding, pattern detection, rule integration, similarity assessment, analogical transfer, and problem solving. Most computational models of the Raven’s intelligence test rely on propositional representations of the visual inputs (e.g., Bringsjord & Schimanski 2003; Carpenter, Just, & Shell 1990; Lovett, Forbus, & Usher 2007). Given that the inputs and outputs of all problems on the Raven’s test are visual, there have been have some recent attempts at building computational models based on purely visual representations and reasoning (Kunda, McGreggor, & Goel 2010). The standard Raven’s test however consists of only 60 problems. In this paper, we present preliminary results and initial analysis from applying our technique to the much larger corpus of problems from the Odd One Out test of intelligence containing nearly 3000 problems (Hampshire 2010). Like our prior work on Raven’s (McGreggor et al. 2011; Kunda et al. 2010), our technique here uses fractal representations of the problems on the test. However, our work on the Odd One Out test develops also develops fractal representations into a cognitive strategy. Two of the advantages of our new strategy are that (1) the technique starts with fractal representations encoded at a high level of resolution, but, if that is not sufficient to resolve ambiguity, it automatically adjusts itself to the right level of resolution for addressing a given problem, and (2) the strategy starts with searching for similarity between simpler relationships, Advances in Cognitive Systems: Papers from the 2011 AAAI Fall Symposium (FS-11-01)