Raven's Progressive Matrices is a family of classical intelligence tests that have been widely used in both research and clinical settings. There have been many exciting efforts in AI communities to computationally model various aspects of problem solving such figural analogical reasoning problems. In this paper, we present a series of computational models for solving Raven's Progressive Matrices using analogies and image transformations. We run our models following three different strategies usually adopted by human testees. These models are tested on the standard version of Raven's Progressive Matrices, in which we can solve 57 out 60 problems in it. Therefore, analogy and image transformation are proved to be effective in solving RPM problems.

We present entrepreneurship as a new frontier for developing a computational science of creativity. Entrepreneurship often requires a large upfront investment, but customer feedback typically is delayed, and while the costs of failure can be considerable, the gains from success too can be significant. Given its importance, how can we help novice entrepreneurs learn about entrepreneurship? We analyze the role human coaches play in mentoring novice entrepreneurs by asking critical questions to help generate business models. We propose that virtual coaches may augment the learning of novice entrepreneurs. We describe a preliminary experiment in designing a virtual coach named Errol for learning about entrepreneurship. When a startup team creates an initial business model, Errol uses semantic and lexical analyses to ask questions about the model, leading to model revision. Our experiment indicates that creativity may emerge out of the interactions between the virtual coach and a startup team, and that this human-computer co-creativity may accelerate the process by which a novice entrepreneurs can learn to create intermediate-level business models.

The characteristic inventiveness of the United States is critically dependent on leading technological institutions rising to the occasion to create the next generat ion of leaders who are entrepreneurial in their thinking. This is especially true given recent data showing the significant impact of independent entrepreneurs on the growth of free-enterprise economies.

This paper provides a starting point for the development of metacognition in a common model of cognition. It identifies significant theoretical work on metacognition from multiple disciplines that the authors believe worthy of consideration. After first defining cognition and metacognition, we outline three general categories of metacognition, provide an initial list of its main components, consider the more difficult problem of consciousness, and present examples of prominent artificial systems that have implemented metacognitive components. Finally, we identify pressing design issues for the future.

Computational agents use knowledge representations to reason about the data world they occupy. A theory of consciousness, Integrated Information Theory, suggests beings that are conscious use experiences to reason about the world they occupy. Herein, the question is considered: Is an experience a knowledge representation?

A visual percept is deemed bistable if there are two potential yet mutually exclusive interpretations of the percept between which the human visual system cannot unambiguously choose. Perhaps the most famous example of such a bistable visual percept is the Necker Cube. In this paper, we present a novel computational model of bistable perception based on visual analogy using fractal representations.

Imitation is a well known method for learning. Case-based reasoning is an important paradigm for imitation learning; thus, case retrieval is a necessary step in case-based interpretation of skill demonstrations. In the context of a case-based robot that learns by imitation, each case may represent a demonstration of a skill that a robot has previously observed. Before it may reuse a familiar, source skill demonstration to address a new, target problem, the robot must first retrieve from its case memory the most relevant source skill demonstration. We describe three techniques for visual case retrieval in this context: feature matching, feature transformation matching, and feature transformation matching using fractal representations. We found that each method enables visual case retrieval under a different set of conditions pertaining to the nature of the skill demonstration.

A theory of general intelligence must account for how an intelligent agent can map percepts into actions at the level of human performance. We sketch the outline of a new approach to this perception-to-action mapping. Our approach is based on four ideas: the world exhibits fractal self-similarity at multiple scales, the structure of representations reflects the structure of the world, similarity and analogy form the core of intelligence, and fractal representations provide a powerful technique for perceptual similarity and analogy. We divide our argument into three parts. In the first part, we describe the nature of visual analogies and fractal representations. In the second, we illustrate a technique of fractal analogies and show how it gives human-level performance on an intelligence test called the Odd One Out. In the third, we describe how the fractal technique enables the percept-to-action mapping in a simple, simulated world.

Learning by observation is an important goal in developing complete intelligent robots that learn interactively. We present a visual analogy approach toward an integrated, intelligent system capable of learning skills from observation. In particular, we focus on the task of retrieving a previously acquired case similar to a new, observed skill. We describe three approaches to case retrieval: feature matching, feature transformation, and fractal analogy. SIFT features and fractal encoding were used to represent the visual state prior to the skill demonstration, the final state after the skill has been executed, and the visual transformation between the two states. We discovered that the three methods (feature matching, feature transformation, and fractal analogy) are useful for retrieval of similar skill cases under different conditions pertaining to the observed skills.

We report a novel approach to addressing the Raven’s Progressive Matrices (RPM) tests, one based upon purely visual representations. Our technique introduces the calculation of confidence in an answer and the automatic adjustment of level of resolution if that confidence is insufficient. We first describe the nature of the visual analogies found on the RPM. We then exhibit our algorithm and work through a detailed example. Finally, we present the performance of our algorithm on the four major variants of the RPM tests, illustrating the impact of confidence. This is the first such account of any computational model against the entirety of the Raven’s.

We report a novel approach to visual analogical reasoning, one afforded expressly by fractal representations. We first describe the nature of visual analogies and fractal representations. Next, we exhibit the Fractal Ravens algorithm through a detailed example, describe its performance on all major variants of the Raven's Progressive Matrices tests, and discuss the implications and next steps. In addition, we illustrate the importance of considering the confidence of the answers, and show how ambiguity may be used as a guide for the automatic adjustment of the problem representation. To our knowledge, this is the first published account of a computational model's attempt at the entire Raven's test suite.

We describe a computational model for solving problems from Raven's Progressive Matrices (RPM), a family of standardized intelligence tests. Existing computational models for solving RPM problems generally reason over amodal propositional representations of test inputs. However, there is considerable evidence that humans can also apply imagery-based reasoning strategies to RPM problems, in which processes rooted in perception operate over modal representations of test inputs. In this paper, we present the ''affine model,'' a computational model that simulates modal reasoning by using iconic visual representations together with affine and set transformations over these representations to solve a given RPM problem. Various configurations of the affine model successfully solve between 33 and 38 of the 60 problems on the Standard Progressive Matrices, which matches levels of performance for typically developing 9- to 11-year-old children. This suggests that, for at least a sizeable subset of RPM problems, it is not always necessary to extract amodal symbols in order to arrive at the correct answer, and iconic visual representations constitute a sufficient form of representation to successfully solve these problems. We intend for the affine model to serve as a complementary computational account to existing propositional models, which together may provide an integrated, dual-process account of human problem solving on the RPM.

A theory of general intelligence must account for how an intelligent agent can map percepts into actions at the level of human performance. We describe a new approach to this percept-to-action mapping. Our approach is based on four ideas: the world exhibits fractal self-similarity at multiple scales, the design of mind reflects the design of the world, similarity and analogy form the core of intelligence, and fractal representations provide a powerful technique for perceptual similarity and analogy. We divide our argument into two parts. In the first part, we describe a technique of fractal analogies and show how it gives human-level performance on an intelligence test called the Odd One Out. In the second, we describe how the fractal technique enables the percept-to-action mapping in a simple, simulated world.

Although the problems on Raven’s Progressive Matrices intelligence tests resemble geometric analogies, studies of human behavior suggest the existence of two qualitatively distinct types of strategies: verbal strategies that use propositional representations and visual strategies that use iconic representations. However, all prior computational models implemented to solve these tests have modeled only verbal strategies: they translate problems into purely propositional representations. We examine here the other half of what may be a dual-process mechanism of reasoning in humans: visual strategies that use iconic representations. In particular, we present two different algorithms that use iconic visual representations to address problems found on the Advanced Progressive Matrices test, the best of which yields performances at levels equivalent to the 75th percentile for human test takers aged from 20 to 62 years-old. We discuss implications of our work for understanding the computational nature of Raven’s and visual analogy in problem solving.

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 technique for addressing visual analogy problems on the Odd One Out test. In our technique, the relationship between images is encoded fractally, capturing inherent self-similarity. The technique starts 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 technique automatically starts with searching for similarity between simpler relationships, but, if that is not sufficient to resolve ambiguity, it automatically searches for similarity between higher-order relationships. We present preliminary results from applying the fractal technique on a representative subset of the problems from the Odd One Out test.

We present two visual algorithms, called the affine and fractal methods, which each solve a considerable portion of the Raven’s Progressive Matrices (RPM) test. The RPM is considered to be one of the premier psychometric measures of general intelligence. Current computational accounts of the RPM assume that visual test inputs are translated into propositional representations before further reasoning takes place. We propose that visual strategies can also solve RPM problems, in line with behavioral evidence showing that humans do use visual strategies to some extent on the RPM. Our two visual methods currently solve RPM problems at the level of typical 9- to 10-year-olds.