Keith McGreggor

A computational model for solving problems from the Raven's Progressive Matrices intelligence test using iconic visual representations

We describe a computational model for solving problems from Ravens 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.

Finding the odd one out: a fractal analogical approach

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.

Fractal analogies for general intelligence

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.

Fractals and Ravens

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 Ravens 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 models attempt at the entire Ravens test suite.

Visual Case Retrieval for Interpreting Skill Demonstrations

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.

Bistable Perception and Fractal Reasoning

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.

A Computational Strategy for Fractal Analogies in Visual Perception

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.

Reports of the AAAI 2010 Conference Workshops

The AAAI-10 Workshop program was held Sunday and Monday, July 11–12, 2010 at the Westin Peachtree Plaza in Atlanta, Georgia. The AAAI-10 workshop program included 13 workshops covering a wide range of topics in artificial intelligence. The titles of the workshops were AI and Fun, Bridging the Gap between Task and Motion Planning, Collaboratively-Built Knowledge Sources and Artificial Intelligence, Goal-Directed Autonomy, Intelligent Security, Interactive Decision Theory and Game Theory, Metacognition for Robust Social Systems, Model Checking and Artificial Intelligence, Neural-Symbolic Learning and Reasoning, Plan, Activity, and Intent Recognition, Statistical Relational AI, Visual Representations and Reasoning, and Abstraction, Reformulation, and Approximation. This article presents short summaries of those events.