A Chaotic Neural Network Model of Insightful Problem Solving and the Generation Process of Constraints

A Chaotic Neural Network Model of Insightful Problem Solving and the Generation Process of Constraints Yuichiro Wajima (wajima@nm.hum.titech.ac.jp) Keiga Abe (abe@nm.hum.titech.ac.jp) Masanori Nakagawa (nakagawa@nm.hum.titech.ac.jp) Graduate School of Decision Science Technology, Tokyo Institute of Technology 2-12-1, Ookayama, Meguro-Ku, Tokyo, 152-8552, Japan Abstract The solution of an insightful problem needs a drastic change from the impasse to the insight stage. It is assumed that in this type of a problem, solvers encounter the impasse stage because of special constraints like common sense. Abe, Wajima, and Nakagawa (2003) proposed a model of insight problem solving using a chaotic neural network. The model successfully simulates an insight problem. Based on this system, we developed a new model to explain the generation process of new constraints. We hypothesized that once people have solved a problem using insight, the experience of the insight generates new constraints. In order to verify the above hypothesis, we conducted a psychological experiment and executed a computational simulation of the model. In the experiment, participants were instructed to solve the two pictorial puzzles, one was an insight problem and the other was a non-insight problem. The experimental results showed that the solution of the insight problem generated a new constraint, while inhibiting the solution of non-insight problem. We constructed a new model that represents a reinforcement state after solving the insightful problem and several simulations were executed. The result of model's simulation showed a close similarity with the experimental result. The model successfully simulated the process of generation of new constraints. Keywords: insight; constraint; generation process; neural network; modeling. Introduction Insight is the process by which a problem is suddenly solved after an impasse, which is the period when the solver is unable to solve the problem (Wallas, 1926). The process of insightful problem solving is the change from the state of impasse to the state of insight, when problem is solved. In previous studies, it is generally assumed that the impasse stage is due to constraints such as common sense (Knoblich, Ohlsson, Haider & Rhenius, 1999). Some constraints can be effective in guiding how people tackle everyday problems, but for problems that require some new insight, such constraints can obstruct the solver from seeing the solution to the problem. It has been suggested that insight is the product of breaking away from such constraints by discovering new effective directions during previous failed attempts at solving the problem. Abe, Wajima, and Nakagawa (2003) proposed a model for insight problem solving using chaotic neural network. This model consists of two components, namely, a constraint component, and an avoidance component. In order to represent these components, a system of simultaneous differential equations is proposed, with each variable denoting a single node of a neural network. In the model, the constraint component is represented by controlling the ease with which the nodes can activate, while the avoidance component is represented by the term causing the system to move in the direction in which the value of an evaluation function becomes the largest. This movement corresponds to the avoidance reaction of humans that is a result of failed trials. The model successfully simulates an insight problem. However, in the previous research, sufficient consideration was not given to the generation process of constraints. Furthermore, the previous research did not refer to the possibility of the insight experience generating a new constraint due to reinforcement, once people had experienced solving a problem using insight. We report here the development of a new model based on the insightful problem solving model to represent the generation of new constraints by hypothesizing that once people solved a problem using insight, the experience of the insight generates new constraints. In order to verify the above hypothesis, we conducted a psychological experiment and a computational simulation of the present model. First, we set up an experiment in order to show that new constraints are generated by insight. In this experiment, participants were instructed to solve a non-insight problem after solving an insight problem to examine how the experience of insight subsequently changed the performance. Second, we constructed a new model, by adding a mechanism to the previous model; a new constraint was generated by reinforcement of insight experience, while computational simulations were executed according to the variation of reinforcement values. Hypothesis We explain our hypothesis of a new constraint generating process by using the T-puzzle and the Arrow-puzzle solving process. The T-puzzle is an example of an insight problem (Figure 1, 2). In the T-puzzle, the solver constructs a T using pieces of the following four shapes: a triangle, a small trapezoid, a large-trapezoid, and a pentagon with a notch.