Errors in a nonlinear graphic-semantic mapping task resulting from lesions in Boltzmann machine: Is it relevant to dyslexia? AMIR B. GEVA, LIOR SHTRAM, and SHAI POLICKER Electrical and Computer Engineering Department, Ben-Gurion University of the Negev, Beer Sheva, Israel (Received August 26, 1999; Revised October 1, 1999; Accepted October 8, 1999) Abstract One of the most fascinating aspects of brain research is the subject of language. As in many other cases, the malfunctions that occur in different persons for various reasons give us insight on the mechanisms that support our ability to talk, read and listen. Following the work of Plaut and associates, we deal with the dyslexia disorder, which is the overall name for a large number of reading disorders. A Boltzmann machine neural network scheme was trained to implement the nonlinear mapping task of graphic representation into semantic representation, which may model the brain sections responsible for the translation of a written word into meanings and syllables. After training, various types of lesions were applied and the performance of the network was tested in order to measure the effect of each lesion on the error rate and type distribution that were detected. The system’s errors were classified into several categories and the distribution of errors between the categories was studied. Using the simulations, it is demonstrated that a finite scheduling process in the Boltzmann machine causes the distribution of the network’s errors to be unique and different from its expected error distribution. The phenomenon is given a mathematical explanation rooted in the statistical mechanics basics of the Boltzmann machine. Test results suggest the localization of certain reading functions within the network. Comparison is made to relevant types of dyslexia and shows resemblance in major symptoms as well as in certain known side effects. (JINS, 2000, 6, 620– 626.) Keywords: Neural networks, Boltzmann machines, Nonlinear mapping, Simulated annealing, Limited scheduling, Lesions, Pruning, Errors analysis, Dyslexia INTRODUCTION The Reading System and Dyslexia The widely accepted model of the human reading system was presented by Adams (1990). The model describes four specialized processors: graphic, phonetic, semantic, and con- text (Figure 1). The reading process utilizes two different pathways of translation: (1) graphic–phonetic–semantic (using the skills of the spoken language), and (2) graphic– semantic (imaging the word as a picture). Dyslexia is a developmental disorder that characterizes the unexpected failure of a child to acquire the skills of read- ing. It is a name for a wide variety of reading disorders in- cluding (1) visual word–form dyslexia, (2) central dyslexia, (3) surface dyslexia, and (4) deep dyslexia. The most com- mon disorders are surface and deep dyslexia. In the view of the Adams model of the reading system, deep dyslexia can be explained as a fault in the connection between the graphic and phonetic processors, while surface dyslexia can be ex- plained as a fault in the connection between the graphic and semantic processors. These explanations give reasons for most of the disorder’s symptoms, though there are some symptoms left unsolved. Boltzmann Machines and Neural Networks Artificial neural networks (ANN) are mathematical models motivated by the structure of neural cells. Wide spans of industrial applications utilize the ANN model, including pat- tern recognition, control systems, and adaptive filters. An interesting aspect of the ANN is the modeling of cognitive functions. Reprint requests to: Dr. Amir Geva, Electrical and Computer Engineer- ing Department, Ben-Gurion University of the Negev, P.O.B. 653, Beer Sheva, 84105, Israel. E-mail: geva@ee.bgu.ac.il Journal of the International Neuropsychological Society (2000), 6, 620–626. Copyright © 2000 INS. Published by Cambridge University Press. Printed in the USA. 620