Modelling Brain Function: The World of Attractor Neural Networks

The study of the physics of the brain from the standpoint of dynamical systems was very popular during the 1980's. The theory of chaotic dynamical systems, and the accompanying concepts of strange attractors, horseshoe maps, and fractal basins of attraction was the subject of intense research at that time. It was inevitable perhaps that these theories would be applied to the understanding of the brain, given the dynamical nature of the neuronal synapse. This book, published in 1989, gives a good overview of what was known at the time. It could be read by anyone with a background in dynamical systems and some elementary knowledge of brain biology. The mathematics is also straightforward in that the author does not bring in any of the heavy tools from differential topology or measure theory, which is normally done in discussions of dynamical systems. There are some points made in the book that must be understood by the reader because the author feels that they are needed to build a successful model of the brain. For example, he discusses the notion of an `input system', which is a system that, for each input, produces and output with the same "status." Cognitive discrimination must be used at the input level, if one is to avoid the use of the `homunculus' (the little external observer), for distinguishing between "good" and "bad" outputs. The major task in the author's view is to produce "exceptional" input-output relations, i.e. relations that correspond to intuitions about cognitive processes. A successful brain model, i.e. one that is able to incorporate memory, should be able to distinguish between stimuli that are familiar from those that are to be submitted to the brain for processing or learning. Thus the model must avoid the use of what the author calls `spontaneous computations', which require an external observer (the homunculus again) to interpret the relation between the input and the output. The author gives an example of a system that performs only spontaneous computations early on in the book. Hence the author proposes the use of artificial neural networks (ANNs) to avoid the occurrence of spontaneous computations. An ANN organizes stimuli in association classes represented by an attractor, and all the stimuli in a particular class are associated with the attractor to which they flow. The author feels that ANNs are more adept at respecting the requirement that for mental computations, which are essentially operations on temporal sequences of data, some record of the initial input sequence must be carried along on a parallel channel, in order to provide the outcome with specific "meaning" and a correspondence to the assigned task. These considerations on the dependence of the processing on the initial input motivate the author to discuss the role of ergodicity in the dynamics of the neural systems of the brain. As the author shows, any generic system subjected to noise will be ergodic, so that eventually the system will access eac