Collective Computation of Many-body Properties by Neural Networks

INTRODUCTION Artiicial neural networks constitute a novel class of many-body systems in which the particles are neuron-like units and the interactions are weighted synapse-like connections between these units. 1;2 The most extraordinary feature of these systems is that the interactions are subject to modiication, depending on the states recently visited by the system. Thus, as the network experiences varied stimuli, knowledge can be stored in the neuron-neuron interactions, for later retrieval in some information-processing task. Indeed, multilayered, feedforward networks of analog neurons can be taught by example to solve complex pattern-categorization problems using the backprop-agation learning algorithm 3 or other procedures for modifying connection weights. During the learning process, inner neurons may evolve into useful feature detectors tailored to regularities or correlations inherent in the ensemble of input stimulus patterns and desired output response patterns used for training. The system builds an internal representation, or model, of its pattern environment, which may provide a good approximation to the actual rules determining the underlying input-output map. Accordingly, the artii-cial neural network may possess a useful generalization or predictive ability, as demonstrated by a high percentage of correct responses when presented with unfamiliar input patterns absent from the training set. The application of neural networks to scientiic problems raises intriguing possibilities and poses stimulating challenges: Can such artiicially intelligent systems, when taught by example, develop economical rules for the correlations implicit in the data on a given class of physical systems, enabling them to make reliable predictions about cases for which experimental results are not available? Can neural networks discover illuminating new