Mathematical Sciences: Analysis of Neural Networks: Stable Category Formation In A Complex Input Environment

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CARPENTER The investigator intends to develop and analyze models of neural systems networks. These models will be designed to carry out a self-organizing pattern recognition and category learning. As formal architectures, the models will be translated into machine designs. As neural networks, the systems will be based on psychological and physiological data and will be used to analyze the brain and behavior in the process of pattern recognition and category learning. From a mathematical point of view, these models are based on nonlinear, singular, high dimensional systems of ordinary differential equations. Network design is constrained by the conflicting requirements of stability and adaptability, and by the complexity. Given an arbitrary complicated sequence of inputs, the system must be able to extract stable categories, without a teacher. However, the system must also remain plastic, open to new learning. New network designs will generalize systems which have been shown to stably encode arbitrary lists of binary input patterns in such a way that, after an initial phase, each input directly activates its category representation. The search mechanism is automatically disengaged once the learning is complete. The more general system will encode graded input patterns, and be embedded in network hierarchies adapted to the particular constraints of natural and artificial vision and speech. Research described in this project is highly cross-disciplinary, as it involves the neural networks science, communications, some aspects of robotics and computer vision, neural cognitive processes, and mathematics.