Nonmonotonic activation functions in multilayer perceptrons

Multilayer perceptrons (MLPs) and radial basis function networks (RBFNs) are the two most common types of feedforward neural networks used for pattern classification and continuous function approximation. MLPs are characterized by slow learning speed, low memory retention, and small node requirements, while RBFNs are known to have high learning speed, high memory retention, but large node requirements. This dissertation asks and answers the question: "Can we do better?" Two types of neural network architectures are introduced: the hyper-ridge and the hyper-hill. A hyper-ridge network is a perceptron with no hidden layers and an activation function in the form g(h) = sgn($c\sp{2} - h\sp2) (h$ is the net input; c is a constant "width"), while a hyper-hill network is a continuos multilayer version with g(h) = exp($-h\sp2/c\sp2)$. Throughout this dissertation theoretical and empirical evidence is presented which strongly indicates that hyper-hills behave similarly to MLPs when the input dimension is large but are more similar to RBFNs when the input dimension is low. Additionally, the fact that hyper-hills learn faster than MLPs and require fewer nodes, but do not suffer the "curse of dimensionality" associated with RBFNs, is offered as evidence that hyper-hills fill a niche between MLPs and RBFNs.

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