tput) is very commonly used to approximate unknown mappings. If the output layer is linear, such a network may have a structure similar to an RBF network. 5.1 Multilayer perceptrons Multilayer perceptrons are commonly used to approximate complex nonlinear mappings. In general, it is possible

Abstract. We investigate layered neural networks with differentiable activation function and student vectors without normalization constraint by means of equilibrium statistical physics. We consider the learning of perfectly realizable rules and find that the length of student vectors becomes

I would first and foremost like to thank my advisor, Dr. Russ Abbott, for his guidance in the completion of this thesis. His input not only helped guide me to meet my goals, but encouraged me to look for a creative path towards those goals. Dr. Abbott’s unique teaching style and fondness for exploration and creativity have inspired me since I began this program, and have constantly reminded me of the reasons why I chose to study mathematics and computer science in the first place. I would also like to thank Dr. Valentino Crespi for reconnecting me with the joys of mathematics and proof, as well as complicated (but impressive looking) mathematical notation. And to Dr. Chengyu Sun for not only contributing to my education, but to my business as well. And finally I would like to thank my wife, Yelena, for her support, and for listening to me go on endlessly about things that surely aren’t as interesting to her as they are to me.

The training of multilayered neural networks in the presence of different types of noise is studied. We consider the learning of realizable rules in nonoverlapping architectures. Achieving optimal generalization depends on the knowledge of the noise level, however its misestimation may lead

We study the number of hidden layers required by a multilayer neural network with threshold units to compute a dichotomy f from R d to f0; 1g, defined by a finite set of hyperplanes. We show that this question is far more intricate than computing Boolean functions, although this well

According to the CARVE algorithm, any pattern classifica-tion problem can be synthesized in three layers without mis-classification. In this paper, we propose to train multilayer neural network classifiers based on the CARVE algorithm. In hidden layer training, we find a hyperplane that sepa

Abstract: In this paper we present a new method for voice disorders classification based on multilayer neural network. The processing algorithm is based on a hybrid technique which uses the wavelets energy coefficients as input of the multilayer neural network. The training step uses a speech

The generalization performance of two learning algorithms, Bayes algorithm and the "optimal learning" algorithm on two classification tasks is studied theoretically. In the first example the task is defined by a restricted two-layer network, a committee machine, and in the second the task

Neural networks capable of encoding sets of patterns are analysed. Solutions are found by theoretical treatment instead of by supervised learning. The behaviour for 2 R (R 2 N) input units is studied and its characteristic features are discussed. The accessibilities for non-spurious patterns

We discuss the dynamics of batch learning of multilayer neural networks in the asymptotic limit, where the number of trining data is much larger than the number of parameters, emphasizing on the parameterization redundancy in overrealizable cases. In addition to showing experimental results