A Boltzmann machine ([AHS], [HS], [AK]) is a neural network model in which the units update their states according to a stochastic decision rule. It consists of a set U of units, a set C of unordered pairs of elements of U, and an assignment of connection strengths S: C -- R. A configuration of a Boltzmann machine is a map k: U -- {O, I}.

Feature selection and creation are two of the most important and difficult tasks in the field of pattern classification. Good features improve the performance of both conventional and neural network pattern classifiers. Exemplar selection is another task that can reduce the memory and computation requirements of a KNN classifier. These three tasks require a search through a space which is typically so large that 797 798 Chang and Lippmann exhaustive search is impractical. The purpose of this research was to explore the usefulness of Genetic search algorithms for these tasks. Details concerning this research are available in (Chang, 1990).

A partially observed Markov decision process (POMDP) is a generalization of a Markov decision process that allows for incomplete information regarding the state of the system. The significant applied potential for such processes remains largely unrealized, due to an historical lack of tractable solution methodologies. The major impediment to exact solution is that, even with a finite set of internal system states, the set of possible information states is uncountably infinite. Finite algorithms are theoretically available for exact solution of the finite horizon problem, but these are computationally intractable for even modest-sized problems. Several approximation methodologies are reviewed that have the potential to generate computationally feasible, high precision solutions.

In recent years many researchers have investigated the use of Markov Random Fields (MRFs) for computer vision. They can be applied for example to reconstruct surfaces from sparse and noisy depth data coming from the output of a visual process, or to integrate early vision processes to label physical discontinuities. In this paper we show that by applying mean field theory to those MRFs models a class of neural networks is obtained. Those networks can speed up the solution for the MRFs models. The method is not restricted to computer vision. 1 Introduction

To achieve high-rate image data compression while maintainig a high quality reconstructed image, a good image model and an efficient way to represent the specific data of each image must be introduced. Based on the physiological knowledge of multi - channel characteristics and inhibitory interactions between them in the human visual system, a mathematically coherent parallel architecture for image data compression which utilizes the Markov random field Image model and interactions between a vast number of filter banks, is proposed.

One of the attractions of neural network approaches to pattern recognition is the use of a discrimination-based training method. We show that once we have modified the output layer of a multilayer perceptron to provide mathematically correct probability distributions, and replaced the usual squared error criterion with a probability-based score, the result is equivalent to Maximum Mutual Information training, which has been used successfully to improve the performance of hidden Markov models for speech recognition. If the network is specially constructed to perform the recognition computations of a given kind of stochastic model based classifier then we obtain a method for discrimination-based training of the parameters of the models. Examples include an HMM-based word discriminator, which we call an'Alphanet'.

Two approaches were explored which integrate neural net classifiers with Hidden Markov Model (HMM) speech recognizers. Both attempt to improve speech pattern discrimination while retaining the temporal processing advantages of HMMs. One approach used neural nets to provide second-stage discrimination following an HMM recognizer. On a small vocabulary task, Radial Basis Function (RBF) and back-propagation neural nets reduced the error rate substantially (from 7.9% to 4.2% for the RBF classifier). In a larger vocabulary task, neural net classifiers did not reduce the error rate. They, however, outperformed Gaussian, Gaussian mixture, and k nearest neighbor (KNN) classifiers. In another approach, neural nets functioned as low-level acoustic-phonetic feature extractors. When classifying phonemes based on single 10 msec.

We are developing a phoneme based.

In this paper, several techniques for addressing this problem are discussed in the context of an isolated word recognition task.

Two approaches were explored which integrate neural net classifiers with Hidden Markov Model (HMM) speech recognizers. Both attempt to improve speech pattern discrimination while retaining the temporal processing advantages of HMMs. One approach used neural nets to provide second-stage discrimination following an HMM recognizer. On a small vocabulary task, Radial Basis Function (RBF) and back-propagation neural nets reduced the error rate substantially (from 7.9% to 4.2% for the RBF classifier). In a larger vocabulary task, neural net classifiers did not reduce the error rate. They, however, outperformed Gaussian, Gaussian mixture, and k nearest neighbor (KNN) classifiers. In another approach, neural nets functioned as low-level acoustic-phonetic feature extractors. When classifying phonemes based on single 10 msec.