Being able to record the electrical activities of a number of neurons simultaneously is likely to be important in the study of the functional organization of networks of real neurons. Using one extracellular microelectrode to record from several neurons is one approach to studying the response properties of sets of adjacent and therefore likely related neurons. However, to do this, it is necessary to correctly classify the signals generated by these different neurons. This paper considers this problem of classifying the signals in such an extracellular recording, based upon their shapes, and specifically considers the classification of signals in the case when spikes overlap temporally. Introduction How single neurons in a network of neurons interact when processing information is likely to be a fundamental question central to understanding how real neural networks compute.

ABSTRACT A computer model of the hippocampal pyramidal cell (HPC) is described which integrates data from a variety of sources in order to develop a consistent description for this cell type. The model presently includes descriptions of eleven nonlinear somatic currents of the HPC, and the electrotonic structure of the neuron is modelled with a soma/short-cable approximation. Model simulations qualitatively or quantitatively reproduce a wide range of somatic electrical behavior i HPCs, and demonstrate possible roles for the various currents in information processing. There are several substrates for neuronal computation, including connectivity, synapses, morphometries of dendritic trees, linear parameters of cell membrane, as well as nonlinear, time-varying membrane conductances, also referred to as currents or channels. In the classical description of neuronal function, the contribution of membrane channels is constrained to that of generating the action potential, setting firing threshold, and establishing the relationship between (steady-state) stimulus intensity and firing frequency.

ANALYSIS AND COMPARISON OF DIFFERENT LEARNING ALGORITHMS FOR PATTERN ASSOCIATION PROBLEMS J. Bernasconi Brown Boveri Research Center CH-S40S Baden, Switzerland ABSTRACT We investigate the behavior of different learning algorithms for networks of neuron-like units. As test cases we use simple pattern association problems, such as the XOR-problem and symmetry detection problems. The algorithms considered are either versions of the Boltzmann machine learning rule or based on the backpropagation of errors. We also propose and analyze a generalized delta rule for linear threshold units. We find that the performance of a given learning algorithm depends strongly on the type of units used.

Centric Models of the Orientation Map in Primary Visual Cortex William Baxter Department of Computer Science, S.U.N.Y. at Buffalo, NY 14620 Bruce Dow Department of Physiology, S.U.N.Y. at Buffalo, NY 14620 Abstract In the visual cortex of the monkey the horizontal organization of the preferred orientations of orientation-selective cells follows two opposing rules: 1) neighbors tend to have similar orientation preferences, and 2) many different orientations are observed in a local region. Several orientation models which satisfy these constraints are found to differ in the spacing and the topological index of their singularities. Using the rate of orientation change as a measure, the models are compared to published experimental results. Introduction It has been known for some years that there exist orientation-sensitive neurons in the visual cortex of cats and mOnkeysl,2. These cells react to highly specific patterns of light occurring in narrowly circumscribed regiOns of the visual field, i.e., the cell's receptive field. The best patterns for such cells are typically not diffuse levels of illumination, but elongated bars or edges oriented at specific angles.

Abstract: We propose that the back propagation algorithm for supervised learning can be generalized, put on a satisfactory conceptual footing, and very likely made more efficient by defining the values of the output and input neurons as probabilities and varying the synaptic weights in the gradient direction of the log likelihood, rather than the'error'. In the past thirty years many researchers have studied the question of supervised learning in'neural'-like networks. Recently a learning algorithm called'back propagation In these applications, it would often be natural to consider imperfect, or probabilistic information. The problem of supervised learning is to model some mapping between input vectors and output vectors presented to us by some real world phenomena. To be specific, coqsider the question of medical diagnosis.

In this article we consider two aspects of computation with neural networks. Firstly we consider the problem of the complexity of the network required to compute classes of specified (structured) functions. We give a brief overview of basic known complexity theorems for readers familiar with neural network models but less familiar with circuit complexity theories. We argue that there is considerable computational and physiological justification for the thesis that shallow circuits (Le., networks with relatively few layers) are computationally more efficient. We hence concentrate on structured (as opposed to random) problems that can be computed in shallow (constant depth) circuits with a relatively few number (polynomial) of elements, and demonstrate classes of structured problems that are amenable to such low cost solutions. We discuss an allied problem-the complexity of learning-and close with some open problems and a discussion of the observed limitations of the theoretical approach. We next turn to a rigourous classification of how much a network of given structure can do; i.e., the computational capacity of a given construct.

In biological systems, it relates to such issues as classical and operant conditioning, temporal coordination of sensorimotor systems and temporal reasoning. In artificial systems, it addresses such real-world tasks as robot control, speech recognition, dynamic image processing, moving target detection by sonars or radars, EEG diagnosis, and seismic signal processing.

The network model considered consists of interconnected groups of neurons, where each group could be fully interconnected (it could have feedback connections, with possibly asymmetric weights), but no loops between the groups are allowed. A stochastic descent algorithm is applied, under a certain inequality constraint on each intragroup weight matrix which ensures for the network to possess a unique equilibrium state for every input. Introduction It has been shown in the last few years that large networks of interconnected "neuron" -like elemp.nts

This paper focuses on the issue of learning in these networks especially with regard to their implementation in an electronic system. Learning phenomena that have been studied include associative memoryllJ.

ABSTRACT How does the connectivity of a neural network (number of synapses per neuron) relate to the complexity of the problems it can handle (measured by the entropy)? Switching theory would suggest no relation at all, since all Boolean functions can be implemented using a circuit with very low connectivity (e.g., using two-input NAND gates). However, for a network that learns a problem from examples using a local learning rule, we prove that the entropy of the problem becomes a lower bound for the connectivity of the network. INTRODUCTION The most distinguishing feature of neural networks is their ability to spontaneously learn the desired function from'training' samples, i.e., their ability to program themselves. Clearly, a given neural network cannot just learn any function, there must be some restrictions on which networks can learn which functions.