A simple method for training the dynamical behavior of a neural network is derived. It is applicable to any training problem in discrete-time networks with arbitrary feedback. The algorithm resembles back-propagation in that an error function is minimized using a gradient-based method, but the optimization is carried out in the hidden part of state space either instead of, or in addition to weight space. Computational results are presented for some simple dynamical training problems, one of which requires response to a signal 100 time steps in the past. 1 INTRODUCTION This paper presents a minimization-based algorithm for training the dynamical behavior of a discrete-time neural network model. The central idea is to treat hidden nodes as target nodes with variable training data.

A new form of the deterministic Boltzmann machine (DBM) learning procedure is presented which can efficiently train network modules to discriminate between input vectors according to some criterion. The new technique directly utilizes the free energy of these "mean field modules" to represent the probability that the criterion is met, the free energy being readily manipulated by the learning procedure. Although conventional deterministic Boltzmann learning fails to extract the higher order feature of shift at a network bottleneck, combining the new mean field modules with the mutual information objective function rapidly produces modules that perfectly extract this important higher order feature without direct external supervision. 1 INTRODUCTION The Boltzmann machine learning procedure (Hinton and Sejnowski, 1986) can be made much more efficient by using a mean field approximation in which stochastic binary units are replaced by deterministic real-valued units (Peterson and Anderson, 1987). Deterministic Boltzmann learning can be used for "multicompletion" tasks in which the subsets of the units that are treated as input or output are varied from trial to trial (Peterson and Hartman, 1988). In this respect it resembles other learning procedures that also involve settling to a stable state (Pineda, 1987). Using the multicompletion paradigm, it should be possible to force a network to explicitly extract important higher order features of an ensemble of training vectors by forcing the network to pass the information required for correct completions through a narrow bottleneck. In back-propagation networks with two or three hidden layers, the use of bottlenecks sometimes allows the learning to explictly discover important.

Oxford OX1 3PJ Edinburgh EH9 3JL U niv. of Edinburgh ABSTRACT We announce new CMOS synapse circuits using only three and four MOSFETsisynapse. Neural states are asynchronous pulse streams, upon which arithmetic is performed directly. Chips implementing over 100 fully programmable synapses are described and projections to networks of hundreds of neurons are made. 1 OVERVIEW OF PULSE FIRING NEURAL VLSI The inspiration for the use of pulse firing in silicon neural networks is clearly the electrical/chemical pulse mechanism in "real" biological neurons. Neurons fire voltage pulses of a frequency determined by their level of activity but of a constant magnitude (usually 5 Volts) [Murray,1989a]. As indicated in Figure 1, synapses perform arithmetic directly on these asynchronous pulses, to increment or decrement the receiving neuron's activity.

The properties of a cluster of multiple back-propagation (BP) networks are examined and compared to the performance of a single BP network. The underlying idea is that a synergistic effect within the cluster improves the perfonnance and fault tolerance. Five networks were initially trained to perfonn the same input-output mapping. Following training, a cluster was created by computing an average of the outputs generated by the individual networks. The output of the cluster can be used as the desired output during training by feeding it back to the individual networks.

We have done an empirical study of the relation of the number of parameters (weights) in a feedforward net to generalization performance.

"Selective sampling" is a form of directed search that can greatly increase the ability of a connectionist network to generalize accurately. Based on information from previous batches of samples, a network may be trained on data selectively sampled from regions in the domain that are unknown. This is realizable in cases when the distribution is known, or when the cost of drawing points from the target distribution is negligible compared to the cost of labeling them with the proper classification. The approach is justified by its applicability to the problem of training a network for power system security analysis. The benefits of selective sampling are studied analytically, and the results are confirmed experimentally. 1 Introduction: Random Sampling vs. Directed Search A great deal of attention has been applied to the problem of generalization based on random samples drawn from a distribution, frequently referred to as "learning from examples." Many natural learning learning systems however, do not simply rely on this passive learning technique, but instead make use of at least some form of directed search to actively examine the problem domain. In many problems, directed search is provably more powerful than passively learning from randomly given examples.

References Baum, E. and Haussler, D. (1989) What size net gives valid generalization? in D. S. Touretzky (Ed.) Advances in neural information processing systems I, Morgan Kaufman.

Traditional methods of studying neural coding characterize the encoding of known stimuli in average neural responses. Organisms face nearly the opposite task - decoding short segments of a spike train to extract information about an unknown, time-varying stimulus. Here we present strategies for characterizing the neural code from the point of view of the organism, culminating in algorithms for real-time stimulus reconstruction based on a single sample of the spike train. These methods are applied to the design and analysis of experiments on an identified movement-sensitive neuron in the fly visual system. As far as we know this is the first instance in which a direct "reading" of the neural code has been accomplished.

In the development of an image segmentation system for real time image processing applications, we apply the classical decision analysis paradigm by viewing image segmentation as a pixel classifica.

We propose a new way to construct a large-scale neural network for 3.000 handwritten Kanji characters recognition. This neural network consists of 3 parts: a collection of small-scale networks which are trained individually on a small number of Kanji characters; a network which integrates the output from the small-scale networks, and a process to facilitate the integration of these neworks. The recognition rate of the total system is comparable with those of the small-scale networks. Our results indicate that the proposed method is effective for constructing a large-scale network without loss of recognition performance.