The exact form of a gradient-following learning algorithm for completely recurrent networks running in continually sampled time is derived and used as the basis for practical algorithms for temporal supervised learning tasks. These algorithms have (1) the advantage that they do not require a precisely defined training interval, operating while the network runs; and (2) the disadvantage that they require nonlocal communication in the network being trained and are computationally expensive. These algorithms allow networks having recurrent connections to learn complex tasks that require the retention of information over time periods having either fixed or indefinite length.

Neurons in area 7a of the posterior parietal cortex of monkeys respond to both the retinal location of a visual stimulus and the position of the eyes and by combining these signals represent the spatial location of external objects. A neural network model, programmed using back-propagation learning, can decode this spatial information from area 7a neurons and accounts for their observed response properties.

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This paper reports the results of our studies with an unsupervised learning paradigm which we have called “Competitive Learning.” We have examined competitive learning using both computer simulation and formal analysis and have found that when it is applied to parallel networks of neuron‐like elements, many potentially useful learning tasks can be accomplished. We were attracted to competitive learning because it seems to provide a way to discover the salient, general features which can be used to classify a set of patterns. We show how a very simply competitive mechanism can discover a set of feature detectors which capture important aspects of the set of stimulus input patterns. We also show how these feature detectors can form the basis of a multilayer system that can serve to learn categorizations of stimulus sets which are not linearly separable. We show how the use of correlated stimuli con serve as a kind of “teaching” input to the system to allow the development of feature detectors which would not develop otherwise. Although we find the competitive learning mechanism a very interesting and powerful learning principle, we do not, of course, imagine thot it is the only learning principle. Competitive learning is an essentially nonassociative statistical learning scheme. We certainly imagine that other kinds of learning mechanisms will be involved in the building of associations among patterns of activation in a more complete neural network. We offer this analysis of these competitive learning mechanisms to further our understanding of how simple adaptive networks can discover features important in the description of the stimulus environment in which the system finds itself.

Studies of cortical neurons in monkeys performing short-term memory tasks have shown that information about a stimulus can be maintained by persistent neuron firing for periods of many seconds after removal of the stimulus. The mechanism by which this sustained activity is initiated and maintained is unknown. In this article we present a spiking neural network model of short-term memory and use it to investigate the hypothesis that recurrent, or "re-entrant," networks with constant connection strengths are sufficient to store graded information temporarily. The synaptic weights that enable the network to mimic the input-output characteristics of an active memory module are computed using an optimization procedure for recurrent networks with non-spiking neurons. This network is then transformed into one with spiking neurons by interpreting the continuous output values of the nonspiking model neurons as spiking probabilities. The behavior of the model neurons in this spiking network is compared with that of 179 single units previously recorded in monkey inferotemporal (IT) cortex during the performance of a short-term memory task. The spiking patterns of almost every model neuron are found to resemble closely those of IT neurons. About 40% of the IT neuron firing patterns are also found to be of the same types as those of model neurons. A property of the spiking model is that the neurons cannot maintain precise graded activity levels indefinitely, but eventually relax to one of a few constant activities called fixed-point attractors. The noise introduced into the model by the randomness of spiking causes the network to jump between these attractors. This switching between attractor states generates spike trains with a characteristic statistical temporal structure. We found evidence for the same kind of structure in the spike trains from about half of the IT neurons in our test set. These results show that the behavior of many real cortical memory neurons is consistent with an active storage mechanism based on recurrent activity in networks with fixed synaptic strengths.