This arises from the parallelism and distributed knowledge representation which gives rise to gentle degradation as faults appear. These functions are attractive to implementation in VLSI and WSI. For example, the natural fault - tolerance could be useful in silicon wafers with imperfect yield, where the network degradation is approximately proportional to the non-functioning silicon area. To cast neural networks in engineering language, a neuron is a state machine that is either "on" or "off', which in general assumes intermediate states as it switches smoothly between these extrema. The synapses weighting the signals from a transmitting neuron such that it is more or less excitatory or inhibitory to the receiving neuron. The set of synaptic weights determines the stable states and represents the learned information in a system. The neural state, VI' is related to the total neural activity stimulated by inputs to the neuron through an activation junction, F. Neural activity is the level of excitation of the neuron and the activation is the way it reacts in a response to a change in activation.

ABSTRACT Intracellular recordings in spinal cord motoneurons and cerebral cortex neurons have provided new evidence on the correlational strength of monosynaptic connections, and the relation between the shapes of postsynaptic potentials and the associated increased firing probability. In these cells, excitatory postsynaptic potentials (EPSPs) produce crosscorrelogram peaks which resemble in large part the derivative of the EPSP. Additional synaptic noise broadens the peak, but the peak area -- i.e., the number of above-chance firings triggered per EPSP -- remains proportional to the EPSP amplitude. The consequences of these data for information processing by polysynaptic connections is discussed. The effects of sequential polysynaptic links can be calculated by convolving the effects of the underlying monosynaptic connections.

As a means of probing these cerebellar mechanisms, my colleagues and I have been conducting microelectrode studies of the neural messages that flow through the intermediate division of the cerebellum and onward to limb muscles via the rubrospinal tract. We regard this cerebellorubrospinal pathway as a useful model system for studying general problems of sensorimotor integration and adaptive brain function.

Current Focus Of Learning Research Most connectionist learning algorithms may be grouped into three general catagories, commonly referred to as supenJised, unsupenJised, and reinforcement learning. Supervised learning requires the explicit participation of an intelligent teacher, usually to provide the learning system with task-relevant input-output pairs (for two recent examples, see [1,2]). Unsupervised learning, exemplified by "clustering" algorithms, are generally concerned with detecting structure in a stream of input patterns [3,4,5,6,7]. In its final state, an unsupervised learning system will typically represent the discovered structure as a set of categories representing regions of the input space, or, more generally, as a mapping from the input space into a space of lower dimension that is somehow better suited to the task at hand. In reinforcement learning, a "critic" rewards or penalizes the learning system, until the system ultimately produces the correct output in response to a given input pattern [8]. It has seemed an inevitable tradeoff that systems needing to rapidly learn specific, behaviorally useful input-output mappings must necessarily do so under the auspices of an intelligent teacher with a ready supply of task-relevant training examples. This state of affairs has seemed somewhat paradoxical, since the processes of Rerceptual and cognitive development in human infants, for example, do not depend on the moment by moment intervention of a teacher of any sort. Learning by Doing The current work has been focused on a fourth type of learning algorithm, i.e. learning-bydoing, an approach that has been very little studied from either a connectionist perspective

A synthetic neural network simulation of cerebral neocortex was developed based on detailed anatomy and physiology. Processing elements possess temporal nonlinearities and connection patterns similar to those of cortical neurons. The network was able to replicate spatial and temporal integration properties found experimentally in neocortex. A certain level of randomness was found to be crucial for the robustness of at least some of the network's computational capabilities. Emphasis was placed on how synthetic simulations can be of use to the study of both artificial and biological neural networks.

Much experimental study of real neural networks relies on the proper classification of extracellulary sampled neural signals (i.e.

We open our eyes and we "see" the world in all its color, brightness, and movement. Yet, we have great difficulties when trying to endow our machines with similar abilities. In this paper we shall describe recent developments in the theory of early vision which lead from the formulation of the motion problem as an illposed oneto its solution by minimizing certain "cost" functions. These cost or energy functions can be mapped onto simple analog and digital resistive networks. Thus, we shall see how the optical flow can be computed by injecting currents into resistive networks and recording the resulting stationary voltage distribution at each node. These networks can be implemented in cMOS VLSI circuits and represent plausible candidates for biological vision systems. APERTURE PROBLEM AND SMOOTHNESS ASSUMPTION In this study, we use intensity-based schemes for recovering motion.

ABSTRACT A single cell theory for the development of selectivity and ocular dominance in visual cortex has been presented previously by Bienenstock, Cooper and Munrol. This has been extended to a network applicable to layer IV of visual cortex2 . In this paper we present a mean field approximation that captures in a fairly transparent manner the qualitative, and many of the quantitative, results of the network theory. Finally, we consider the application of this theory to artificial neural networks and show that a significant reduction in architectural complexity is possible. ASINGLE LAYER NETWORK AND THE MEAN FIELD APPROXIMATION We consider a receive signals from the layer (Figure 1).

Centric Models of the Orientation Map in Primary Visual Cortex William Baxter of Computer Science, S.U.N.Y. at Buffalo, NY 14620Department Bruce Dow Department of Physiology, S.U.N.Y. at Buffalo, NY 14620 Abstract the visual cortex of the monkey the horizontal organization of the preferredIn of orientation-selective cells follows two opposing rules: 1) neighbors tendorientations Several orientation models which satisfy these constraints are found in the spacing and the topological index of their singularities. Using the rateto differ 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 but elongated bars or edges oriented at specific angles.

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 theoremsfor 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. Wediscuss an allied problem-the complexity of learning-and close with some open problems and a discussion of the observed limitations of the theoretical approach. Wenext turn to a rigourous classification of how much a network of given structure can do; i.e., the computational capacity of a given construct.