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 cortex 2. 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. A SINGLE LAYER NETWORK AND THE MEAN FIELD APPROXIMATION We consider a single layer network of ideal neurons which receive signals from outside of the layer and from cells within the layer (Figure 1). The activity of the ith cell in the network is c' - m' d J d is a vector of afferent signals to the network. Each cell receives input from n fibers outside of the cortical network through the matrix of synapses mi' Intra-layer input to each cell is then transmitted through the matrix of cortico-cortical synapses L. Light circles are the LGN -cortical synapses.

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.

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

TOWARDS AN ORGANIZING PRINCIPLE FOR A LAYERED PERCEPTUAL NETWORK Ralph Linsker IBM Thomas J. Watson Research Center, Yorktown Heights, NY 10598 Abstract An information-theoretic optimization principle is proposed for the development of each processing stage of a multilayered perceptual network. This principle of "maximum information preservation" states that the signal transformation that is to be realized at each stage is one that maximizes the information that the output signal values (from that stage) convey about the input signals values (to that stage), subject to certain constraints and in the presence of processing noise. The quantity being maximized is a Shannon information rate. I provide motivation for this principle and -- for some simple model cases -- derive some of its consequences, discuss an algorithmic implementation, and show how the principle may lead to biologically relevant neural architectural features such as topographic maps, map distortions, orientation selectivity, and extraction of spatial and temporal signal correlations. A possible connection between this information-theoretic principle and a principle of minimum entropy production in nonequilibrium thermodynamics is suggested. Introduction This paper describes some properties of a proposed information-theoretic organizing principle for the development of a layered perceptual network.

To illustrate the extent of this additional complexity, Fig. Input 6a shows a schematized circuit for a computational unit of method V

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.

ENCODING GEOMETRIC INVARIANCES IN HIGHER-ORDER NEURAL NETWORKS C.L. Giles Air Force Office of Scientific Research, Bolling AFB, DC 20332 R.D. Griffin Naval Research Laboratory, Washington, DC 20375-5000 T. Maxwell Sachs-Freeman Associates, Landover, MD 20785 ABSTRACT We describe a method of constructing higher-order neural networks that respond invariantly under geometric transformations on the input space. By requiring each unit to satisfy a set of constraints on the interconnection weights, a particular structure is imposed on the network. A network built using such an architecture maintains its invariant performance independent of the values the weights assume, of the learning rules used, and of the form of the nonlinearities in the network. The invariance exhibited by a firstorder network is usually of a trivial sort, e.g., responding only to the average input in the case of translation invariance, whereas higher-order networks can perform useful functions and still exhibit the invariance. We derive the weight constraints for translation, rotation, scale, and several combinations of these transformations, and report results of simulation studies.

Patterns of activity over real neural structures are known to exhibit timedependent behavior. It would seem that the brain may be capable of utilizing temporal behavior of activity in neural networks as a way of performing functions which cannot otherwise be easily implemented. These might include the origination of sequential behavior and the recognition of time-dependent stimuli. A model is presented here which uses neuronal populations with recurrent feedback connections in an attempt to observe and describe the resulting time-dependent behavior. Shortcomings and problems inherent to this model are discussed. Current models by other researchers are reviewed and their similarities and differences discussed.

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.

There are three existing connection::;t models in which network states are assigned a computational energy.