SUMMARY To process sensory data, sensory brain areas must preserve information about both the similarities and differences among learned cues: without the latter, acuity would be lost, whereas without the former, degraded versions of a cue would be erroneously thought to be distinct cues, and would not be recognized. We have constructed a model of piriform cortex incorporating a large number of biophysical, anatomical and physiological parameters, such as two-step excitatory firing thresholds, necessary and sufficient conditions for long-term potentiation (LTP) of synapses, three distinct types of inhibitory currents (short IPSPs, long hyperpolarizing currents (LHP) and long cellspecific afterhyperpolarization (AHP)), sparse connectivity between bulb and layer-II cortex, caudally-flowing excitatory collateral fibers, nonlinear dendritic summation, etc. We have tested the model for its ability to learn similarity-and difference-preserving encodings of incoming sensory cueSj the biological characteristics of the model enable it to produce multiple encodings of each input cue in such a way that different readouts of the cell firing activity of the model preserve both similarity and difference'information. In particular, probabilistic quantal transmitter-release properties of piriform synapses give rise to probabilistic postsynaptic voltage levels which, in combination with the activity of local patches of inhibitory interneurons in layer II, differentially select bursting vs. single-pulsing layer-II cells. Time-locked firing to the theta rhythm (Larson and Lynch, 1986) enables distinct spatial patterns to be read out against a relatively quiescent background firing rate. Training trials using the physiological rules for induction of LTP yield stable layer-II-cell spatial firing patterns for learned cues. Multiple simulated olfactory input patterns (Le., those that share many chemical features) will give rise to strongly-overlapping bulb firing patterns, activating many shared lateral olfactory tract (LOT) axons innervating layer Ia of piriform cortex, which in tum yields highly overlapping layer-II-cell excitatory potentials, enabling this spatial layer-II-cell encoding to preserve the overlap (similarity) among similar inputs. At the same time, those synapses that are enhanced by the learning process cause stronger cell firing, yielding strong, cell-specific afterhyperpolarizing (AHP) currents. Local inhibitory intemeurons effectively select alternate cells to fire once strongly-firing cells have undergone AHP. These alternate cells then activate their caudally-flowing recurrent collaterals, activating distinct populations of synapses in caudal layer lb.

This viewpoint allows the class of probability distributions, P, the neural network can acquire to be explicitly specified. Learning algorithms for the neural network which search for the "most probable" member of P can then be designed. Statistical tests which decide if the "true" or environmental probability distribution is in P can also be developed. Example applications of the theory to the highly nonlinear back-propagation learning algorithm, and the networks of Hopfield and Anderson are discussed. INTRODUCTION A connectionist system is a network of simple neuron-like computing elements which can store and retrieve information, and most importantly make generalizations. Using terminology suggested by Rumelhart & McClelland 1, the computing elements of a connectionist system are called units, and each unit is associated with a real number indicating its activity level. The activity level of a given unit in the system can also influence the activity level of another unit. The degree of influence between two such units is often characterized by a parameter of the system known as a connection strength. During the information retrieval process some subset of the units in the system are activated, and these units in turn activate neighboring units via the inter-unit connection strengths.

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.

CYCLES: A Simulation Tool for Studying Cyclic Neural Networks Michael T. Gately Texas Instruments Incorporated, Dallas, TX 75265 ABSTRACT A computer program has been designed and implemented to allow a researcher to analyze the oscillatory behavior of simulated neural networks with cyclic connectivity. The computer program, implemented on the Texas Instruments Explorer / Odyssey system, and the results of numerous experiments are discussed. The program, CYCLES, allows a user to construct, operate, and inspect neural networks containing cyclic connection paths with the aid of a powerful graphicsbased interface. Numerous cycles have been studied, including cycles with one or more activation points, non-interruptible cycles, cycles with variable path lengths, and interacting cycles. The final class, interacting cycles, is important due to its ability to implement time-dependent goal processing in neural networks.

The generalization replaces two state neurons by neurons taking a richer set of values. Two classes of neuron input output relations are developed guaranteeing convergence to stable states. The first is a class of "continuous" relations and the second is a class of allowed quantization rules for the neurons.

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.

ON TROPISTIC PROCESSING AND ITS APPLICATIONS Manuel F. Fernandez General Electric Advanced Technology Laboratories Syracuse, New York 13221 ABSTRACT The interaction of a set of tropisms is sufficient in many cases to explain the seemingly complex behavioral responses exhibited by varied classes of biological systems to combinations of stimuli. It can be shown that a straightforward generalization of the tropism phenomenon allows the efficient implementation of effective algorithms which appear to respond "intelligently" to changing environmental conditions. Examples of the utilization of tropistic processing techniques will be presented in this paper in applications entailing simulated behavior synthesis, path-planning, pattern analysis (clustering), and engineering design optimization. INTRODUCTION The goal of this paper is to present an intuitive overview of a general unsupervised procedure for addressing a variety of system control and cost minimization problems. This procedure is hased on the idea of utilizing "stimuli" produced by the environment in which the systems are designed to operate as basis for dynamically providing the necessary system parameter updates.

ABSTRACT Advances in brain theory need two complementary approaches: Analytical investigations by in situ measurements and as well synthetic modelling supported by computer simulations to generate suggestive hypothesis on purposeful structures in the neural tissue. In this paper research of the second line is described: Starting from a neurophysiologically inspired model of stimulusresponse (SR) and/or associative memorization and a psychologically motivated ministructure for basic control tasks, preconditions and conditions are studied for cooperation of such units in a hierarchical organisation, as can be assumed to be the general layout of macrostructures in the brain. I. INTRODUCTION Theoretic modelling in brain theory is a highly speculative subject. However, it is necessary since it seems very unlikely to get a clear picture of this very complicated device by just analyzing the available measurements on sound and/or damaged brain parts only. As in general physics, one has to realize, that there are different levels of modelling: in physics stretching from the atomary level over atom assemblies till up to general behavioural models like kinematics and mechanics, in brain theory stretching from chemical reactions over electrical spikes and neuronal cell assembly cooperation till general human behaviour.

THE SIGMOID NONLINEARITY IN PREPYRIFORM CORTEX Frank H. Eeckman University of California, Berkeley, CA 94720 ABSlRACT We report a study ·on the relationship between EEG amplitude values and unit spike output in the prepyriform cortex of awake and motivated rats. This relationship takes the form of a sigmoid curve, that describes normalized pulse-output for normalized wave input. The curve is fitted using nonlinear regression and is described by its slope and maximum value. Measurements were made for both excitatory and inhibitory neurons in the cortex. These neurons are known to form a monosynaptic negative feedback loop. Both classes of cells can be described by the same parameters.

We propose learning rules for recurrent neural networks with high-order interactions between some or all neurons. The designed networks exhibit the desired associative memory function: perfect storage and retrieval of pieces of information and/or sequences of information of any complexity.