Kai-Yeung Siu Dept. of Electrical & Computer Engineering University of California, Irvine Irvine, CA 92717 Jehoshua Bruck IBM Research Division Almaden Research Center San Jose, CA 95120-6099 Abstract An important issue in neural computation is the dynamic range of weights in the neural networks. Many experimental results on learning indicate that the weights in the networks can grow prohibitively large with the size of the inputs. We show that there is an efficient way of simulating a network of LTEs with large weights by a network of LTEs with small weights. To prove these results, we use tools from harmonic analysis of Boolean functions. Our technique is quite general, it provides insights to some other problems.

Using the double-step target displacement paradigm the mechanisms underlying armtrajectory modification were investigated. Using short (10-110 msec) inter-stimulus intervals the resulting hand motions were initially directed in between the first and second target locations. The kinematic features of the modified motions were accounted for by the superposition scheme, which involves the vectorial addition of two independent point-topoint motionunits: one for moving the hand toward an internally specified location and a second one for moving between that location and the final target location. The similarity between the inferred internally specified locations andpreviously reported measured endpoints of the first saccades in double-step eye-movement studies may suggest similarities between perceived targetlocations in eye and hand motor control.

We develop a model-independent method for characterizing the reliability of neural responses to brief stimuli. This approach allows us to measure the discriminability of similar stimuli, based on the real-time response of a single neuron. Neurophysiological data were obtained from a movementsensitive neuron(HI) in the visual system of the blowfly Calliphom erythrocephala. Furthermore,recordings were made from blowfly photoreceptor cells to quantify the signal to noise ratios in the peripheral visual system. As photoreceptors form the input to the visual system, the reliability oftheir signals ultimately determines the reliability of any visual discrimination task. For the case of movement detection, this limit can be computed, and compared to the HI neuron's reliability. Under favorable conditions,the performance of the HI neuron closely approaches the theoretical limit, which means that under these conditions the nervous system adds little noise in the process of computing movement from the correlations of signals in the photoreceptor array.

Visual attention is the ability to dynamically restrict processing to a subset of the visual field. Researchers have long argued that such a mechanism is necessary to efficiently perform many intermediate level visual tasks. This paper describes VISIT, a novel neural network model of visual attention.

THE MODEL; STOCHASTIC RESONANCE The reduced neuron model consists of a single Hopfield-type computational element, which may be modeled as a R-C circuit with nonlinear feedback provided by an operational amplifier having a sigmoid transfer function.

Because eye muscles never cocontract and do not deal with external loads, one can write an equation that relates motoneuron firing rate to eye position and velocity - a very uncommon situation in the CNS. The semicircular canals transduce head velocity in a linear manner by using a high background discharge rate, imparting linearity to the premotor circuits that generate eye movements. This has allowed deducing some of the signal processing involved, including a neural network that integrates. These ideas are often summarized by block diagrams. Unfortunately, they are of little value in describing the behavior of single neurons - a fmding supported by neural network models.

Accurate saccades require interaction between brainstem circuitry and the cerebeJJum. A model of this interaction is described, based on Kawato's principle of feedback-error-Iearning. In the model a part of the brainstem (the superior colliculus) acts as a simple feedback controJJer with no knowledge of initial eye position, and provides an error signal for the cerebeJJum to correct for eye-muscle nonIinearities. This teaches the cerebeJJum, modelled as a CMAC, to adjust appropriately the gain on the brainstem burst-generator's internal feedback loop and so alter the size of burst sent to the motoneurons. With direction-only errors the system rapidly learns to make accurate horizontal eye movements from any starting position, and adapts realistically to subsequent simulated eye-muscle weakening or displacement of the saccadic target.

In single cells of the cat striate cortex, lateral inhibition across orientation and/orspatial frequency is found to enhance preexisting biases. A contrast-dependent but spatially non-selective inhibitory component is also found. Stimulation with ascending and descending contrasts reveals the latter as a response hysteresis that is sensitive, powerful and rapid, suggesting thatit is active in day-to-day vision. Both forms of inhibition are not recurrent but are rather network properties. These findings suggest two fundamental inhibitory mechanisms: a global mechanism that limits dynamic range and creates spatial selectivity through thresholding and a local mechanism that specifically refines spatial filter properties.

The nature of information processing in complex dendritic trees has remained an open question since the origin of the neuron doctrine 100 years ago. With respect to learning, for example, it is not known whether a neuron is best modeled as 35 36 Mel a pseudo-linear unit, equivalent in power to a simple Perceptron, or as a general nonlinear learning device, equivalent in power to a multi-layered network. In an attempt tocharacterize the input-output behavior of a whole dendritic tree containing voltage-dependent membrane mechanisms, a recent compartmental modeling study in an anatomically reconstructed neocortical pyramidal cell (anatomical data from Douglas et al., 1991; "NEURON" simulation package provided by Michael Hines and John Moore) showed that a dendritic tree rich in NMDA-type synaptic channels isselectively responsive to spatially clustered, as opposed to diffuse, pattens of synaptic activation (Mel, 1992). For example, 100 synapses which were simultaneously activatedat 100 randomly chosen locations about the dendritic arbor were less effective at firing the cell than 100 synapses activated in groups of 5, at each of 20 randomly chosen dendritic locations. The cooperativity among the synapses in each group is due to the voltage dependence of the NMDA channel: Each activated NMDA synapse becomes up to three times more effective at injecting synaptic current whenthe post-synaptic membrane is locally depolarized by 30-40 m V from the resting potential.

During waking and sleep, the brain and mind undergo a tightly linked and precisely specified set of changes in state. At the level of neurons, this process has been modeled by variations of Volterra-Lotka equations for cyclic fluctuations of brainstem cell populations. However, neural network models based upon rapidly developing knowledge ofthe specific population connectivities and their differential responses to drugs have not yet been developed. Furthermore, only the most preliminary attempts have been made to model across states. Some of our own attempts to link rapid eye movement (REM) sleep neurophysiology and dream cognition using neural network approaches are summarized in this paper.