It is known from biological data that the response patterns of interneurons in the olfactory macroglomerulus (MGC) of insects are of central importance for the coding of the olfactory signal. We propose an analytically tractable model of the MGC which allows us to relate the distribution of response patterns to the architecture of the network.

We are interested in the use of analog neural networks for recognizing visual objects. Objects are described by the set of parts they are composed of and their structural relationship. Structural models are stored in a database and the recognition problem reduces to matching data to models in a structurally consistent way. The object recognition problem is in general very difficult in that it involves coupled problems of grouping, segmentation and matching. We limit the problem here to the simultaneous labelling of the parts of a single object and the determination of analog parameters. This coupled problem reduces to a weighted match problem in which an optimizing neural network must minimize E(M, p) LO'i MO'i WO'i(p), where the {MO'd are binary match variables for data parts i to model parts a and {Wai(P)} are weights dependent on parameters p.

Human VlSlon systems integrate information nonlocally, across long spatial ranges. For example, a moving stimulus appears smeared when viewed briefly (30 ms), yet sharp when viewed for a longer exposure (100 ms) (Burr, 1980). This suggests that visual systems combine information along a trajectory that matches the motion of the stimulus. Our self-organizing neural network model shows how developmental exposure to moving stimuli can direct the formation of horizontal trajectory-specific motion integration pathways that unsmear representations of moving stimuli. These results account for Burr's data and can potentially also model ot.her phenomena, such as visual inertia. 1 INTRODUCTION N onlocal interactions strongly influence the processing of visual motion information and the response characteristics of visual neurons. Examples include: attentional modulation of receptive field shape; modulation of neural response by stimuli beyond the classical receptive field; and neural response to large-field background motion. In this paper we present a model of the development of nonlocal neural mechanisms for visual motion processing.

A parallel stochastic algorithm is investigated for error-descent learning and optimization in deterministic networks of arbitrary topology. No explicit information about internal network structure is needed. The method is based on the model-free distributed learning mechanism of Dembo and Kailath. A modified parameter update rule is proposed by which each individual parameter vector perturbation contributes a decrease in error. A substantially faster learning speed is hence allowed. Furthermore, the modified algorithm supports learning time-varying features in dynamical networks. We analyze the convergence and scaling properties of the algorithm, and present simulation results for dynamic trajectory learning in recurrent networks.

An incremental, higher-order, non-recurrent network combines two properties found to be useful for learning sequential tasks: higherorder connections and incremental introduction of new units. The network adds higher orders when needed by adding new units that dynamically modify connection weights. Since the new units modify the weights at the next time-step with information from the previous step, temporal tasks can be learned without the use of feedback, thereby greatly simplifying training. Furthermore, a theoretically unlimited number of units can be added to reach into the arbitrarily distant past. Experiments with the Reber grammar have demonstrated speedups of two orders of magnitude over recurrent networks.

In visual processing the ability to deal with missing and noisy information is crucial. Occlusions and unreliable feature detectors often lead to situations where little or no direct information about features is available. However the available information is usually sufficient to highly constrain the outputs. We discuss Bayesian techniques for extracting class probabilities given partial data. The optimal solution involves integrating over the missing dimensions weighted by the local probability densities. We show how to obtain closed-form approximations to the Bayesian solution using Gaussian basis function networks. The framework extends naturally to the case of noisy features.

An artificial neural network (ANN) is commonly modeled by a threshold circuit, a network of interconnected processing units called linear threshold gates. The depth of a network represents the number of unit delays or the time for parallel computation. The SIze of a circuit is the number of gates and measures the amount of hardware. It was known that traditional logic circuits consisting of only unbounded fan-in AND, OR, NOT gates would require at least O(log n/log log n) depth to compute common arithmetic functions such as the product or the quotient of two n-bit numbers, unless we allow the size (and fan-in) to increase exponentially (in n). We show in this paper that ANNs can be much more powerful than traditional logic circuits. In particular, we prove that that iterated addition can be computed by depth-2 ANN, and multiplication and division can be computed by depth-3 ANNs with polynomial size and polynomially bounded integer weights, respectively. Moreover, it follows from known lower bound results that these ANNs are optimal in depth. We also indicate that these techniques can be applied to construct polynomial-size depth-3 ANN for powering, and depth-4 ANN for mUltiple product.

How can artificial neural nets generalize better from fewer examples? In order to generalize successfully, neural network learning methods typically require large training data sets. We introduce a neural network learning method that generalizes rationally from many fewer data points, relying instead on prior knowledge encoded in previously learned neural networks. For example, in robot control learning tasks reported here, previously learned networks that model the effects of robot actions are used to guide subsequent learning of robot control functions. For each observed training example of the target function (e.g. the robot control policy), the learner explains the observed example in terms of its prior knowledge, then analyzes this explanation to infer additional information about the shape, or slope, of the target function. This shape knowledge is used to bias generalization when learning the target function. Results are presented applying this approach to a simulated robot task based on reinforcement learning.

Holographic Recurrent Networks (HRNs) are recurrent networks which incorporate associative memory techniques for storing sequential structure. HRNs can be easily and quickly trained using gradient descent techniques to generate sequences of discrete outputs and trajectories through continuous spaee. The performance of HRNs is found to be superior to that of ordinary recurrent networks on these sequence generation tasks.

The implementation uses noise injection and multiplicative correlation to estimate derivatives, as in [Anderson, Kerns 92]. One intended application of this technique is setting circuit parameters on-chip automatically, rather than manually [Kirk 91]. Gradient descent optimization may be used to adjust synapse weights for a backpropagation or other on-chip learning implementation. The approach combines the features of continuous multidimensional gradient descent and the potential for an annealing style of optimization. We present data measured from our analog VLSI implementation. 1 Introduction This work is similar to [Anderson, Kerns 92], but represents two advances. First, we describe the extension of the technique to multiple dimensions. Second, we demonstrate an implementation of the multidimensional technique in analog VLSI, and provide results measured from the chip. Unlike previous work using noise sources in adaptive systems, we use the noise as a means of estimating the gradient of a function f(y), rather than performing an annealing process [Alspector 88]. We also estimate gr-;:dients continuously in position and time, in contrast to [Umminger 89] and [J abri 91], which utilize discrete position gradient estimates.