The bootstrap method offers an computation intensive alternative to estimate the predictive distribution for a neural network even if the analytic derivation is intractable. The available asymptotic results show that it is valid for a large number of linear, nonlinear and even nonparametric regression problems. It has the potential to model the distribution of estimators to a higher precision than the usual normal asymptotics. It even may be valid if the normal asymptotics fail. However, the theoretical properties of bootstrap procedures for neural networks - especially nonlinear models - have to be investigated more comprehensively.

He is now at the University of California, Berkeley.

A performance comparison of two self-organizing networks, the Kohonen Feature Map and the recently proposed Growing Cell Structures is made. For this purpose several performance criteria for self-organizing networks are proposed and motivated. The models are tested with three example problems of increasing difficulty. The Kohonen Feature Map demonstrates slightly superior results only for the simplest problem.

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.

The relationships between learning, development and evolution in Nature is taken seriously, to suggest a model of the developmental process whereby the genotypes manipulated by the Genetic Algorithm (GA) might be expressed to form phenotypic neural networks (NNet) that then go on to learn. ONTOL is a grammar for generating polynomial NN ets for time-series prediction. Genomes correspond to an ordered sequence of ONTOL productions and define a grammar that is expressed to generate a NNet. The NNet's weights are then modified by learning, and the individual's prediction error is used to determine GA fitness. A new gene doubling operator appears critical to the formation of new genetic alternatives in the preliminary but encouraging results presented.

Platt's resource-allocation network (RAN) (Platt, 1991a, 1991b) is modified for a reinforcement-learning paradigm and to "restart" existing hidden units rather than adding new units. After restarting, units continue to learn via back-propagation. The resulting restart algorithm is tested in a Q-Iearning network that learns to solve an inverted pendulum problem. Solutions are found faster on average with the restart algorithm than without it.

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.

Some improved generalization properties are demonstrat.ed

This is motivated by experimental evidencethat these phenomena may be subserved by the same mechanisms. An important aspect of this model is that ocular dominance segregationcan occur when input activity is both distributed, and positively correlated between the eyes. This allows investigation of the dependence of the pattern of ocular dominance stripes on the degree of correlation between the eyes: it is found that increasing correlation leads to narrower stripes. Experiments are suggested to test whether such behaviour occursin the natural system.

A switching between apparently coherent (oscillatory) and stochastic episodes of activity has been observed in responses from cat and monkey visual cortex. We describe the dynamics of these phenomena in two parallel approaches,a phenomenological and a rather microscopic one. On the one hand we analyze neuronal responses in terms of a hidden state model (HSM). The parameters of this model are extracted directly from experimental spiketrains. They characterize the underlying dynamics as well as the coupling of individual neurons to the network. This phenomenological modelthus provides a new framework for the experimental analysis of network dynamics.