This tendency to preserve information about the path is not a characteristic of traditional finite-state automata. ENCODING PATH INFORMATION In a different set of experiments, we asked whether the SRN could learn to use the infonnation about the path that is encoded in the hidden units' patterns of activation. In one of these experiments, we tested whether the network could master length constraints. When strings generated from the small finite-state grammar may only have a maximum of 8 letters, the prediction following the presentation of the same letter in position number six or seven may be different. For example, following the sequence'TSSSXXV', 'V' is the seventh letter and only another'V' would be a legal successor.

We have tested this assumption in the hippocampus, a cortical structure or the brain that is involved in long-term memory. A brier, high-frequency activation or excitatory synapses in the hippocampus produces an increase in synaptic strength known as long-term potentiation, or L TP (BUss and Lomo, 1973), that can last ror many days. LTP is known to be Hebbian since it requires the simultaneous release or neurotransmitter from presynaptic terminals coupled with postsynaptic depolarization (Kelso et al, 1986; Malinow and Miller, 1986; Gustatrson et al, 1987). However, a mechanism ror the persistent reduction or synaptic strength that could balance LTP has not yet been demonstrated. We studied the associative interactions between separate inputs onto the same dendritic trees or hippocampal pyramidal cells or field CAl, and round that a low-frequency input which, by itselr, does not persistently change synaptic strength, can either increase (associative L TP) or decrease in strength (associative long-term depression or LTD) depending upon whether it is positively or negatively correlated in time with a second, high-frequency bursting input. LTP or synaptic strength is Hebbian, and LTD is anti-Hebbian since it is elicited by pairing presynaptic firing with postsynaptic hyperpolarization sufficient to block postsynaptic activity.

A pool of handwritten signatures is used to train a neural network for the task of deciding whether or not a given signature is a forgery. The network is a feedforward net, with a binary image as input. There is a hidden layer, with a single unit output layer. The weights are adjusted according to the backpropagation algorithm. The signatures are entered into a C software program through the use of a Datacopy Electronic Digitizing Camera. The binary signatures are normalized and centered. The performance is examined as a function of the training set and network structure. The best scores are on the order of 2% true signature rejection with 2-4% false signature acceptance.

Secondly, he now deals with the much more difficult problem of reaching in the presence of obstacles.

Encouraged by these results we wanted to explore the question, how we might expand on these models to make them useful for the design of speech recognition systems. A problem that emerges as we attempt to apply neural network models to the full speech recognition problem is the problem of scaling. Simply extending neural networks to ever larger structures and retraining them as one monolithic net quickly exceeds the capabilities of the fastest and largest supercomputers. The search complexity of finding a good solutions in a huge space of possible network configurations also soon assumes unmanageable proportions. Moreover, having to decide on all possible classes for recognition ahead of time as well as collecting sufficient data to train such a large monolithic network is impractical to say the least. In an effort to extend our models from small recognition tasks to large scale speech recognition systems, we must therefore explore modularity and incremental learning as design strategies to break up a large learning task into smaller subtasks. Breaking up a large task into subtasks to be tackled by individual black boxes interconnected in ad hoc arrangements, on the other hand, would mean to abandon one of the most attractive aspects of connectionism: the ability to perform complex constraint satisfaction in a massively parallel and interconnected fashion, in view of an overall optimal perfonnance goal.

We address the question of when a network can be expected to generalize from m random training examples chosen from some arbitrary probability distribution, assuming that future test examples are drawn from the same distribution. Among our results are the following bounds on appropriate sample vs. network size.

Nearly optimal solutions to many combinatorial problems can be found using stochastic simulated annealing. This paper extends the concept of simulated annealing from its original formulation as a Markov process to a new formulation based on mean field theory. Mean field annealing essentially replaces the discrete degrees of freedom in simulated annealing with their average values as computed by the mean field approximation. The net result is that equilibrium at a given temperature is achieved 1-2 orders of magnitude faster than with simulated annealing. A general framework for the mean field annealing algorithm is derived, and its relationship to Hopfield networks is shown. The behavior of MFA is examined both analytically and experimentally for a generic combinatorial optimization problem: graph bipartitioning. This analysis indicates the presence of critical temperatures which could be important in improving the performance of neural networks.

A new class of neural network aimed at early visual processing is described; we call it a Neural Analog Diffusion-Enhancement Layer or "NADEL." The network consists of two levels which are coupled through feedfoward and shunted feedback connections. The lower level is a two-dimensional diffusion map which accepts visual features as input, and spreads activity over larger scales as a function of time. The upper layer is periodically fed the activity from the diffusion layer and locates local maxima in it (an extreme form of contrast enhancement) using a network of local comparators. These local maxima are fed back to the diffusion layer using an on-center/off-surround shunting anatomy. The maxima are also available as output of the network. The network dynamics serves to cluster features on multiple scales as a function of time, and can be used in a variety of early visual processing tasks such as: extraction of comers and high curvature points along edge contours, line end detection, gap filling in contours, generation of fixation points, perceptual grouping on multiple scales, correspondence and path impletion in long-range apparent motion, and building 2-D shape representations that are invariant to location, orientation, scale, and small deformation on the visual field.

Parallelizable optimization techniques are applied to the problem of learning in feedforward neural networks. In addition to having superior convergence properties, optimization techniques such as the Polak Ribiere method are also significantly more efficient than the Backpropagation algorithm. These results are based on experiments performed on small boolean learning problems and the noisy real-valued learning problem of handwritten character recognition. 1 INTRODUCTION The problem of learning in feedforward neural networks has received a great deal of attention recently because of the ability of these networks to represent seemingly complex mappings in an efficient parallel architecture. This learning problem can be characterized as an optimization problem, but it is unique in several respects. Function evaluation is very expensive. However, because the underlying network is parallel in nature, this evaluation is easily parallelizable.

A nonlinearity is required before matched filtering in mInimum error receivers when additive noise is present which is impulsive and highly non-Gaussian. Experiments were performed to determine whether the correct clipping nonlinearity could be provided by a single-input singleoutput multi-layer perceptron trained with back propagation. It was found that a multi-layer perceptron with one input and output node, 20 nodes in the first hidden layer, and 5 nodes in the second hidden layer could be trained to provide a clipping nonlinearity with fewer than 5,000 presentations of noiseless and corrupted waveform samples. A network trained at a relatively high signal-to-noise (SIN) ratio and then used as a front end for a linear matched filter detector greatly reduced the probability of error. The clipping nonlinearity formed by this network was similar to that used in current receivers designed for impulsive noise and provided similar substantial improvements in performance.