(June 1987).

TIME-SEQUENTIAL SELF-ORGANIZATION OF HIERARCHICAL NEURAL NETWORKS Ronald H. Silverman Cornell University Medical College, New York, NY 10021 Andrew S. Noetzel polytechnic University, Brooklyn, NY 11201 ABSTRACT Self-organization of multi-layered networks can be realized by time-sequential organization of successive neural layers. Lateral inhibition operating in the surround of firing cells in each layer provides for unsupervised capture of excitation patterns presented by the previous layer. By presenting patterns of increasing complexity, in coordination with network selforganization, higher levels of the hierarchy capture concepts implicit in the pattern set. INTRODUCTION A fundamental difficulty in self-organization of hierarchical, multi-layered, networks of simple neuron-like cells is the determination of the direction of adjustment of synaptic link weights between neural layers not directly connected to input or output patterns. Several different approaches have been used to address this problem.

The net is defined as a set of units, each witb an activation, and weights between units which determine the activations. The algorithm uses a gradient descent technique to calculate the direction by which each weight should be changed in order to minimise the summed squared difference between the desired output and the actual output. Using this algorithm it is believed that a net can be trained to make an arbitrary nonlinear mapping of the input units onto the output units if given enough intermediate units. This'static' net can be used as part of a larger system with more complex behaviour. The static net has no memory for past inputs, but many problems require the context of the input in order to c.ompute the answer.

Box 150, Cheongryang, Seoul, Korea ABSTRACT Inverse matrix calculation can be considered as an optimization. We have demonstrated that this problem can be rapidly solved by highly interconnected simple neuron-like analog processors. A network for matrix inversion based on the concept of Hopfield's neural network was designed, and implemented with electronic hardware. With slight modifications, the network is readily applicable to solving a linear simultaneous equation efficiently. Notable features of this circuit are potential speed due to parallel processing, and robustness against variations of device parameters.

Patterns of activity over real neural structures are known to exhibit timedependent behavior. It would seem that the brain may be capable of utilizing temporal behavior of activity in neural networks as a way of performing functions which cannot otherwise be easily implemented. These might include the origination of sequential behavior and the recognition of time-dependent stimuli. A model is presented here which uses neuronal populations with recurrent feedback connections in an attempt to observe and describe the resulting time-dependent behavior. Shortcomings and problems inherent to this model are discussed. Current models by other researchers are reviewed and their similarities and differences discussed.

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 Artificial neural networks (ANNs) are capable of accurate recognition of simple speech vocabularies such as isolated digits [1]. This paper looks at two more difficult vocabularies, the alphabetic E-set and a set of polysyllabic words. The E-set is difficult because it contains weak discriminants and polysyllables are difficult because of timing variation. Polysyllabic word recognition is aided by a time pre-alignment technique based on dynamic programming and E-set recognition is improved by focusing attention. Recognition accuracies are better than 98% for both vocabularies when implemented with a single layer perceptron.

LEARNING IN NETWORKS OF NONDETERMINISTIC ADAPTIVE LOGIC ELEMENTS Richard C. Windecker* AT&T Bell Laboratories, Middletown, NJ 07748 ABSTRACT This paper presents a model of nondeterministic adaptive automata that are constructed from simpler nondeterministic adaptive information processing elements. The first half of the paper describes the model. Chief among these properties is that network aggregates of the model elements can adapt appropriately when a single reinforcement channel provides the same positive or negative reinforcement signal to all adaptive elements of the network at the same time. This holds for multiple-input, multiple-output, multiple-layered, combinational and sequential networks. It also holds when some network elements are "hidden" in that their outputs are not directly seen by the external environment. INTRODUCTION There are two primary motivations for studying models of adaptive automata constructed from simple parts. First, they let us learn things about real biological systems whose properties are difficult to study directly: We form a hypothesis about such systems, embody it in a model, and then see if the model has reasonable learning and behavioral properties. In the present work, the hypothesis being tested is: that much of an animal's behavior as determined by its nervous system is intrinsically nondeterministic; that learning consists of incremental changes in the probabilities governing the animal's behavior; and that this is a consequence of the animal's nervous system consisting of an aggregate of information processing elements some of which are individually nondeterministic and adaptive. The second motivation for studying models of this type is to find ways of building machines that can learn to do (artificially) intelligent and practical things.

SYNCHRONIZATION IN NEURAL NETS Jacques J. Vidal University of California Los Angeles, Los Angeles, Ca. 90024 John Haggerty· ABSTRACT The paper presents an artificial neural network concept (the Synchronizable Oscillator Networks) where the instants of individual firings in the form of point processes constitute the only form of information transmitted between joining neurons. This type of communication contrasts with that which is assumed in most other models which typically are continuous or discrete value-passing networks. Limiting the messages received by each processing unit to time markers that signal the firing of other units presents significant implemen tation advantages. When interaction is present, the scheduled firings are advanced or delayed by the firing of neighboring neurons. Networks of such neurons become global oscillators which exhibit multiple synchronizing attractors.

Here, X is a finite or infinite set, and Y is another finite or infinite set. A learning machine observes any set of pairs (x, y) sampled randomly from X x Y. (X x Y means the Cartesian product of X and Y.) And, it computes some estimate j: