LEARNING BY ST ATE RECURRENCE DETECfION Bruce E. Rosen, James M. Goodwint, and Jacques J. Vidal University of California, Los Angeles, Ca. 90024 ABSTRACT This research investigates a new technique for unsupervised learning of nonlinear control problems. The approach is applied both to Michie and Chambers BOXES algorithm and to Barto, Sutton and Anderson's extension, the ASE/ACE system, and has significantly improved the convergence rate of stochastically based learning automata. Recurrence learning is a new nonlinear reward-penalty algorithm. It exploits information found during learning trials to reinforce decisions resulting in the recurrence of nonfailing states. Recurrence learning applies positive reinforcement during the exploration of the search space, whereas in the BOXES or ASE algorithms, only negative weight reinforcement is applied, and then only on failure. Simulation results show that the added information from recurrence learning increases the learning rate. Our empirical results show that recurrence learning is faster than both basic failure driven learning and failure prediction methods. Although recurrence learning has only been tested in failure driven experiments, there are goal directed learning applications where detection of recurring oscillations may provide useful information that reduces the learning time by applying negative, instead of positive reinforcement.

Department of Electrical and Computer Engineering University of Notre Dame Notre Dame, IN 46556 ABSTRACT In the present paper we survey and utilize results from the qualitative theory of large scale interconnected dynamical systems in order to develop a qualitative theory for the Hopfield model of neural networks. In our approach we view such networks as an interconnection of many single neurons. Our results are phrased in terms of the qualitative properties of the individual neurons and in terms of the properties of the interconnecting structure of the neural networks. Aspects of neural networks which we address include asymptotic stability, exponential stability, and instability of an equilibrium; estimates of trajectory bounds; estimates of the domain of attraction of an asymptotically stable equilibrium; and stability of neural networks under structural perturbations. INTRODUCTION In recent years, neural networks have attracted considerable attention as candidates for novel computational systemsl-3.

THE SIGMOID NONLINEARITY IN PREPYRIFORM CORTEX Frank H. Eeckman University of California, Berkeley, CA 94720 ABSlRACT We report a study ·on the relationship between EEG amplitude values and unit spike output in the prepyriform cortex of awake and motivated rats. This relationship takes the form of a sigmoid curve, that describes normalized pulse-output for normalized wave input. The curve is fitted using nonlinear regression and is described by its slope and maximum value. Measurements were made for both excitatory and inhibitory neurons in the cortex. These neurons are known to form a monosynaptic negative feedback loop. Both classes of cells can be described by the same parameters.

We show how to estimate (1) the number of functions that can be implemented by a particular network architecture, (2) how much analog precision is needed in the connections in the network, and (3) the number of training examples the network must see before it can be expected to form reliable generalizations.

The network model considered consists of interconnected groups of neurons, where each group could be fully interconnected (it could have feedback connections, with possibly asymmetric weights), but no loops between the groups are allowed. A stochastic descent algorithm is applied, under a certain inequality constraint on each intragroup weight matrix which ensures for the network to possess a unique equilibrium state for every input. Introduction It has been shown in the last few years that large networks of interconnected "neuron" -like elemp.nts

Abstract: We propose that the back propagation algorithm for supervised learning can be generalized, put on a satisfactory conceptual footing, and very likely made more efficient by defining the values of the output and input neurons as probabilities and varying the synaptic weights in the gradient direction of the log likelihood, rather than the'error'. In the past thirty years many researchers have studied the question of supervised learning in'neural'-like networks. Recently a learning algorithm called'back propagation In these applications, it would often be natural to consider imperfect, or probabilistic information. The problem of supervised learning is to model some mapping between input vectors and output vectors presented to us by some real world phenomena. To be specific, coqsider the question of medical diagnosis.

This viewpoint allows the class of probability distributions, P, the neural network can acquire to be explicitly specified. Learning algorithms for the neural network which search for the "most probable" member of P can then be designed. Statistical tests which decide if the "true" or environmental probability distribution is in P can also be developed. Example applications of the theory to the highly nonlinear back-propagation learning algorithm, and the networks of Hopfield and Anderson are discussed. INTRODUCTION A connectionist system is a network of simple neuron-like computing elements which can store and retrieve information, and most importantly make generalizations. Using terminology suggested by Rumelhart & McClelland 1, the computing elements of a connectionist system are called units, and each unit is associated with a real number indicating its activity level. The activity level of a given unit in the system can also influence the activity level of another unit. The degree of influence between two such units is often characterized by a parameter of the system known as a connection strength. During the information retrieval process some subset of the units in the system are activated, and these units in turn activate neighboring units via the inter-unit connection strengths.

Please address all further correspondence to: John Y. Cheung School of EECS 202 W. Boyd, CEC 219 Norman, OK 73019 (405)325-4721 MATHEMATICAL ANALYSIS OF LEARNING BEHAVIOR OF NEURONAL MODELS John Y. Cheung and Massoud Omidvar School of Electrical Engineering and Computer Science ABSTRACT In this paper, we wish to analyze the convergence behavior of a number of neuronal plasticity models. Recent neurophysiological research suggests that the neuronal behavior is adaptive. In particular, memory stored within a neuron is associated with the synaptic weights which are varied or adjusted to achieve learning. A number of adaptive neuronal models have been proposed in the literature. Three specific models will be analyzed in this paper, specifically the Hebb model, the Sutton-Barto model, and the most recent trace model.

There is a widespread misconception that the delta-rule is in some sense guaranteed to work on networks without hidden units. As previous authors have mentioned, there is no such guarantee for classification tasks. We will begin by presenting explicit counterexamples illustrating two different interesting ways in which the delta rule can fail. We go on to provide conditions which do guarantee that gradient descent will successfully train networks without hidden units to perform two-category classification tasks. We discuss the generalization of our ideas to networks with hidden units and to multicategory classification tasks.

In this article we consider two aspects of computation with neural networks. Firstly we consider the problem of the complexity of the network required to compute classes of specified (structured) functions. We give a brief overview of basic known complexity theorems for readers familiar with neural network models but less familiar with circuit complexity theories. We argue that there is considerable computational and physiological justification for the thesis that shallow circuits (Le., networks with relatively few layers) are computationally more efficient. We hence concentrate on structured (as opposed to random) problems that can be computed in shallow (constant depth) circuits with a relatively few number (polynomial) of elements, and demonstrate classes of structured problems that are amenable to such low cost solutions. We discuss an allied problem-the complexity of learning-and close with some open problems and a discussion of the observed limitations of the theoretical approach. We next turn to a rigourous classification of how much a network of given structure can do; i.e., the computational capacity of a given construct.