A new concept for unsupervised learning based upon examples introduced to the neural network is proposed. Each example is considered as an interpolation node of the velocity field in the phase space. The velocities at these nodes are selected such that all the streamlines converge to an attracting set imbedded in the subspace occupied by the cluster of examples. The synaptic interconnections are found from learning procedure providing selected field. The theory is illustrated by examples. This paper is devoted to development of a new concept for unsupervised learning based upon examples introduced to an artificial neural network.

One popular class of unsupervised algorithms are competitive algorithms. In the traditional view of competition, only one competitor, the winner, adapts for any given case. I propose to view competitive adaptation as attempting to fit a blend of simple probability generators (such as gaussians) to a set of data-points. The maximum likelihood fit of a model of this type suggests a "softer" form of competition, in which all competitors adapt in proportion to the relative probability that the input came from each competitor. I investigate one application of the soft competitive model, placement of radial basis function centers for function interpolation, and show that the soft model can give better performance with little additional computational cost. 1 INTRODUCTION Interest in unsupervised learning has increased recently due to the application of more sophisticated mathematical tools (Linsker, 1988; Plumbley and Fallside, 1988; Sanger, 1989) and the success of several elegant simulations of large scale selforganization (Linsker, 1986; Kohonen, 1982). One popular class of unsupervised algorithms are competitive algorithms, which have appeared as components in a variety of systems (Von der Malsburg, 1973; Fukushima, 1975; Grossberg, 1978). Generalizing the definition of Rumelhart and Zipser (1986), a competitive adaptive system consists of a collection of modules which are structurally identical except, possibly, for random initial parameter variation.

"Selective sampling" is a form of directed search that can greatly increase the ability of a connectionist network to generalize accurately. Based on information from previous batches of samples, a network may be trained on data selectively sampled from regions in the domain that are unknown. This is realizable in cases when the distribution is known, or when the cost of drawing points from the target distribution is negligible compared to the cost of labeling them with the proper classification. The approach is justified by its applicability to the problem of training a network for power system security analysis. The benefits of selective sampling are studied analytically, and the results are confirmed experimentally. 1 Introduction: Random Sampling vs. Directed Search A great deal of attention has been applied to the problem of generalization based on random samples drawn from a distribution, frequently referred to as "learning from examples." Many natural learning learning systems however, do not simply rely on this passive learning technique, but instead make use of at least some form of directed search to actively examine the problem domain. In many problems, directed search is provably more powerful than passively learning from randomly given examples.

A simple method for training the dynamical behavior of a neural network is derived. It is applicable to any training problem in discrete-time networks with arbitrary feedback. The algorithm resembles back-propagation in that an error function is minimized using a gradient-based method, but the optimization is carried out in the hidden part of state space either instead of, or in addition to weight space. Computational results are presented for some simple dynamical training problems, one of which requires response to a signal 100 time steps in the past. 1 INTRODUCTION This paper presents a minimization-based algorithm for training the dynamical behavior of a discrete-time neural network model. The central idea is to treat hidden nodes as target nodes with variable training data.

In associative reinforcement learning, an environment generates input vectors, a learning system generates possible output vectors, and a reinforcement function computes feedback signals from the input-output pairs. The task is to discover and remember input-output pairs that generate rewards. Especially difficult cases occur when rewards are rare, since the expected time for any algorithm can grow exponentially with the size of the problem. Nonetheless, if a reinforcement function possesses regularities, and a learning algorithm exploits them, learning time can be reduced below that of non-generalizing algorithms. This paper describes a neural network algorithm called complementary reinforcement back-propagation (CRBP), and reports simulation results on problems designed to offer differing opportunities for generalization.

This work introduces a new method called Self Organizing Neural Network (SONN) algorithm and compares its performance with Back Propagation in a signal separation application. The problem is to separate two signals; a modem data signal and a male speech signal, added and transmitted through a 4 khz channel. The signals are sampled at 8 khz, and using supervised learning, an attempt is made to reconstruct them. The SONN is an algorithm that constructs its own network topology during training, which is shown to be much smaller than the BP network, faster to trained, and free from the trial-anderror network design that characterize BP. 1. INTRODUCTION The research in Neural Networks has witnessed major changes in algorithm design focus, motivated by the limitations perceived in the algorithms available at the time.

A central problem in connectionist modelling is the control of network and architectural resources during learning. In the present approach, weights reflect a coarse prediction history as coded by a distribution of values and parameterized in the mean and standard deviation of these weight distributions. Weight updates are a function of both the mean and standard deviation of each connection in the network and vary as a function of the error signal ("stochastic delta rule"; Hanson, 1990). Consequently, the weights maintain information on their central tendency and their "uncertainty" in prediction. Such information is useful in establishing a policy concerning the size of the nodal complexity of the network and growth of new nodes. For example, during problem solving the present network can undergo "meiosis", producing two nodes where there was one "overtaxed" node as measured by its coefficient of variation. It is shown in a number of benchmark problems that meiosis networks can find minimal architectures, reduce computational complexity, and overall increase the efficiency of the representation learning interaction.

A new form of the deterministic Boltzmann machine (DBM) learning procedure is presented which can efficiently train network modules to discriminate between input vectors according to some criterion. The new technique directly utilizes the free energy of these "mean field modules" to represent the probability that the criterion is met, the free energy being readily manipulated by the learning procedure. Although conventional deterministic Boltzmann learning fails to extract the higher order feature of shift at a network bottleneck, combining the new mean field modules with the mutual information objective function rapidly produces modules that perfectly extract this important higher order feature without direct external supervision. 1 INTRODUCTION The Boltzmann machine learning procedure (Hinton and Sejnowski, 1986) can be made much more efficient by using a mean field approximation in which stochastic binary units are replaced by deterministic real-valued units (Peterson and Anderson, 1987). Deterministic Boltzmann learning can be used for "multicompletion" tasks in which the subsets of the units that are treated as input or output are varied from trial to trial (Peterson and Hartman, 1988). In this respect it resembles other learning procedures that also involve settling to a stable state (Pineda, 1987). Using the multicompletion paradigm, it should be possible to force a network to explicitly extract important higher order features of an ensemble of training vectors by forcing the network to pass the information required for correct completions through a narrow bottleneck. In back-propagation networks with two or three hidden layers, the use of bottlenecks sometimes allows the learning to explictly discover important.

A methodology for faster supervised learning in dynamical nonlinear neural networks is presented. It exploits the concept of adjoint operntors to enable computation of changes in the network's response due to perturbations in all system parameters, using the solution of a single set of appropriately constructed linear equations. The lower bound on speedup per learning iteration over conventional methods for calculating the neuromorphic energy gradient is O(N2), where N is the number of neurons in the network. 1 INTRODUCTION The biggest promise of artifcial neural networks as computational tools lies in the hope that they will enable fast processing and synthesis of complex information patterns. In particular, considerable efforts have recently been devoted to the formulation of efficent methodologies for learning (e.g., Rumelhart et al., 1986; Pineda, 1988; Pearlmutter, 1989; Williams and Zipser, 1989; Barhen, Gulati and Zak, 1989). The development of learning algorithms is generally based upon the minimization of a neuromorphic energy function. The fundamental requirement of such an approach is the computation of the gradient of this objective function with respect to the various parameters of the neural architecture, e.g., synaptic weights, neural Adjoint Operator Algorithms 499

The computational territory between the linearly summing McCulloch-Pitts neuron and the nonlinear differential equations of Hodgkin & Huxley is relatively sparsely populated. Connectionists use variants of the former and computational neuroscientists struggle with the exploding parameter spaces provided by the latter. However, evidence from biophysical simulations suggests that the voltage transfer properties of synapses, spines and dendritic membranes involve many detailed nonlinear interactions, not just a squashing function at the cell body. Real neurons may indeed be higher-order nets. For the computationally-minded, higher order interactions means, first of all, quadratic terms. This contribution presents a simple learning principle for a binary tree with a logistic/quadratic transfer function at each node. These functions, though highly nested, are shown to be capable of changing their shape in concert. The resulting tree structure receives inputs at its leaves, and outputs an estimate of the probability that the input pattern is a member of one of two classes at the top.