We prove that except possibly for small exceptional sets, discretetime analog neural nets are globally observable, i.e. all their corrupted pseudo-orbits on computer simulations actually reflect the true dynamical behavior of the network. Locally finite discrete (boolean) neural networks are observable without exception.

The satisfiability of random CNF formulae with precisely k variables per clause ("k-SAT") is a popular testbed for the performance of search algorithms. Formulae have M clauses from N variables, randomly negated, keeping the ratio a M / N fixed.

Solvable models of nonlinear learning machines are proposed, and learning in artificial neural networks is studied based on the theory of ordinary differential equations. A learning algorithm is constructed, by which the optimal parameter can be found without any recursive procedure. The solvable models enable us to analyze the reason why experimental results by the error backpropagation often contradict the statistical learning theory.

The problem of learning from examples in multilayer networks is studied within the framework of statistical mechanics. Using the replica formalism we calculate the average generalization error of a fully connected committee machine in the limit of a large number of hidden units. If the number of training examples is proportional to the number of inputs in the network, the generalization error as a function of the training set size approaches a finite value. If the number of training examples is proportional to the number of weights in the network we find first-order phase transitions with a discontinuous drop in the generalization error for both binary and continuous weights. 1 INTRODUCTION Feedforward neural networks are widely used as nonlinear, parametric models for the solution of classification tasks and function approximation. Trained from examples of a given task, they are able to generalize, i.e. to compute the correct output for new, unknown inputs.

The first class of network adaptation algorithms start out with a redundant architecture and proceed by pruning away seemingly unimportant weights (Sietsma and Dow, 1988; Le Cun et aI, 1990). A second class of algorithms starts off with a sparse architecture and grows the network to the complexity required by the problem. Several algorithms have been proposed for growing feedforward networks. The upstart algorithm of Frean (1990) and the cascade-correlation algorithm of Fahlman (1990) are examples of this approach.

Bumptrees are geometric data structures introduced by Omohundro (1991) to provide efficient access to a collection of functions on a Euclidean space of interest. We describe a modified bumptree structure that has been employed as a neural network classifier, and compare its performance on several classification tasks against that of radial basis function networks and the standard mutIi-Iayer perceptron. 1 INTRODUCTION A number of neural network studies have demonstrated the utility of the multi-layer perceptron (MLP) and shown it to be a highly effective paradigm. Studies have also shown, however, that the MLP is not without its problems, in particular it requires an extensive training time, is susceptible to local minima problems and its perfonnance is dependent upon its internal network architecture. In an attempt to improve upon the generalisation performance and computational efficiency a number of studies have been undertaken principally concerned with investigating the parametrisation of the MLP. It is well known, for example, that the generalisation performance of the MLP is affected by the number of hidden units in the network, which have to be determined empirically since theory provides no guidance.

We propose a method for improving the performance of any network designed to predict the next value of a time series. Vve advocate analyzing the deviations of the network's predictions from the data in the training set. This can be carried out by a secondary network trained on the time series of these residuals. The combined system of the two networks is viewed as the new predictor. We demonstrate the simplicity and success of this method, by applying it to the sunspots data. The small corrections of the secondary network can be regarded as resulting from a Taylor expansion of a complex network which includes the combined system.

We propose a learning algorithm for a variable memory length Markov process. Human communication, whether given as text, handwriting, or speech, has multi characteristic time scales. On short scales it is characterized mostly by the dynamics that generate the process, whereas on large scales, more syntactic and semantic information is carried. For that reason the conventionally used fixed memory Markov models cannot capture effectively the complexity of such structures. On the other hand using long memory models uniformly is not practical even for as short memory as four.

The distance measure and learning problem are formally described as nested objective functions. We derive an efficient algorithm by using optimization techniques that allow us to divide up the objective function into parts which may be minimized in distinct phases. The algorithm has accurately recreated 10 prototypes from a randomly generated sample database of 100 images consisting of 20 points each in 120 experiments. Finally, by incorporating permutation invariance in our distance measure, we have a technique that we may be able to apply to the clustering of graphs. Our goal is to develop measures which will enable the learning of objects with shape or structure. Acknowledgements This work has been supported by AFOSR grant F49620-92-J-0465 and ONR/DARPA grant N00014-92-J-4048.

This paper introduces GNARL, an evolutionary program which induces recurrent neural networks that are structurally unconstrained. In contrast to constructive and destructive algorithms, GNARL employs a population of networks and uses a fitness function's unsupervised feedback to guide search through network space. Annealing is used in generating both gaussian weight changes and structural modifications. Applying GNARL to a complex search and collection task demonstrates that the system is capable of inducing networks with complex internal dynamics.