Many applications of neural networks can be formulated in terms of a multivariate nonlinear mapping from an input vector x to a target vector t. A conventional neural network approach, based on least squares for example, leads to a network mapping which approximates the regression of t on x. A more complete description of the data can be obtained by estimating the conditional probability density of t, conditioned on x, which we write as p(tlx). Various techniques exist for modelling such densities when the target variables live in a Euclidean space. However, a number of potential applications involve angle-like output variables which are periodic on some finite interval (usually chosen to be (0,271")).

Almost all models of orientation and direction selectivity in visual cortex are based on feedforward connection schemes, where geniculate input provides all excitation to both pyramidal and inhibitory neurons. The latter neurons then suppress the response of the former for non-optimal stimuli. However, anatomical studies show that up to 90 % of the excitatory synaptic input onto any cortical cell is provided by other cortical cells. The massive excitatory feedback nature of cortical circuits is embedded in the canonical microcircuit of Douglas &. Martin (1991). We here investigate analytically and through biologically realistic simulations the functioning of a detailed model of this circuitry, operating in a hysteretic mode. In the model, weak geniculate input is dramatically amplified by intracortical excitation, while inhibition has a dual role: (i) to prevent the early geniculate-induced excitation in the null direction and (ii) to restrain excitation and ensure that the neurons fire only when the stimulus is in their receptive-field.

This paper presents results from the first use of neural networks for the real-time feedback control of high temperature plasmas in a tokamak fusion experiment. The tokamak is currently the principal experimental device for research into the magnetic confinement approach to controlled fusion. In the tokamak, hydrogen plasmas, at temperatures of up to 100 Million K, are confined by strong magnetic fields. Accurate control of the position and shape of the plasma boundary requires real-time feedback control of the magnetic field structure on a timescale of a few tens of microseconds. Software simulations have demonstrated that a neural network approach can give significantly better performance than the linear technique currently used on most tokamak experiments. The practical application of the neural network approach requires high-speed hardware, for which a fully parallel implementation of the multilayer perceptron, using a hybrid of digital and analogue technology, has been developed.

Semi-Markov Decision Problems are continuous time generalizations of discrete time Markov Decision Problems. A number of reinforcement learning algorithms have been developed recently for the solution of Markov Decision Problems, based on the ideas of asynchronous dynamic programming and stochastic approximation. Among these are TD(,x), Q-Iearning, and Real-time Dynamic Programming. After reviewing semi-Markov Decision Problems and Bellman's optimality equation in that context, we propose algorithms similar to those named above, adapted to the solution of semi-Markov Decision Problems. We demonstrate these algorithms by applying them to the problem of determining the optimal control for a simple queueing system. We conclude with a discussion of circumstances under which these algorithms may be usefully applied.

This paper presents results from the first use of neural networks for the real-time feedback control of high temperature plasmas in a tokamak fusion experiment. The tokamak is currently the principal experimental device for research into the magnetic confinement approach to controlled fusion. In the tokamak, hydrogen plasmas, at temperatures of up to 100 Million K, are confined by strong magnetic fields. Accurate control of the position and shape of the plasma boundary requires real-time feedback control of the magnetic field structure on a timescale of a few tens of microseconds. Software simulations have demonstrated that a neural network approach can give significantly better performance than the linear technique currently used on most tokamak experiments. The practical application of the neural network approach requires high-speed hardware, for which a fully parallel implementation of the multilayer perceptron, using a hybrid of digital and analogue technology, has been developed.

Second order properties of cost functions for recurrent networks are investigated. We analyze a layered fully recurrent architecture, the virtue of this architecture is that it features the conventional feedforward architecture as a special case. A detailed description of recursive computation of the full Hessian of the network cost function is provided. We discuss the possibility of invoking simplifying approximations of the Hessian and show how weight decays iron the cost function and thereby greatly assist training. We present tentative pruning results, using Hassibi et al.'s Optimal Brain Surgeon, demonstrating that recurrent networks can construct an efficient internal memory. 1 LEARNING IN RECURRENT NETWORKS Time series processing is an important application area for neural networks and numerous architectures have been suggested, see e.g. (Weigend and Gershenfeld, 94). The most general structure is a fully recurrent network and it may be adapted using Real Time Recurrent Learning (RTRL) suggested by (Williams and Zipser, 89). By invoking a recurrent network, the length of the network memory can be adapted to the given time series, while it is fixed for the conventional lag-space net (Weigend et al., 90). In forecasting, however, feedforward architectures remain the most popular structures; only few applications are reported based on the Williams&Zipser approach.

This paper presents a new method for image compression by neural networks. First, we show that we can use neural networks in a pyramidal framework, yielding the so-called PCA pyramids. Then we present an image compression method based on the PCA pyramid, which is similar to the Laplace pyramid and wavelet transform. Some experimental results with real images are reported. Finally, we present a method to combine the quantization step with the learning of the PCA pyramid. 1 Introduction In the past few years, a lot of work has been done on using neural networks for image compression, d. e.g.

This paper presents instance-based state identification, an approach to reinforcement learning and hidden state that builds disambiguating amounts of short-term memory online, and also learns with an order of magnitude fewer training steps than several previous approaches. Inspired by a key similarity between learning with hidden state and learning in continuous geometrical spaces, this approach uses instance-based (or "memory-based") learning, a method that has worked well in continuous spaces. 1 BACKGROUND AND RELATED WORK When a robot's next course of action depends on information that is hidden from the sensors because of problems such as occlusion, restricted range, bounded field of view and limited attention, the robot suffers from hidden state. More formally, we say a reinforcement learning agent suffers from the hidden state problem if the agent's state representation is non-Markovian with respect to actions and utility. The hidden state problem arises as a case of perceptual aliasing: the mapping between states of the world and sensations of the agent is not one-to-one [Whitehead, 1992]. If the agent's perceptual system produces the same outputs for two world states in which different actions are required, and if the agent's state representation consists only of its percepts, then the agent will fail to choose correct actions.

Increasing attention has been paid to reinforcement learning algorithms in recent years, partly due to successes in the theoretical analysis of their behavior in Markov environments. If the Markov assumption is removed, however, neither generally the algorithms nor the analyses continue to be usable. We propose and analyze a new learning algorithm to solve a certain class of non-Markov decision problems. Our algorithm applies to problems in which the environment is Markov, but the learner has restricted access to state information. The algorithm involves a Monte-Carlo policy evaluation combined with a policy improvement method that is similar to that of Markov decision problems and is guaranteed to converge to a local maximum. The algorithm operates in the space of stochastic policies, a space which can yield a policy that performs considerably better than any deterministic policy. Although the space of stochastic policies is continuous-even for a discrete action space-our algorithm is computationally tractable.

An application of reinforcement learning to a linear-quadratic, differential game is presented. The reinforcement learning system uses a recently developed algorithm, the residual gradient form of advantage updating. The game is a Markov Decision Process (MDP) with continuous time, states, and actions, linear dynamics, and a quadratic cost function. The game consists of two players, a missile and a plane; the missile pursues the plane and the plane evades the missile. The reinforcement learning algorithm for optimal control is modified for differential games in order to find the minimax point, rather than the maximum. Simulation results are compared to the optimal solution, demonstrating that the simulated reinforcement learning system converges to the optimal answer. The performance of both the residual gradient and non-residual gradient forms of advantage updating and Q-learning are compared. The results show that advantage updating converges faster than Q-learning in all simulations.