We use statistical mechanics to study generalization in large committee machines. For an architecture with nonoverlapping receptive fields a replica calculation yields the generalization error in the limit of a large number of hidden units.

In stochastic learning, weights are random variables whose time evolution is governed by a Markov process. We summarize the theory of the time evolution of P, and give graphical examples of the time evolution that contrast the behavior of stochastic learning with true gradient descent (batch learning). Finally, we use the formalism to obtain predictions of the time required for noise-induced hopping between basins of different optima. We compare the theoretical predictions with simulations of large ensembles of networks for simple problems in supervised and unsupervised learning. Despite the recent application of convergence theorems from stochastic approximation theory to neural network learning (Oja 1982, White 1989) there remain outstanding questions about the search dynamics in stochastic learning.

We analyse the effects of analog noise on the synaptic arithmetic during MultiLayer Perceptron training, by expanding the cost function to include noise-mediated penalty terms. Predictions are made in the light of these calculations which suggest that fault tolerance, generalisation ability and learning trajectory should be improved by such noise-injection. Extensive simulation experiments on two distinct classification problems substantiate the claims. The results appear to be perfectly general for all training schemes where weights are adjusted incrementally, and have wide-ranging implications for all applications, particularly those involving "inaccurate" analog neural VLSI.

The ensemble dynamics of stochastic learning algorithms can be studied using theoretical techniques from statistical physics. We develop the equations of motion for the weight space probability densities for stochastic learning algorithms. We discuss equilibria in the diffusion approximation and provide expressions for special cases of the LMS algorithm. The equilibrium densities are not in general thermal (Gibbs) distributions in the objective function being minimized, but rather depend upon an effective potential that includes diffusion effects. Finally we present an exact analytical expression for the time evolution of the density for a learning algorithm with weight updates proportional to the sign of the gradient.

Human VlSlon systems integrate information nonlocally, across long spatial ranges. For example, a moving stimulus appears smeared when viewed briefly (30 ms), yet sharp when viewed for a longer exposure (100 ms) (Burr, 1980). This suggests that visual systems combine information along a trajectory that matches the motion of the stimulus. Our self-organizing neural network model shows how developmental exposure to moving stimuli can direct the formation of horizontal trajectory-specific motion integration pathways that unsmear representations of moving stimuli. These results account for Burr's data and can potentially also model ot.her phenomena, such as visual inertia. 1 INTRODUCTION N onlocal interactions strongly influence the processing of visual motion information and the response characteristics of visual neurons. Examples include: attentional modulation of receptive field shape; modulation of neural response by stimuli beyond the classical receptive field; and neural response to large-field background motion. In this paper we present a model of the development of nonlocal neural mechanisms for visual motion processing.

In visual processing the ability to deal with missing and noisy information is crucial. Occlusions and unreliable feature detectors often lead to situations where little or no direct information about features is available. However the available information is usually sufficient to highly constrain the outputs. We discuss Bayesian techniques for extracting class probabilities given partial data. The optimal solution involves integrating over the missing dimensions weighted by the local probability densities. We show how to obtain closed-form approximations to the Bayesian solution using Gaussian basis function networks. The framework extends naturally to the case of noisy features.

Within a simple test-bed, application of feed-forward neurocontrol for short-term planning of robot trajectories in a dynamic environment is studied. The action network is embedded in a sensorymotoric system architecture that contains a separate world model. It is continuously fed with short-term predicted spatiotemporal obstacle trajectories, and receives robot state feedback. The action net allows for external switching between alternative planning tasks. It generates goal-directed motor actions - subject to the robot's kinematic and dynamic constraints - such that collisions with moving obstacles are avoided.

A peg-in-hole insertion task is used as an example to illustrate the utility of direct associative reinforcement learning methods for learning control under real-world conditions of uncertainty and noise. Task complexity due to the use of an unchamfered hole and a clearance of less than 0.2mm is compounded by the presence of positional uncertainty of magnitude exceeding 10 to 50 times the clearance. Despite this extreme degree of uncertainty, our results indicate that direct reinforcement learning can be used to learn a robust reactive control strategy that results in skillful peg-in-hole insertions.

Recent research on reinforcement learning has focused on algorithms based on the principles of Dynamic Programming (DP). One of the most promising areas of application for these algorithms is the control of dynamical systems, and some impressive results have been achieved. However, there are significant gaps between practice and theory. In particular, there are no con vergence proofs for problems with continuous state and action spaces, or for systems involving nonlinear function approximators (such as multilayer perceptrons). This paper presents research applying DPbased reinforcement learning theory to Linear Quadratic Regulation (LQR), an important class of control problems involving continuous state and action spaces and requiring a simple type of nonlinear function approximator. We describe an algorithm based on Q-Iearning that is proven to converge to the optimal controller for a large class of LQR problems. We also describe a slightly different algorithm that is only locally convergent to the optimal Q-function, demonstrating one of the possible pitfalls of using a nonlinear function approximator with DPbased learning.

How can artificial neural nets generalize better from fewer examples? In order to generalize successfully, neural network learning methods typically require large training data sets. We introduce a neural network learning method that generalizes rationally from many fewer data points, relying instead on prior knowledge encoded in previously learned neural networks. For example, in robot control learning tasks reported here, previously learned networks that model the effects of robot actions are used to guide subsequent learning of robot control functions. For each observed training example of the target function (e.g. the robot control policy), the learner explains the observed example in terms of its prior knowledge, then analyzes this explanation to infer additional information about the shape, or slope, of the target function. This shape knowledge is used to bias generalization when learning the target function. Results are presented applying this approach to a simulated robot task based on reinforcement learning.