IR is typically a sigmoidal function such as (1.2) but other choices than (1.2) are possible and of interest.

Learning curves show how a neural network is improved as the number of t.raiuing examples increases and how it is related to the network complexity. The present paper clarifies asymptotic properties and their relation of t.wo learning curves, one concerning the predictive loss or generalization loss and the other the training loss. The result gives a natural definition of the complexity of a neural network. Moreover, it provides a new criterion of model selection.

We present a methodological framework enabling a detailed description of the performance of Hopfield-like attractor neural networks (ANN) in the first two iterations. Using the Bayesian approach, we find that performance is improved when a history-based term is included in the neuron's dynamics. A further enhancement of the network's performance is achieved by judiciously choosing the censored neurons (those which become active in a given iteration) on the basis of the magnitude of their post-synaptic potentials. The contribution of biologically plausible, censored, historydependent dynamics is especially marked in conditions of low firing activity and sparse connectivity, two important characteristics of the mammalian cortex. In such networks, the performance attained is higher than the performance of two'independent' iterations, which represents an upper bound on the performance of history-independent networks.

The occurence of chaos in recurrent neural networks is supposed to depend on the architecture and on the synaptic coupling strength. It is studied here for a randomly diluted architecture. By normalizing the variance of synaptic weights, we produce a bifurcation parameter, dependent on this variance and on the slope of the transfer function but independent of the connectivity, that allows a sustained activity and the occurence of chaos when reaching a critical value. Even for weak connectivity and small size, we find numerical results in accordance with the theoretical ones previously established for fully connected infinite sized networks. Moreover the route towards chaos is numerically checked to be a quasi-periodic one, whatever the type of the first bifurcation is (Hopf bifurcation, pitchfork or flip).

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.

We analyze the "query by committee" algorithm, a method for filtering informative queries from a random stream of inputs. We show that if the two-member committee algorithm achieves information gain with positive lower bound, then the prediction error decreases exponentially with the number of queries. We show that, in particular, this exponential decrease holds for query learning of thresholded smooth functions.

Principal Component Analysis (PCA) is an essential technique for data compression and feature extraction, and has been widely used in statistical data analysis, communication theory, pattern recognition and image processing. In the neural network literature, a lot of studies have been made on learning rules for implementing PCA or on networks closely related to PCA (see Xu & Yuille, 1993 for a detailed reference list which contains more than 30 papers related to these issues).

The invariance of an objects' identity as it transformed over time provides a powerful cue for perceptual learning. We present an unsupervised learning procedure which maximizes the mutual information between the representations adopted by a feed-forward network at consecutive time steps. We demonstrate that the network can learn, entirely unsupervised, to classify an ensemble of several patterns by observing pattern trajectories, even though there are abrupt transitions from one object to another between trajectories. The same learning procedure should be widely applicable to a variety of perceptual learning tasks. 1 INTRODUCTION A promising approach to understanding human perception is to try to model its developmental stages. There is ample evidence that much of perception is learned.

The primate brain must solve two important problems in grasping movements. The first problem concerns the recognition of grasped objects: specifically, how does the brain integrate visual and motor information on a grasped object? The second problem concerns hand shape planning: specifically, how does the brain design the hand configuration suited to the shape of the object and the manipulation task? A neural network model that solves these problems has been developed. The operations of the network are divided into a learning phase and an optimization phase. In the learning phase, internal representations, which depend on the grasped objects and the task, are acquired by integrating visual and somatosensory information. In the optimization phase, the most suitable hand shape for grasping an object is determined by using a relaxation computation of the network.

The overall goal is to reduce spacecraft weight.