A Lyapunov function for excitatory-inhibitory networks is constructed. The construction assumes symmetric interactions within excitatory and inhibitory populations of neurons, and antisymmetric interactions between populations. The Lyapunov function yields sufficient conditions for the global asymptotic stability of fixed points. If these conditions are violated, limit cycles may be stable. The relations of the Lyapunov function to optimization theory and classical mechanics are revealed by minimax and dissipative Hamiltonian forms of the network dynamics.

We present a method for determining the globally optimal online learning rule for a soft committee machine under a statistical mechanics framework. This work complements previous results on locally optimal rules, where only the rate of change in generalization error was considered. We maximize the total reduction in generalization error over the whole learning process and show how the resulting rule can significantly outperform the locally optimal rule. 1 Introduction We consider a learning scenario in which a feed-forward neural network model (the student) emulates an unknown mapping (the teacher), given a set of training examples produced by the teacher. The performance of the student network is typically measured by its generalization error, which is the expected error on an unseen example. The aim of training is to reduce the generalization error by adapting the student network's parameters appropriately. A common form of training is online learning, where training patterns are presented sequentially and independently to the network at each learning step.

We employ both master equation and order parameter approaches to analyze the asymptotic dynamics of online learning with different learning rate annealing schedules. We examine the relations between the results obtained by the two approaches and obtain new results on the optimal decay coefficients and their dependence on the number of hidden nodes in a two layer architecture.

This observation has boosted interest in the field of artificial neural networks [Hopfield 82], [Rumelhart 82]. The latter are built by interconnecting artificial neurons whose behavior is inspired by that of biological neurons.

Our model consists of a classical energy mechanism whose output is divided by nonclassical gain control and texture contrast mechanisms. We apply this model to review movies, a stimulus sequence that replicates the stimulation a cell receives during free viewing of natural images. Data were collected from three cells using five different review movies, and the model was fit separately to the data from each movie. For the energy mechanism alone we find modest but significant correlations (rE 0.41, 0.43, 0.59, 0.35) between model and data. These correlations are improved somewhat when we allow for suppressive surround effects (rE G 0.42, 0.56, 0.60, 0.37). In one case the inclusion of a delayed suppressive surround dramatically improves the fit to the data by modifying the time course of the model's response.

We have studied the application of an independent component analysis (ICA) approach to the identification and possible removal of artifacts from a magnetoencephalographic (MEG) recording.

In macaque inferotemporal cortex (IT), neurons have been found to respond selectively to complex shapes while showing broad tuning ("invariance") with respect to stimulus transformations such as translation and scale changes and a limited tuning to rotation in depth.

Further, the greater the similarity between objects, the stronger is the dependence on object appearance, and the more important twodimensional (2D) image information becomes. These findings, however, do not rule out the use of 3D structural information in recognition, and the degree to which 3D information is used in visual memory is an important issue. Liu, Knill, & Kersten (1995) showed that any model that is restricted to rotations in the image plane of independent 2D templates could not account for human performance in discriminating novel object views. We now present results from models of generalized radial basis functions (GRBF), 2D nearest neighbor matching that allows 2D affine transformations, and a Bayesian statistical estimator that integrates over all possible 2D affine transformations. The performance of the human observers relative to each of the models is better for the novel views than for the familiar template views, suggesting that humans generalize better to novel views from template views. The Bayesian estimator yields the optimal performance with 2D affine transformations and independent 2D templates. Therefore, models of 2D affine matching operations with independent 2D templates are unlikely to account for human recognition performance.

In most neural network models, synapses are treated as static weights that change only on the slow time scales of learning. In fact, however, synapses are highly dynamic, and show use-dependent plasticity over a wide range of time scales. Moreover, synaptic transmission is an inherently stochastic process: a spike arriving at a presynaptic terminal triggers release of a vesicle of neurotransmitter from a release site with a probability that can be much less than one. Changes in release probability represent one of the main mechanisms by which synaptic efficacy is modulated in neural circuits. We propose and investigate a simple model for dynamic stochastic synapses that can easily be integrated into common models for neural computation. We show through computer simulations and rigorous theoretical analysis that this model for a dynamic stochastic synapse increases computational power in a nontrivial way. Our results may have implications for the processing of time-varying signals by both biological and artificial neural networks. A synapse 8 carries out computations on spike trains, more precisely on trains of spikes from the presynaptic neuron. Each spike from the presynaptic neuron mayor may not trigger the release of a neurotransmitter-filled vesicle at the synapse.

In normal vision, the inputs from the two eyes are integrated into a single percept. When dissimilar images are presented to the two eyes, however, perceptual integration gives way to alternation between monocular inputs, a phenomenon called binocular rivalry. Although recent evidence indicates that binocular rivalry involves a modulation of neuronal responses in extrastriate cortex, the basic mechanisms responsible for differential processing of con:6.icting