We study several statistically and biologically motivated learning rules using the same visual environment, one made up of natural scenes, and the same single cell neuronal architecture. This allows us to concentrate on the feature extraction and neuronal coding properties of these rules. Included in these rules are kurtosis and skewness maximization, the quadratic form of the BCM learning rule, and single cell ICA. Using a structure removal method, we demonstrate that receptive fields developed using these rules depend on a small portion of the distribution. We find that the quadratic form of the BCM rule behaves in a manner similar to a kurtosis maximization rule when the distribution contains kurtotic directions, although the BCM modification equations are computationally simpler.

Online learning is one of the most common forms of neural network training. We present an analysis of online learning from finite training sets for nonlinear networks (namely, soft-committee machines), advancing the theory to more realistic learning scenarios. Dynamical equations are derived for an appropriate set of order parameters; these are exact in the limiting case of either linear networks or infinite training sets. Preliminary comparisons with simulations suggest that the theory captures some effects of finite training sets, but may not yet account correctly for the presence of local minima.

This simple modification brings increased representational power, as illustrated by two multimodal examples of the rectified Gaussian, the competitive and the cooperative distributions. The modes of the competitive distribution are well-separated by regions of low probability. The modes of the cooperative distribution are closely spaced along a nonlinear continuous manifold. Neither distribution can be accurately approximated by a single standard Gaussian. In short, the rectified Gaussian is able to represent both discrete and continuous variability in a way that a standard Gaussian cannot.

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.