The development of projections from the retinas to the cortex is mathematically analyzed according to the previously proposed thermodynamic formulation of the self-organization of neural networks. Three types of submodality included in the visual afferent pathways are assumed in two models: model (A), in which the ocularity and retinotopy are considered separately, and model (B), in which on-center/off-center pathways are considered in addition to ocularity and retinotopy. Model (A) shows striped ocular dominance spatial patterns and, in ocular dominance histograms, reveals a dip in the binocular bin. Model (B) displays spatially modulated irregular patterns and shows single-peak behavior in the histograms. When we compare the simulated results with the observed results, it is evident that the ocular dominance spatial patterns and histograms for models (A) and (B) agree very closely with those seen in monkeys and cats.

A network based on splines is described.

We present a new way to derive dissipative, optimizing dynamics from the Lagrangian formulation of mechanics. It can be used to obtain both standard and novel neural net dynamics for optimization problems. To demonstrate this we derive standard descent dynamics as well as nonstandard variants that introduce a computational attention mechanism.

This paper explores the effect of initial weight selection on feed-forward networks learning simple functions with the back-propagation technique.

A new class of data structures called "bumptrees" is described. These structures are useful for efficiently implementing a number of neural network related operations. An empirical comparison with radial basis functions is presented on a robot ann mapping learning task.

We present a unified framework for a number of different ways of failing to generalize properly.

ABSTRACT A large number of VLSI implementations of neural network models have been reported. The diversity of these implementations is noteworthy. This paper attempts to put a group of representative VLSI implementations in perspective by comparing and contrasting them. Design tradeoffs are discussed and some suggestions forthe direction of future implementation efforts are made. IMPLEMENTATION Changing the way information is represented can be beneficial.

In this paper, we prove that the vectors in the LVQ learning algorithm converge. We do this by showing that the learning algorithm performs stochastic approximation. Convergence is then obtained by identifying the appropriate conditions on the learning rate and on the underlying statistics of the classification problem. We also present a modification to the learning algorithm which we argue results in convergence of the LVQ error to the Bayesian optimal error as the appropriate parameters become large.

Recent progress in network design demonstrates that nonlinear feedforward neural networks can perform impressive pattern classification for a variety of real-world applications (e.g., Le Cun et al., 1990; Waibel et al., 1989). Various simulations and relationships between the neural network and machine learning theoretical literatures also suggest that too large a number of free parameters ("weight overfitting") could substantially reduce generalization performance.

Robustness is a commonly bruited property of neural networks; in particular, a folk theorem in neural computation asserts that neural networks-in contexts with large interconnectivity-continue to function efficiently, albeit with some degradation, in the presence of component damage or loss. A second folk theorem in such contexts asserts that dense interconnectivity between neural elements is a sine qua non for the efficient usage of resources. These premises are formally examined in this communication in a setting that invokes the notion of the "devil"