We show analytically how the stability of two-dimensional lateral inhibition neural networks depends on the local connection topology. For various network topologies, we calculate the critical time delay for the onset of oscillation in continuous-time networks and present analytic phase diagrams characterizing the dynamics of discrete-time networks.

A simple architecture and algorithm for analytically guaranteed associative memory storage of analog patterns, continuous sequences, and chaotic attractors in the same network is described. A matrix inversion determines network weights, given prototype patterns to be stored.

The Hopfield network (Hopfield, 1982,1984) provides a simple model of an associative memory in a neuronal structure. This model, however, is based on highly artificial assumptions, especially the use of formal-two state neurons (Hopfield, 1982) or graded-response neurons (Hopfield, 1984).

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.

Combining neuropharmacological experiments with computational modeling, we have shown that cholinergic modulation may enhance associative memory function in piriform (olfactory) cortex. We have shown that the acetylcholine analogue carbachol selectively suppresses synaptic transmission between cells within piriform cortex, while leaving input connections unaffected. When tested in a computational model of piriform cortex, this selective suppression, applied during learning, enhances associative memory performance.

We are exploring the significance of biological complexity for neuronal computation. Here we demonstrate that Hebbian synapses in realistically-modeled hippocampal pyramidal cells may give rise to two novel forms of self -organization in response to structured synaptic input. First, on the basis of the electrotonic relationships between synaptic contacts, a cell may become tuned to a small subset of its input space. Second, the same mechanisms may produce clusters of potentiated synapses across the space of the dendrites. The latter type of self-organization may be functionally significant in the presence of nonlinear dendritic conductances.

A three-layered neural network model was used to explore the organization of the vestibulo-ocular reflex (VOR). The dynamic model was trained using recurrent back-propagation to produce compensatory, long duration eye muscle motoneuron outputs in response to short duration vestibular afferent head velocity inputs. The network learned to produce this response prolongation, known as velocity storage, by developing complex, lateral inhibitory interactions among the interneurons. These had the low baseline, long time constant, rectified and skewed responses that are characteristic of real VOR interneurons. The model suggests that all of these features are interrelated and result from lateral inhibition.

Simple classical spin models well-known to physicists as the ANNNI and Heisenberg XY Models. in which long-range interactions occur in a pattern given by the Mexican Hat operator.

Feature selective cells in the primary visual cortex of several species are organized in hierarchical topographic maps of stimulus features like "position in visual space", "orientation" and" ocular dominance". In order to understand and describe their spatial structure and their development, we investigate a self-organizing neural network model based on the feature map algorithm. The model explains map formation as a dimension-reducing mapping from a high-dimensional feature space onto a two-dimensional lattice, such that "similarity" between features (or feature combinations) is translated into "spatial proximity" between the corresponding feature selective cells. The model is able to reproduce several aspects of the spatial structure of cortical maps in the visual cortex. 1 Introduction Cortical maps are functionally defined structures of the cortex, which are characterized by an ordered spatial distribution of functionally specialized cells along the cortical surface. In the primary visual area(s) the response properties of these cells must be described by several independent features, and there is a strong tendency to map combinations of these features onto the cortical surface in a way that translates "similarity" into "spatial proximity" of the corresponding feature selective cells (see e.g.

We describe a computational model of the development and regeneration of specific eye-brain circuits. The model comprises a self-organizing map-forming network which uses local Hebb rules, constrained by (genetically determined) molecular markers. Various simulations of the development and regeneration of eye-brain maps in fish and frogs are described, in particular successful simulations of experiments by Schmidt-Cicerone-Easter; Meyer; and Y oon. 1 INTRODUCTION In a previous paper published in last years proceedings (Cowan & Friedman 1990) we outlined a new computational model for the development and regeneration of eye-brain maps. We indicated that such a model can simulate the results of a number of the more complicated surgical manipulations carried out on the visual pathways of goldfish and frogs. In this paper we describe in more detail some of these experiments, and our simulations of them.