A nonlinear dynamic system is called contracting if initial conditions are forgotten exponentially fast, so that all trajectories converge to a single trajectory. We use contraction theory to derive an upper bound for the strength of recurrent connections that guarantees contraction for complex neural networks. Specifically, we apply this theory to a special class of recurrent networks, often called Cooperative Competitive Networks (CCNs), which are an abstract representation of the cooperative-competitive connectivity observed in cortex. This specific type of network is believed to play a major role in shaping cortical responses and selecting the relevant signal among distractors and noise. In this paper, we analyze contraction of combined CCNs of linear threshold units and verify the results of our analysis in a hybrid analog/digital VLSI CCN comprising spiking neurons and dynamic synapses.

A non--linear dynamic system is called contracting if initial conditions are forgotten exponentially fast, so that all trajectories converge to a single trajectory.

Cooperative competitive networks are believed to play a central role in cortical processing and have been shown to exhibit a wide set of useful computational properties. We propose a VLSI implementation of a spiking cooperative competitive networkand show how it can perform context dependent computation both in the mean firing rate domain and in spike timing correlation space. In the mean rate case the network amplifies the activity of neurons belonging to the selected stimulus and suppresses the activity of neurons receiving weaker stimuli. In the event correlation case, the recurrent network amplifies with a higher gain the correlation betweenneurons which receive highly correlated inputs while leaving the mean firing rate unaltered. We describe the network architecture and present experimental datademonstrating its context dependent computation capabilities.

The neurons of the neocortex communicate by asynchronous events called action potentials (or'spikes'). However, for simplicity of simulation, most models of processing by cortical neural networks have assumed that the activations of their neurons can be approximated by event rates rather than taking account of individual spikes.The obstacle to exploring the more detailed spike processing of these networks has been reduced considerably in recent years by the development of hybrid analog-digital Very-Large Scale Integrated (hVLSI) neural networks composed ofspiking neurons that are able to operate in real-time. In this paper we describe sucha hVLSI neural network that performs an interesting task of selective attentional processing that was previously described for a simulated'pointer-map' rate model by Hahnloser and colleagues. We found that most of the computational features of their rate model can be reproduced in the spiking implementation; but, that spike-based processing requires a modification of the original network architecture inorder to memorize a previously attended target.

To control the walking gaits of a four-legged robot we present a novel neuromorphic VLSI chip that coordinates the relative phasing of the robot's legs similar to how spinal Central Pattern Generators are believed to control vertebrate locomotion [3]. The chip controls the leg movements by driving motors with time varying voltages which are the outputs of a small network of coupled oscillators. The characteristics of the chip's output voltages depend on a set of input parameters. The relationship between input parameters and output voltages can be computed analytically for an idealized system. In practice, however, this ideal relationship is only approximately true due to transistor mismatch and offsets. Fine tuning of the chip's input parameters is done automatically by the robotic system, using an unsupervised Support Vector (SV) learning algorithm introduced recently [7]. The learning requires only that the description of the desired output is given. The machine learns from (unlabeled) examples how to set the parameters to the chip in order to obtain a desired motor behavior.

To control the walking gaits of a four-legged robot we present a novel neuromorphic VLSI chip that coordinates the relative phasing of the robot's legs similar to how spinal Central Pattern Generators are believed to control vertebrate locomotion [3]. The chip controls the leg movements bydriving motors with time varying voltages which are the outputs of a small network of coupled oscillators. The characteristics of the chip's output voltages depend on a set of input parameters.

In 1986, Tanner and Mead [1] implemented an interesting constraint satisfaction circuitfor global motion sensing in aVLSI. We report here a new and improved aVLSI implementation that provides smooth optical flow as well as global motion in a two dimensional visual field. The computation ofoptical flow is an ill-posed problem, which expresses itself as the aperture problem. However, the optical flow can be estimated by the use of regularization methods, in which additional constraints are introduced interms of a global energy functional that must be minimized. We show how the algorithmic constraints of Hom and Schunck [2] on computing smoothoptical flow can be mapped onto the physical constraints of an equivalent electronic network.

In 1986, Tanner and Mead [1] implemented an interesting constraint satisfaction circuit for global motion sensing in a VLSI. We report here a new and improved a VLSI implementation that provides smooth optical flow as well as global motion in a two dimensional visual field. The computation of optical flow is an ill-posed problem, which expresses itself as the aperture problem. However, the optical flow can be estimated by the use of regularization methods, in which additional constraints are introduced in terms of a global energy functional that must be minimized. We show how the algorithmic constraints of Hom and Schunck [2] on computing smooth optical flow can be mapped onto the physical constraints of an equivalent electronic network.

About half the pyramidal neurons in layer 5 of neocortex have long apical dendrites that arborize extensively in layers 1-3. There the dendrites receive synaptic input from the inter-areal feedback projections (Felleman and van Essen, 1991) that play an important role in many models of brain function (Rockland and Virga, 1989). At first sight this seems to be an unsatisfactory arrangement. In light of traditional passive models of dendritic function the distant inputs cannot have a significant effect on the output discharge of the pyramidal cell. The distal inputs are at least one to two space constants removed from the soma in layer 5 and so only a small fraction of the voltage signal will reach there.

About half the pyramidal neurons in layer 5 of neocortex have long apical dendrites that arborize extensively in layers 1-3. There the dendrites receive synaptic input from the inter-areal feedback projections (Felleman and van Essen, 1991) that play an important role in many models of brain function (Rockland and Virga, 1989). At first sight this seems to be an unsatisfactory arrangement. In light of traditional passive models of dendritic function the distant inputs cannot have a significant effect on the output discharge of the pyramidal cell. The distal inputs are at least one to two space constants removed from the soma in layer 5 and so only a small fraction of the voltage signal will reach there.