The performance sensitivity of Albus' CMAC network was studied for the scenario in which faults are introduced into the adjustable weights after training has been accomplished. It was found that fault sensitivity was reduced with increased generalization when "loss of weight" faults were considered, but sensitivity was increased for "saturated weight" faults. 1 INTRODUCTION Fault-tolerance is often cited as an inherent property of neural networks, and is thought by many to be a natural consequence of "massively parallel" computational architectures. Numerous anecdotal reports of fault-tolerance experiments, primarily in pattern classification tasks, abound in the literature. However, there has been surprisingly little rigorous investigation of the fault-tolerance properties of various network architectures in other application areas. In this paper we investigate the fault-tolerance of the CMAC (Cerebellar Model Arithmetic Computer) network [Albus 1975] in a systematic manner. CMAC networks have attracted much recent attention because of their successful application in robotic manipulator control [Ersu 1984, Miller 1986, Lane 1988].

We study networks of spiking neurons in which spikes are fired as a Poisson process. The state of a cell is determined by the instantaneous firing rate, and in the limit of high firing rates our model reduces to that studied by Hopfield. We find that the inclusion of spiking results in several new features, such as a noise-induced asymmetry between "on" and "off" states of the cells and probability currents which destroy the usual description of network dynamics in terms of energy surfaces. Taking account of spikes also allows us to calibrate network parameters such as "synaptic weights" against experiments on real synapses. Realistic forms of the post synaptic response alters the network dynamics, which suggests a novel dynamical learning mechanism.

The performance sensitivity of Albus' CMAC network was studied for the scenario in which faults are introduced into the adjustable weights after training has been accomplished. It was found that fault sensitivity was reduced with increased generalization when "loss of weight" faults were considered, but sensitivity was increased for "saturated weight" faults. 1 INTRODUCTION Fault-tolerance is often cited as an inherent property of neural networks, and is thought by many to be a natural consequence of "massively parallel" computational architectures. Numerous anecdotal reports of fault-tolerance experiments, primarily in pattern classification tasks, abound in the literature. However, there has been surprisingly little rigorous investigation of the fault-tolerance properties of various network architectures in other application areas. In this paper we investigate the fault-tolerance of the CMAC (Cerebellar Model Arithmetic Computer) network [Albus 1975] in a systematic manner. CMAC networks have attracted much recent attention because of their successful application in robotic manipulator control [Ersu 1984, Miller 1986, Lane 1988]. Since fault-tolerance is a key concern in critical control tasks, there is added impetus to study Operational Fault Tolerance of CMAC Networks 341 this aspect of CMAC performance.

The brain represents the skin surface as a topographic map in the somatosensory cortex. This map has been shown experimentally to be modifiable in a use-dependent fashion throughout life. We present a neural network simulation of the competitive dynamics underlying this cortical plasticity by detailed analysis of receptive field properties of model neurons during simulations of skin coactivation, corticallesion, digit amputation and nerve section. 1 INTRODUCTION Plasticity of adult somatosensory cortical maps has been demonstrated experimentally in a variety of maps and species (Kass, et al., 1983; Wall, 1988). This report focuses on modelling primary somatosensory cortical plasticity in the adult monkey. We model the long-term consequences of four specific experiments, taken in pairs.

We study networks of spiking neurons in which spikes are fired as a Poisson process. The state of a cell is determined by the instantaneous firingrate, and in the limit of high firing rates our model reduces to that studied by Hopfield. We find that the inclusion of spiking results in several new features, such as a noise-induced asymmetry between "on" and "off" states of the cells and probability currentswhich destroy the usual description of network dynamics interms of energy surfaces. Taking account of spikes also allows usto calibrate network parameters such as "synaptic weights" against experiments on real synapses. Realistic forms of the post synaptic response alters the network dynamics, which suggests a novel dynamical learning mechanism.

The brain represents the skin surface as a topographic map in the somatosensory cortex. This map has been shown experimentally to be modifiable in a use-dependent fashion throughout life. We present a neural network simulation of the competitive dynamics underlying this cortical plasticity by detailed analysis of receptive field properties of model neurons during simulations of skin coactivation, cortical lesion, digit amputation and nerve section. 1 INTRODUCTION Plasticity of adult somatosensory cortical maps has been demonstrated experimentally in a variety of maps and species (Kass, et al., 1983; Wall, 1988). This report focuses on modelling primary somatosensory cortical plasticity in the adult monkey. We model the long-term consequences of four specific experiments, taken in pairs. With the first pair, behaviorally controlled stimulation of restricted skin surfaces (Jenkins, et al., 1990) and induced cortical lesions (Jenkins and Merzenich, 1987), we demonstrate that Hebbian-type dynamics is sufficient to account for the inverse relationship between cortical magnification (area of cortical map representing a unit area of skin) and receptive field size (skin surface which when stimulated excites a cortical unit) (Sur, et al., 1980; Grajski and Merzenich, 1990). These results are obtained with several variations of the basic model. We conclude that relying solely on cortical magnification and receptive field size will not disambiguate the contributions of each of the myriad circuits known to occur in the brain. With the second pair, digit amputation (Merzenich, et al., 1984) and peripheral nerve cut (without regeneration) (Merzenich, ct al., 1983), we explore the role of local excitatory connections in the model Neural Network Simulation of Somatosensory Representational Plasticity S3

The performance sensitivity of Albus' CMAC network was studied for the scenario in which faults are introduced into the adjustable weights after training has been accomplished. It was found that fault sensitivity was reduced with increased generalization when "loss of weight" faults were considered, but sensitivity was increased for "saturated weight" faults. 1 INTRODUCTION Fault-tolerance is often cited as an inherent property of neural networks, and is thought by many to be a natural consequence of "massively parallel" computational architectures. Numerous anecdotal reports of fault-tolerance experiments, primarily in pattern classification tasks, abound in the literature. However, there has been surprisingly little rigorous investigation of the fault-tolerance properties of various network architectures in other application areas. In this paper we investigate the fault-tolerance of the CMAC (Cerebellar Model Arithmetic Computer) network [Albus 1975] in a systematic manner. CMAC networks have attracted much recent attention because of their successful application in robotic manipulator control [Ersu 1984, Miller 1986, Lane 1988].

Two approaches are described which allow parallel computation of a model's nonlinear functions, parallel modification of a model's weights, and parallel propagation of a model's activation and error. Each approach also allows a model's interconnect structure to be physically dynamic. A Hopfield model is implemented with each approach at six sizes over the same number of CM processors to provide a performance comparison. INTRODUCflON Simulations of neural network models on digital computers perform various computations by applying linear or nonlinear functions, defined in a program, to weighted sums of integer or real numbers retrieved and stored by array reference. The numerical values are model dependent parameters like time averaged spiking frequency (activation), synaptic efficacy (weight), the error in error back propagation models, and computational temperature in thermodynamic models. The interconnect structure of a particular model is implied by indexing relationships between arrays defined in a program. On the Connection Machine (CM), these relationships are expressed in hardware processors interconnected by a 16-dimensional hypercube communication network. Mappings are constructed to defme higher dimensional interconnectivity between processors on top of the fundamental geometry of the communication network.

Two approaches are described which allow parallel computation of a model's nonlinear functions, parallel modification of a model's weights, and parallel propagation of a model's activation and error. Each approach also allows a model's interconnect structure to be physically dynamic. A Hopfield model is implemented with each approach at six sizes over the same number of CM processors to provide a performance comparison. INTRODUCflON Simulations of neural network models on digital computers perform various computations by applying linear or nonlinear functions, defined in a program, to weighted sums of integer or real numbers retrieved and stored by array reference. The numerical values are model dependent parameters like time averaged spiking frequency (activation), synaptic efficacy (weight), the error in error back propagation models, and computational temperature in thermodynamic models. The interconnect structure of a particular model is implied by indexing relationships between arrays defined in a program. On the Connection Machine (CM), these relationships are expressed in hardware processors interconnected by a 16-dimensional hypercube communication network. Mappings are constructed to defme higher dimensional interconnectivity between processors on top of the fundamental geometry of the communication network.

Asa means of probing these cerebellar mechanisms, my colleagues and I have been conducting microelectrode studies of the neural messages that flow through the intermediate divisionof the cerebellum and onward to limb muscles via the rubrospinal tract. We regard this cerebellorubrospinal pathwayas a useful model system for studying general problems of sensorimotor integration and adaptive brain function.