Box 150, Cheongryang, Seoul, Korea ABSTRACT Inverse matrix calculation can be considered as an optimization. We have demonstrated that this problem can be rapidly solved by highly interconnected simple neuron-like analog processors. A network for matrix inversion based on the concept of Hopfield's neural network was designed, and implemented with electronic hardware. With slight modifications, the network is readily applicable to solving a linear simultaneous equation efficiently. Notable features of this circuit are potential speed due to parallel processing, and robustness against variations of device parameters.

(June 1987).

Here, X is a finite or infinite set, and Y is another finite or infinite set. A learning machine observes any set of pairs (x, y) sampled randomly from X x Y. (X x Y means the Cartesian product of X and Y.) And, it computes some estimate j:

The generalization replaces two state neurons by neurons taking a richer set of values. Two classes of neuron input output relations are developed guaranteeing convergence to stable states. The first is a class of "continuous" relations and the second is a class of allowed quantization rules for the neurons.

Box 150, Cheongryang, Seoul, Korea ABSTRACT Inverse matrix calculation can be considered as an optimization. We have demonstrated that this problem can be rapidly solved by highly interconnected simple neuron-like analog processors. A network for matrix inversion based on the concept of Hopfield's neural network was designed, and implemented with electronic hardware. With slight modifications, the network is readily applicable to solving a linear simultaneous equation efficiently. Notable features of this circuit are potential speed due to parallel processing, and robustness against variations of device parameters.

The generalization replaces two state neurons by neurons taking a richer set of values. Two classes of neuron input output relations are developed guaranteeing convergence to stable states. The first is a class of "continuous" relations and the second is a class of allowed quantization rules for the neurons.

(June 1987).

Here, X is a finite or infinite set, and Y is another finite or infinite set. A learning machine observes any set of pairs (x, y) sampled randomly from X x Y. (X x Y means the Cartesian product of X and Y.) And, it computes some estimate j:

The generalization replaces two state neurons by neurons taking a richer set of values. Two classes of neuron input output relations are developed guaranteeing convergence to stable states. The first is a class of "continuous" relations andthe second is a class of allowed quantization rules for the neurons.

Here, X is a finite or infinite set, and Y is another finite or infinite set. A learning machine observes any set of pairs (x, y) sampled randomly from X x Y. (X x Y means the Cartesian product of X and Y.) And, it computes some estimate j: