US 5,671,336 AGranted

Apparatus based on n-variable unlimited recurrent adjustable network

AssigneeNissan Motor Co., Ltd.

InventorsKazumi Yoshida, Norimasa Kishi

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Abstract

An apparatus based on an n-variable unlimited recurrent adjustable network (URAN.sub.n) comprises: two layers, each layer having the same number (n) of neuron elements; linear neuron elements x.sub.i constituting a first layer; nonlinear artificial neuron elements y.sub.j having respective temperature-dependent parameters Tj and constituting a second layer. Each linear and nonlinear neuron element of the first and second layers is connected using a feedforward connection part, a recurrent connection part, and an auto connection part. A nonlinear oscillation apparatus having the recurrent neural network is generally operated in accordance with the equation (1) described below: ##EQU1##

Claims26

Dependent claims

A nonlinear oscillation apparatus having a recurrent neural network having a two-layer hierarchical structure and a recurrent connection, each layer of said recurrent neural network including the same number of neuron elements, and said recurrent neural network comprising:

a) a first layer including a plurality of circuits of linear artificial neurons X.sub.i (i=1, 2, - - - , i, - - - n);
b) a second layer including a plurality of circuits of nonlinear artificial neurons y.sub.j (j=1, 2, - - - , j, - - - , n) and arranged to convert input signals thereto into output signals by means of given same nonlinear functions f, their temperature parameters being denoted by T.sub.j ;
c) a feedforward connection part arranged to multiply outputs of the first layer circuits of linear artificial neurons x.sub.i by feedforward connection coefficients w.sub.ji and to output each of the multiplied outputs to a corresponding one of all of the circuits of nonlinear artificial neurons y.sub.j of said second layer;
d) a recurrent connecting part arranged to multiply outputs of the respective circuits of nonlinear artificial neurons y.sub.j of said second layer by recurrent connection coefficients .gamma..sub.j, to output first-order delays of time constants .tau..sub.j for the multiplied outputs of the respective circuits of nonlinear artificial neurons y.sub.j, and to input the delayed multiplied output of each respective circuit of onlinear artificial neurons y.sub.j to a corresponding one of the circuits of linear artificial neurons x.sub.j of said first layer;
and
e) an auto connection part arranged to multiply the outputs of the respective circuits of linear artificial neurons x.sub.i of the first layer, to output the first-order delays of the time constants .tau..sub.i for the multiplied outputs from said auto connection part, and to input again each of the first-order delayed outputs to the corresponding one of said circuits of linear artificial neurons x.sub.i, and wherein said recurrent neural network operates in accordance with the following equation (1) and said nonlinear oscillation apparatus generates a nonlinear oscillation when said recurrent neural network operates in accordance with the following equation (1), ##EQU18## wherein f denotes the given nonlinear function having saturation characteristics, and g denotes a characteristic function to discuss a stability of a differential equation and a nullcline when g=0.

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An apparatus based on an n-variable unlimited recurrent adjustable network, comprising:

a) at least two hierarchically structured layers, each layer having the same number (n) of neuron circuit elements;
b) a plurality of linear artificial neuron circuit elements x.sub.i (i1, 2, - - - , i, - - - , n) constituting a first layer of the two layers;
c) a plurality of nonlinear artificial neuron circuit elements y.sub.j (j=1, 2, - - - , j, - - - , n) having respective temperature-dependent parameters T.sub.j constituting a second layer of the two layers, each nonlinear artificial neuron circuit element y.sub.j converting an input signal thereto into an output signal using a predetermined nonlinear function f;
d) a feedforward connection part arranged to multiply each output signal derived from each one of the linear artificial neuron circuit elements (x.sub.i) of the first layer by a feedforward connection coefficient w.sub.ji and to output each of the multiplied output signals (w.sub.11, w.sub.12, - - - w.sub.1j, - - - , w.sub.1n, w.sub.21, w.sub.22, - - - , w.sub.2j, - - - , w.sub.2n, - - - , w.sub.n1, w.sub.n2, - - - , w.sub.nj, - - - , w.sub.nn) for all of the nonlinear artificial neuron circuit elements y.sub.j of the second layer;
e) a recurrent connection part arranged to multiply each output signal derived from the nonlinear artificial neuron circuit elements y.sub.j of the second layer by a recurrent connection coefficient .lambda..sub.j, to output a first-order time delay corresponding to a time constant .tau..sub.j for the .lambda..sub.j multiplied output signal, and, thereafter, to provide the .tau..sub.j delayed and .lambda..sub.j multiplied output signal again to the corresponding one x.sub.j of the linear artificial neuron circuit elements of the first layer;
and
f) an auto connection part arranged to multiply the output signal derived from each one x.sub.i of the respective linear artificial neuron circuit elements of the first layer by an auto connection coefficient .mu..sub.i, to output the first-order delay corresponding to the time constant .tau..sub.i for the .mu..sub.i multiplied signal, and to output the .mu..sub.i multiplied, .mu..sub.i delayed signal again for the corresponding one x.sub.i of the respective linear artificial neuron circuit elements.

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An apparatus based on an n-variable unlimited recurrent adjustable network, wherein n is an arbitrary number, and said apparatus comprising:

a) at least two hierarchically structured layers, each layer having the same number (n) of neuron circuit elements;
b) a plurality of linear artificial neuron circuit elements X.sub.i (i=1 - - - n) constituting a first layer of the two layers and comprising first adders (100);
c) a plurality of nonlinear artificial neuron circuit elements y.sub.j (j=1 - - - n), having respective temperature-dependent parameters Tj, constituting a second layer of the two layers, comprising second adders and nonlinear amplifiers (200), each nonlinear artificial neuron circuit element y.sub.j converting an input signal thereto into an output signal using a predetermined nonlinear function f to tanh(x);
d) a feedforward connection part, connection between said linear artificial neuron circuit element and said nonlinear artificial neuron circuit element and comprising a plurality of multipliers, to multiply each output signal derived from each one of the linear artificial neuron circuit elements (x.sub.i) of the first layer by a feedforward connection coefficient w.sub.ji and to output each of the multiplied output signals (w.sub.ji x.sub.i) for all of the nonlinear artificial neuron circuit elements (y.sub.i) of the second layer;
e) a recurrent connection part, connected between output ends of the nonlinear artificial neuron circuit element and input ends of the linear artificial neuron circuit element and comprising delay circuit elements (312) and associated multipliers (311), to multiply each output signal derived from the nonlinear artificial neuron circuit elements y.sub.j of the second layer by a recurrent connection coefficient .lambda..sub.j, to output a first-order time delay corresponding to a time constant .tau..sub.j for the .lambda..sub.j multiplied output signal, and, thereafter, to output the .tau..sub.j delayed and the .lambda..sub.j multiplied output signal again to the corresponding one (x.sub.j) of the linear artificial neuron circuit elements of the first layer;
and
f) an auto connection part, connected between the linear artificial neuron circuit element and the same linear artificial neuron circuit element and comprising delay circuit elements (322) and multipliers (321), to multiply the output signal derived from each one x.sub.i of the respective linear artificial neuron circuit elements of the first layer by an auto connection coefficient .mu..sub.i, to output the first-order delay corresponding to the time constant .tau..sub.i for the .mu..sub.i multiplied signal, and to output the .mu. multiplied, .tau..sub.i delayed signal again for the corresponding one x.sub.i of the respective linear artificial neuron circuit elements.

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Dependencies are inferred from the claim text.

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Abstract

a) a first layer including a plurality of circuits of linear artificial neurons X.sub.i (i=1, 2, - - - , i, - - - n);
b) a second layer including a plurality of circuits of nonlinear artificial neurons y.sub.j (j=1, 2, - - - , j, - - - , n) and arranged to convert input signals thereto into output signals by means of given same nonlinear functions f, their temperature parameters being denoted by T.sub.j ;
c) a feedforward connection part arranged to multiply outputs of the first layer circuits of linear artificial neurons x.sub.i by feedforward connection coefficients w.sub.ji and to output each of the multiplied outputs to a corresponding one of all of the circuits of nonlinear artificial neurons y.sub.j of said second layer;
d) a recurrent connecting part arranged to multiply outputs of the respective circuits of nonlinear artificial neurons y.sub.j of said second layer by recurrent connection coefficients .gamma..sub.j, to output first-order delays of time constants .tau..sub.j for the multiplied outputs of the respective circuits of nonlinear artificial neurons y.sub.j, and to input the delayed multiplied output of each respective circuit of onlinear artificial neurons y.sub.j to a corresponding one of the circuits of linear artificial neurons x.sub.j of said first layer;
and
e) an auto connection part arranged to multiply the outputs of the respective circuits of linear artificial neurons x.sub.i of the first layer, to output the first-order delays of the time constants .tau..sub.i for the multiplied outputs from said auto connection part, and to input again each of the first-order delayed outputs to the corresponding one of said circuits of linear artificial neurons x.sub.i, and wherein said recurrent neural network operates in accordance with the following equation (1) and said nonlinear oscillation apparatus generates a nonlinear oscillation when said recurrent neural network operates in accordance with the following equation (1), ##EQU18## wherein f denotes the given nonlinear function having saturation characteristics, and g denotes a characteristic function to discuss a stability of a differential equation and a nullcline when g=0.

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