Chaotic recurrent neural network and learning method therefor

• US 5,613,042 A
• Filed: 01/27/1995
• Issued: 03/18/1997
• Est. Priority Date: 02/14/1994
• Status: Expired due to Term

• Current Assignee: Gold Star Electron Company Limited
• Original Assignee: Gold Star Electron Company Limited
• Inventors: Chung, Ho-sun, Tak, Hye-young
• Primary Examiner(s): Downs, Robert W.
• Assistant Examiner(s): KATBAB, ABDOLLAH
• Application Number:
  US08/379,211
• Time in Patent Office: 781 Days
• Field of Search: 395/21, 395/23, 395/24
• US Class Current: 706/30
• CPC Class Codes: G06N 3/0418 using chaos or fractal principles

Abstract

A chaotic recurrent neural network includes N chaotic neural networks for receiving an external input and the outputs of N-1 chaotic neural networks among said N chaotic neural networks and performing an operation according to the following dynamic equation ##EQU1## wherein W_ij is a synapse connection coefficient of the feedback input from the "j"th neuron to the "i"th neuron, X_i (t) is the output of the "i"th neuron at time t, and γ_i, α and and k are a time-delaying constant, a non-negative parameter and a refractory time attenuation constant, respectively, and wherein Z_i (t) represents X_i (t) when i belongs to the neuron group I and represents a_i (t) when i belongs to the external input group E. Also, a learning algorithm for the chaotic recurrent neural network increases its learning efficiency.

Claims

1. A chaotic recurrent neural network comprising:

N neurons configured to receive an external input and the outputs of selected ones of said N neurons and performing an operation according to the following dynamic equations ##EQU21## wherein W_ij is a synapse connection coefficient of the feedback input from the "j"th neuron to the "i"th neuron, X_i (t) is the output of the "i"th neuron at time t, and γ

_i, α and

k are a time-delaying constant, a non-negative parameter and a refractory time attenuation constant, respectively, and wherein Z_i (t) represents X_i (t) when i belongs to the neuron group I and represents a_i (t) when i belongs to the external input group E.

3. The chaotic recurrent neural network of claim 1 wherein said selected ones of said neurons includes N-1 of said neurons.

2. A learning method for a chaotic recurrent neural network comprising N neurons for receiving an external input and the outputs of selected ones of said N chaotic neurons and performing an operation according to the following dynamic equation ##EQU22## wherein W_ij is a synapse connection coefficient of the feedback input from the "j"th neuron to the "i"th neuron, X_i (t) is the output of the "i"th neuron at time t, and γ

_i, α and

k are a time-delaying constant, a non-negative parameter and a refractory time attenuation constant, respectively, and wherein Z_i (t) represents X_i (t) when i belongs to the neuron group I and represents a_i (t) when i belongs to the external input group E, said method comprising the steps of;

(a) initializing an initial condition X_i (O) and connection weights using a random value;

(b) operating the neurons for a time period "T" according to the dynamic equation where the initial condition is X_i (O) and the external input is a_i (t);

(c) reversely calculating a Lagrange multiplier for a boundary condition L_i (T/W)=0 and a teacher signal Q_i (t)=0 from time t, according to the following equation ##EQU23## wherein X_i (t) is the value calculated in said step (b); and

(d) summing total errors after said steps (b) and (c) are completed for all inputs, and terminating the learning if the error is below a predetermined limit and otherwise correcting the weight according to the following weight correction equation ##EQU24## and repeating said steps (b) to (d).

4. A chaotic recurrent neural network comprising

N neuron means, each of said neuron means configured to satisfy the dynamic equations ##EQU25## where, i is a natural number from one to N, Y_i (t) is the output of the "i"th neuron, f_i is the output function of a neuron, γ

_i is a time delay constant, W_ij is a connecting weight of the "j"th neuron, which is a time-invariant value and a(t) is the network bias signal which is externally provided at time t, as a time-variant function;

said N neuron means configured to receive an external input and the outputs of selected ones of said N neuron means and for performing an operation according to the following dynamic equations ##EQU26## wherein W_ij is a synapse connection coefficient of the feedback input from the "j"th neuron to the "i"th neuron, X_i (t) is the output of the "i"th neuron at time t, and γ

_i, α and

k are a time-delaying constant, a non-negative parameter and a refractory time attenuation constant, respectively, and wherein Z_i (t) represents X_i (t) when i belongs to the neuron group I and represents a_i (t) when i belongs to the external input group E.