Entrenamiento de red perceptrón simple para compuerta AND de dos entradas

Sean los patrones siguientes, los cuales responden al comportamiento de una compuerta AND de dos entradas:

x1	x2	s
0	0	0
0	1	0
1	0	0
1	1	1

Y la arquitectura de perceptrón simple siguiente:

Parámetros de la red:

Pesos iniciales: w1 = 0.5 w2 = 0.5 w3 = 0.5

Definición de la salida: s = f(y) = 1 si y >= 0; 0 si y < 0

El entrenamiento de la red neuronal se lleva a cabo como se muestra en los siguientes cálculos:

0 – 0 – 0
y = (0)(0.5) + (0)(0.5) + 0.5 = 0.5 f(y) = 1
e = 0 – 1 = -1
w1 = 0.5 + -1 * 0 = 0.5
w2 = 0.5 + -1 * 0 = 0.5
w0 = 0.5 + (-1) = -0.5


0 – 0 – 0
y = 0*0.5 + 0*0.5 + (-0.5) = -0.5 f(y) = 0
0 – 1 – 0
y = 0*0.5 + 1*0.5 + (-0.5) = 0 f(y) = 1
e = 0 – 1 = -1
w1 = 0.5 + -(-1) * 0 = 0.5
w2 = 0.5 + -(-1) * 1 = -0.5
w0 = -0.5 + (-1) = -1.5


0 – 0 – 0
y = 0*0.5 + 0*-0.5 + (-1.5) = -1.5 f(y) = 0
0 – 1 – 0
y = 0*0.5 + 1*-0.5 + (-1.5) = -2 f(y) = 0
1 – 0 – 0
y = 1*0.5 + 0*-0.5 + (-1.5) = -1 f(y) = 0
1 – 1 – 1
y = 1*0.5 + 1*-0.5 + (-1.5) = -1.5 f(y) = 0
e = 1 – 0 = 1
w1 = 0.5 + (1) * 1 = 1.5
w2 = -0.5 + (1) * 1 = 0.5
w0 = -1.5 + (1) = -0.5


0 – 0 – 0
y = 0*1.5 + 0*0.5 + (-0.5) = -0.5 f(y) = 0
0 – 1 – 0
y = 0*1.5 + 1*0.5 + (-0.5) = 0 f(y) = 1
e = 0 – 1 = -1
w1 = 1.5 + (-1) * 0 = 1.5
w2 = 0.5 + (-1) * 1 = -0.5
w0 = -0.5 + (-1) = -1.5


0 – 0 – 0
y = 0*1.5 + 0*-0.5 + (-1.5) = -1.5 f(y) = 0
0 – 1 – 0
y = 0*1.5 + 1*-0.5 + (-1.5) = -2 f(y) = 0
1 – 0 – 0
y = 1*1.5 + 0*-0.5 + (-1.5) = 0 f(y) = 1
e = 0 – 1 = -1
w1 = 1.5 + (-1) * 1 = 0.5
w2 = -0.5 + (-1) * 0 = -0.5
w0 = -1.5 + (-1) = -2.5


0 – 0 – 0
y = 0*0.5 + 0*-0.5 + (-2.5) = -2.5 f(y) = 0
0 – 1 – 0
y = 0*0.5 + 1*-0.5 + (-2.5) = -3 f(y) = 0
1 – 0 – 0
y = 1*0.5 + 0*-0.5 + (-2.5) = -2 f(y) = 0
1 – 1 – 1
y = 1*0.5 + 1*-0.5 + (-2.5) = -2.5 f(y) = 0
e = 1 – 0 = 1
w1 = 0.5 + (1) * 1 = 1.5
w2 = -0.5 + (1) * 1 = 0.5
w0 = -2.5 + (-1) = -1.5


0 – 0 – 0
y = 0*1.5 + 0*0.5 + (-1.5) = -1.5 f(y) = 0
0 – 1 – 0
y = 0*1.5 + 1*0.5 + (-1.5) = -1 f(y) = 0
1 – 0 – 0
y = 1*1.5 + 0*0.5 + (-1.5) = 0 f(y) = 1
e = 0 – 1 = -1
w1 = 1.5 + (-1) * 1 = 0.5
w2 = 0.5 + (-1) * 0 = 0.5
w0 = -1.5 + (-1) = -2.5


0 – 0 – 0
y = 0*0.5 + 0*0.5 + (-2.5) = -2.5 f(y) = 0
0 – 1 – 0
y = 0*0.5 + 1*0.5 + (-2.5) = -2 f(y) = 0
1 – 0 – 0
y = 1*0.5 + 0*0.5 + (-2.5) = -2 f(y) = 0
1 – 1 – 1
y = 1*0.5 + 1*0.5 + (-2.5) = -1.5 f(y) = 0
e = 1 – 0 = 1
w1 = 0.5 + (1) * 1 = 1.5
w2 = 0.5 + (1) * 1 = 1.5
w0 = -2.5 + (1) = -1.5


0 – 0 – 0
y = 0*1.5 + 0*1.5 + (-1.5) = -1.5 f(y) = 0
0 – 1 – 0
y = 0*1.5 + 1*1.5 + (-1.5) = 0 f(y) = 1
e = 0 – 1 = -1
w1 = 1.5 + (-1) * 0 = 1.5
w2 = 1.5 + (-1) * 1 = 0.5
w0 = -1.5 + (-1) = -2.5


0 – 0 – 0
y = 0*1.5 + 0*0.5 + (-2.5) = -2.5 f(y) = 0
0 – 1 – 0
y = 0*1.5 + 1*0.5 + (-2.5) = -2 f(y) = 0
1 – 0 – 0
y = 1*1.5 + 0*0.5 + (-2.5) = -1 f(y) = 0
1 – 1 – 1
y = 1*1.5 + 1*0.5 + (-2.5) = -0.5 f(y) = 0
e = 1 – 0 = 1
w1 = 1.5 + (1) * 1 = 2.5
w2 = 0.5 + (1) * 1 = 1.5
w0 = -2.5 + (1) = -1.5


0 – 0 – 0
y = 0*2.5 + 0*1.5 + (-1.5) = -1.5 f(y) = 0
0 – 1 – 0
y = 0*2.5 + 1*1.5 + (-1.5) = 0 f(y) = 1
e = 0 – 1 = -1
w1 = 2.5 + (-1) * 0 = 2.5
w2 = 1.5 + (-1) * 1 = 0.5
w0 = -1.5 + (-1) = -2.5


0 – 0 – 0
y = 0*2.5 + 0*0.5 + (-2.5) = -2.5 f(y) = 0
0 – 1 – 0
y = 0*2.5 + 1*0.5 + (-2.5) = -2 f(y) = 0
1 – 0 – 0
y = 1*2.5 + 0*0.5 + (-2.5) = 0 f(y) = 1
e = 0 – 1 = -1
w1 = 2.5 + (-1) * 1 = 1.5
w2 = 0.5 + (-1) * 0 = 0.5
w0 = -2.5 + (-1) = -3.5


0 – 0 – 0
y = 0*1.5 + 0*0.5 + (-3.5) = -3.5 f(y) = 0
0 – 1 – 0
y = 0*1.5 + 1*0.5 + (-3.5) = -3 f(y) = 0
1 – 0 – 0
y = 1*1.5 + 0*0.5 + (-3.5) = -2 f(y) = 0
1 – 1 – 1
y = 1*1.5 + 1*0.5 + (-3.5) = -1.5 f(y) = 0
e = 1 – 0 = 1
w1 = 1.5 + (1) * 1 = 2.5
w2 = 0.5 + (1) * 1 = 1.5
w0 = -3.5 + (1) = -2.5


0 – 0 – 0
y = 0*2.5 + 0*1.5 + (-2.5) = -2.5 f(y) = 0
0 – 1 – 0
y = 0*2.5 + 1*1.5 + (-2.5) = -1 f(y) = 0
1 – 0 – 0
y = 1*2.5 + 0*1.5 + (-2.5) = 0 f(y) = 1
e = 0 – 1 = -1
w1 = 2.5 + (-1) * 1 = 1.5
w2 = 1.5 + (-1) * 0 = 1.5
w0 = -2.5 + (-1) = -3.5


0 – 0 – 0
y = 0*1.5 + 0*1.5 + (-3.5) = -3.5 f(y) = 0
0 – 1 – 0
y = 0*1.5 + 1*1.5 + (-3.5) = -2 f(y) = 0
1 – 0 – 0
y = 1*1.5 + 0*1.5 + (-3.5) = -2 f(y) = 0
1 – 1 – 1
y = 1*1.5 + 1*1.5 + (-3.5) = -0.5 f(y) = 0
e = 1 – 0 = 1
w1 = 1.5 + (1) * 1 = 2.5
w2 = 1.5 + (1) * 1 = 2.5
w0 = -3.5 + (1) = -2.5


0 – 0 – 0
y = 0*2.5 + 0*2.5 + (-2.5) = -2.5 f(y) = 0
0 – 1 – 0
y = 0*2.5 + 1*2.5 + (-2.5) = 0 f(y) = 1
e = 0 – 1 = -1
w1 = 2.5 + (-1) * 0 = 2.5
w2 = 2.5 + (-1) * 1 = 1.5
w0 = -2.5 + (-1) = -3.5


0 – 0 – 0
y = 0*2.5 + 0*1.5 + (-3.5) = -3.5 f(y) = 0
0 – 1 – 0
y = 0*2.5 + 1*1.5 + (-3.5) = -2 f(y) = 0
1 – 0 – 0
y = 1*2.5 + 0*1.5 + (-3.5) = -1 f(y) = 0
1 – 1 – 1
y = 1*2.5 + 1*1.5 + (-3.5) = 0.5 f(y) = 1


Pesos finales de la red:
w1 = 2.5
w2 = 1.5
w0 = -3.5