Realizamos las importaciones necesarias
import numpy as np
from keras.models import Sequential
from keras.layers.core import Dense
Haremos que la información de las columnas p y q será la información de entrada a nuestra red neuronal, de modo que podremos ingresar a ésta los valores $(1,1), (1,0), (0,1), (0,0)$. Así, crearemos entonces dos nodos de entrada en la primer capa
Crearemos una capa oculta de 16 nodos y la capa de salida será de un nodo; la función de activiación relu y en la capa de salida será la función sigmoid. La información objetivo a la cual queremos llegar son los valores de la columna p XOR q: 0, 1, 1, 0.
# Datos de entrenamiento
train = np.array([[0,0], [0,1], [1,0], [1,1]])
# Datos objetivo
target = np.array([[0], [1], [1], [0]])
Procedemos a crear la arquitectura de nuestra red neuronal
model = Sequential()
# Capa de entrada de más capa oculta de 16 nodos
model.add(Dense(16, activation='relu', input_shape=(2,)))
# Capa de salida
model.add(Dense(1, activation='sigmoid'))
Ahora entrenaremos las red neuronal que acabamos de modelar
# Primero copilamos la red
# Funcion de perdidad | optimizar la | copilacion del modelo
# | tasa de aprendizaje| paso a paso
model.compile(loss='mean_squared_error', optimizer='adam', metrics=['binary_accuracy'])
# Entrenamos la red
# Cantidad de iteraciones
# de aprendizaje de
# entrenamiento
model.fit(train, target, epochs=150)
Epoch 1/150 1/1 [==============================] - 1s 999ms/step - loss: 0.2460 - binary_accuracy: 0.7500 Epoch 2/150 1/1 [==============================] - 0s 7ms/step - loss: 0.2452 - binary_accuracy: 0.5000 Epoch 3/150 1/1 [==============================] - 0s 7ms/step - loss: 0.2444 - binary_accuracy: 0.5000 Epoch 4/150 1/1 [==============================] - 0s 4ms/step - loss: 0.2436 - binary_accuracy: 0.5000 Epoch 5/150 1/1 [==============================] - 0s 4ms/step - loss: 0.2428 - binary_accuracy: 0.5000 Epoch 6/150 1/1 [==============================] - 0s 4ms/step - loss: 0.2420 - binary_accuracy: 0.5000 Epoch 7/150 1/1 [==============================] - 0s 4ms/step - loss: 0.2412 - binary_accuracy: 0.5000 Epoch 8/150 1/1 [==============================] - 0s 4ms/step - loss: 0.2404 - binary_accuracy: 0.5000 Epoch 9/150 1/1 [==============================] - 0s 4ms/step - loss: 0.2397 - binary_accuracy: 0.5000 Epoch 10/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2389 - binary_accuracy: 0.5000 Epoch 11/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2382 - binary_accuracy: 0.5000 Epoch 12/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2375 - binary_accuracy: 0.5000 Epoch 13/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2367 - binary_accuracy: 0.5000 Epoch 14/150 1/1 [==============================] - 0s 4ms/step - loss: 0.2360 - binary_accuracy: 0.5000 Epoch 15/150 1/1 [==============================] - 0s 4ms/step - loss: 0.2353 - binary_accuracy: 0.5000 Epoch 16/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2347 - binary_accuracy: 0.5000 Epoch 17/150 1/1 [==============================] - 0s 4ms/step - loss: 0.2340 - binary_accuracy: 0.5000 Epoch 18/150 1/1 [==============================] - 0s 4ms/step - loss: 0.2333 - binary_accuracy: 0.5000 Epoch 19/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2327 - binary_accuracy: 0.5000 Epoch 20/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2321 - binary_accuracy: 0.5000 Epoch 21/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2315 - binary_accuracy: 0.5000 Epoch 22/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2309 - binary_accuracy: 0.5000 Epoch 23/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2303 - binary_accuracy: 0.5000 Epoch 24/150 1/1 [==============================] - 0s 4ms/step - loss: 0.2297 - binary_accuracy: 0.5000 Epoch 25/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2291 - binary_accuracy: 0.5000 Epoch 26/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2285 - binary_accuracy: 0.5000 Epoch 27/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2280 - binary_accuracy: 0.5000 Epoch 28/150 1/1 [==============================] - 0s 4ms/step - loss: 0.2274 - binary_accuracy: 0.5000 Epoch 29/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2269 - binary_accuracy: 0.5000 Epoch 30/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2264 - binary_accuracy: 0.5000 Epoch 31/150 1/1 [==============================] - 0s 4ms/step - loss: 0.2259 - binary_accuracy: 0.5000 Epoch 32/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2253 - binary_accuracy: 0.5000 Epoch 33/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2248 - binary_accuracy: 0.5000 Epoch 34/150 1/1 [==============================] - 0s 4ms/step - loss: 0.2243 - binary_accuracy: 0.5000 Epoch 35/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2238 - binary_accuracy: 0.5000 Epoch 36/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2234 - binary_accuracy: 0.5000 Epoch 37/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2229 - binary_accuracy: 0.5000 Epoch 38/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2224 - binary_accuracy: 0.5000 Epoch 39/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2220 - binary_accuracy: 0.5000 Epoch 40/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2215 - binary_accuracy: 0.5000 Epoch 41/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2211 - binary_accuracy: 0.5000 Epoch 42/150 1/1 [==============================] - 0s 2ms/step - loss: 0.2207 - binary_accuracy: 0.5000 Epoch 43/150 1/1 [==============================] - 0s 4ms/step - loss: 0.2202 - binary_accuracy: 0.5000 Epoch 44/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2198 - binary_accuracy: 0.5000 Epoch 45/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2194 - binary_accuracy: 0.5000 Epoch 46/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2189 - binary_accuracy: 0.5000 Epoch 47/150 1/1 [==============================] - 0s 4ms/step - loss: 0.2185 - binary_accuracy: 0.5000 Epoch 48/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2181 - binary_accuracy: 0.5000 Epoch 49/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2177 - binary_accuracy: 0.5000 Epoch 50/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2173 - binary_accuracy: 0.5000 Epoch 51/150 1/1 [==============================] - 0s 4ms/step - loss: 0.2168 - binary_accuracy: 0.5000 Epoch 52/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2164 - binary_accuracy: 0.5000 Epoch 53/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2160 - binary_accuracy: 0.5000 Epoch 54/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2156 - binary_accuracy: 0.5000 Epoch 55/150 1/1 [==============================] - 0s 2ms/step - loss: 0.2152 - binary_accuracy: 0.5000 Epoch 56/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2148 - binary_accuracy: 0.5000 Epoch 57/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2144 - binary_accuracy: 0.5000 Epoch 58/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2140 - binary_accuracy: 0.5000 Epoch 59/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2136 - binary_accuracy: 0.5000 Epoch 60/150 1/1 [==============================] - 0s 4ms/step - loss: 0.2131 - binary_accuracy: 0.5000 Epoch 61/150 1/1 [==============================] - 0s 4ms/step - loss: 0.2127 - binary_accuracy: 0.5000 Epoch 62/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2123 - binary_accuracy: 0.5000 Epoch 63/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2119 - binary_accuracy: 0.5000 Epoch 64/150 1/1 [==============================] - 0s 4ms/step - loss: 0.2115 - binary_accuracy: 0.5000 Epoch 65/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2111 - binary_accuracy: 0.7500 Epoch 66/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2107 - binary_accuracy: 0.7500 Epoch 67/150 1/1 [==============================] - 0s 4ms/step - loss: 0.2103 - binary_accuracy: 0.7500 Epoch 68/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2099 - binary_accuracy: 0.7500 Epoch 69/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2095 - binary_accuracy: 0.7500 Epoch 70/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2091 - binary_accuracy: 0.7500 Epoch 71/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2087 - binary_accuracy: 0.7500 Epoch 72/150 1/1 [==============================] - 0s 2ms/step - loss: 0.2083 - binary_accuracy: 0.7500 Epoch 73/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2079 - binary_accuracy: 0.7500 Epoch 74/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2075 - binary_accuracy: 0.7500 Epoch 75/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2071 - binary_accuracy: 0.7500 Epoch 76/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2068 - binary_accuracy: 0.7500 Epoch 77/150 1/1 [==============================] - 0s 4ms/step - loss: 0.2064 - binary_accuracy: 0.7500 Epoch 78/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2060 - binary_accuracy: 0.7500 Epoch 79/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2057 - binary_accuracy: 0.7500 Epoch 80/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2053 - binary_accuracy: 0.7500 Epoch 81/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2049 - binary_accuracy: 0.7500 Epoch 82/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2046 - binary_accuracy: 0.7500 Epoch 83/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2042 - binary_accuracy: 0.7500 Epoch 84/150 1/1 [==============================] - 0s 4ms/step - loss: 0.2038 - binary_accuracy: 0.7500 Epoch 85/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2035 - binary_accuracy: 0.7500 Epoch 86/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2031 - binary_accuracy: 0.7500 Epoch 87/150 1/1 [==============================] - 0s 4ms/step - loss: 0.2027 - binary_accuracy: 0.7500 Epoch 88/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2024 - binary_accuracy: 0.7500 Epoch 89/150 1/1 [==============================] - 0s 2ms/step - loss: 0.2020 - binary_accuracy: 0.7500 Epoch 90/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2016 - binary_accuracy: 0.7500 Epoch 91/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2013 - binary_accuracy: 0.7500 Epoch 92/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2009 - binary_accuracy: 0.7500 Epoch 93/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2006 - binary_accuracy: 0.7500 Epoch 94/150 1/1 [==============================] - 0s 3ms/step - loss: 0.2002 - binary_accuracy: 0.7500 Epoch 95/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1998 - binary_accuracy: 0.7500 Epoch 96/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1995 - binary_accuracy: 0.7500 Epoch 97/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1992 - binary_accuracy: 0.7500 Epoch 98/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1989 - binary_accuracy: 0.7500 Epoch 99/150 1/1 [==============================] - 0s 2ms/step - loss: 0.1985 - binary_accuracy: 0.7500 Epoch 100/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1981 - binary_accuracy: 0.7500 Epoch 101/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1978 - binary_accuracy: 0.7500 Epoch 102/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1974 - binary_accuracy: 0.7500 Epoch 103/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1971 - binary_accuracy: 0.7500 Epoch 104/150 1/1 [==============================] - 0s 4ms/step - loss: 0.1968 - binary_accuracy: 0.7500 Epoch 105/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1965 - binary_accuracy: 0.7500 Epoch 106/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1962 - binary_accuracy: 0.7500 Epoch 107/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1959 - binary_accuracy: 0.7500 Epoch 108/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1956 - binary_accuracy: 0.7500 Epoch 109/150 1/1 [==============================] - 0s 2ms/step - loss: 0.1953 - binary_accuracy: 1.0000 Epoch 110/150 1/1 [==============================] - 0s 4ms/step - loss: 0.1950 - binary_accuracy: 1.0000 Epoch 111/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1947 - binary_accuracy: 1.0000 Epoch 112/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1944 - binary_accuracy: 1.0000 Epoch 113/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1941 - binary_accuracy: 1.0000 Epoch 114/150 1/1 [==============================] - 0s 4ms/step - loss: 0.1937 - binary_accuracy: 1.0000 Epoch 115/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1934 - binary_accuracy: 1.0000 Epoch 116/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1931 - binary_accuracy: 1.0000 Epoch 117/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1928 - binary_accuracy: 1.0000 Epoch 118/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1925 - binary_accuracy: 1.0000 Epoch 119/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1922 - binary_accuracy: 1.0000 Epoch 120/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1919 - binary_accuracy: 1.0000 Epoch 121/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1916 - binary_accuracy: 1.0000 Epoch 122/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1913 - binary_accuracy: 1.0000 Epoch 123/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1910 - binary_accuracy: 1.0000 Epoch 124/150 1/1 [==============================] - 0s 4ms/step - loss: 0.1907 - binary_accuracy: 1.0000 Epoch 125/150 1/1 [==============================] - 0s 4ms/step - loss: 0.1903 - binary_accuracy: 1.0000 Epoch 126/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1900 - binary_accuracy: 1.0000 Epoch 127/150 1/1 [==============================] - 0s 4ms/step - loss: 0.1897 - binary_accuracy: 1.0000 Epoch 128/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1894 - binary_accuracy: 1.0000 Epoch 129/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1891 - binary_accuracy: 1.0000 Epoch 130/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1888 - binary_accuracy: 1.0000 Epoch 131/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1885 - binary_accuracy: 1.0000 Epoch 132/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1882 - binary_accuracy: 1.0000 Epoch 133/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1879 - binary_accuracy: 1.0000 Epoch 134/150 1/1 [==============================] - 0s 4ms/step - loss: 0.1876 - binary_accuracy: 1.0000 Epoch 135/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1873 - binary_accuracy: 1.0000 Epoch 136/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1870 - binary_accuracy: 1.0000 Epoch 137/150 1/1 [==============================] - 0s 4ms/step - loss: 0.1866 - binary_accuracy: 1.0000 Epoch 138/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1863 - binary_accuracy: 1.0000 Epoch 139/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1860 - binary_accuracy: 1.0000 Epoch 140/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1857 - binary_accuracy: 1.0000 Epoch 141/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1854 - binary_accuracy: 1.0000 Epoch 142/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1851 - binary_accuracy: 1.0000 Epoch 143/150 1/1 [==============================] - 0s 4ms/step - loss: 0.1848 - binary_accuracy: 1.0000 Epoch 144/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1844 - binary_accuracy: 1.0000 Epoch 145/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1841 - binary_accuracy: 1.0000 Epoch 146/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1838 - binary_accuracy: 1.0000 Epoch 147/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1835 - binary_accuracy: 1.0000 Epoch 148/150 1/1 [==============================] - 0s 4ms/step - loss: 0.1832 - binary_accuracy: 1.0000 Epoch 149/150 1/1 [==============================] - 0s 3ms/step - loss: 0.1829 - binary_accuracy: 1.0000 Epoch 150/150 1/1 [==============================] - 0s 4ms/step - loss: 0.1826 - binary_accuracy: 1.0000
<keras.callbacks.History at 0x1d2bdb860d0>
Notamos que, a partir de la época 109 comenzó a tener una precisión del 100%, a partir de ahí la precisión se mantuvo igual y la función de pérdida continúo decreciendo. Luego, evaluaremos nuestro modelo
scores = model.evaluate(train, target)
print('%s: %.4f%%' % (model.metrics_names[1], scores[1] * 100))
1/1 [==============================] - 0s 138ms/step - loss: 0.1822 - binary_accuracy: 1.0000 binary_accuracy: 100.0000%
Podemos guardar nuestro modelo:
from keras.models import load_model
model.save('XOR.h5')
Y posteriormento lo podremos utilizar cuando queramos, por ejemplo vamos a utilizarlo para hacer predicciones, lo cual no tendría mucho sentido para nuestro ejemplo pues la red neuronal dará el valor correcto a las 4 posibilidades de la tabla de verdad del XOR
# Cargamos el modelo guardado
model_xor = load_model('XOR.h5')
# Hacemos las 4 predicciones posibles de XOR
pred = model_xor.predict(train)
pred
1/1 [==============================] - 0s 80ms/step
array([[0.4879571 ],
[0.57188183],
[0.61815906],
[0.40221503]], dtype=float32)
Lo cual podemos ver de manera más visual si realizamos el redondeo, pues lo anterior nos arroja probabilidades (lo cual logramos con la función de activación sigmoide, donde el umbral por defecto es 0.5)
pred.round()
array([[0.],
[1.],
[1.],
[0.]], dtype=float32)