A Neural Network That Learns Bitwise XOR

Question

I am trying to build a deep neural network that learns the coordinate-coordinate bitwise XOR of two matrices, but it performs poorly.

For example, in the 2 bits case, its accuracy stays around 0.5. Here is the code snippet:

from keras.layers import Dense, Activation
from keras.layers import Input
import numpy as np 
from keras.layers.merge import concatenate
from keras.models import Model


size=1
data1 = np.random.choice([0, 1], size=(50000,size,size))
data2 = np.random.choice([0, 1], size=(50000,size,size))
labels  = np.bitwise_xor(data1, data2)
a = Input(shape=(size,size))
b = Input(shape=(size,size))
a1 = Dense(size, activation='sigmoid')(a)
b1 = Dense(size, activation='sigmoid')(b)
merged = concatenate([a1, b1])
hidden = Dense(1, activation='sigmoid')(merged)
hidden = Dense(3, activation='sigmoid')(hidden)
hidden = Dense(5, activation='relu')(hidden)
hidden = Dense(4, activation='sigmoid')(hidden)
hidden = Dense(3, activation='sigmoid')(hidden)
outputs = Dense(1, activation='relu')(hidden)

model = Model(inputs=[a, b], outputs=outputs)
model.compile(loss='binary_crossentropy', optimizer='adam', metrics=['accuracy'])
model.fit([data1, data2], np.array(labels), epochs=15, batch_size=32)

What's going on here?

Epoch 1/15
50000/50000 [==============================] - 7s 130us/step - loss: 0.7118 - acc: 0.5044
Epoch 2/15
50000/50000 [==============================] - 4s 78us/step - loss: 0.6933 - acc: 0.5023
Epoch 3/15
50000/50000 [==============================] - 4s 74us/step - loss: 0.6934 - acc: 0.5030
Epoch 4/15
50000/50000 [==============================] - 4s 86us/step - loss: 0.6935 - acc: 0.5002
Epoch 5/15
50000/50000 [==============================] - 4s 79us/step - loss: 0.6934 - acc: 0.5015
Epoch 6/15
50000/50000 [==============================] - 5s 96us/step - loss: 0.6935 - acc: 0.5030
Epoch 7/15
50000/50000 [==============================] - 5s 105us/step - loss: 0.6934 - acc: 0.5026