python - How do I train multiple neural nets simultaneously in keras?

Question

How do I train 1 model multiple times and combine them at the output layer?

For example:

model_one = Sequential() #model 1
model_one.add(Convolution2D(32, 3, 3, activation='relu', input_shape=(1,28,28)))
model_one.add(Flatten())
model_one.add(Dense(128, activation='relu'))

model_two = Sequential() #model 2
model_two.add(Dense(128, activation='relu', input_shape=(784)))
model_two.add(Dense(128, activation='relu'))

model_???.add(Dense(10, activation='softmax')) #combine them here

model.compile(loss='categorical_crossentropy', #continu together
          optimizer='adam',
          metrics=['accuracy'])


model.fit(X_train, Y_train, #continu together somehow, even though this would never work because X_train and Y_train have wrong formats
      batch_size=32, nb_epoch=10, verbose=1)

I've heard I can do this through a graph model but I can't find any documentation on it.

EDIT: in reply to the suggestion below:

A1 = Conv2D(20,kernel_size=(5,5),activation='relu',input_shape=( 28, 28, 1))
---> B1 = MaxPooling2D(pool_size=(2,2))(A1)

throws this error:

AttributeError: 'Conv2D' object has no attribute 'get_shape'

Answer 1

Graph notation would do it for you. Essentially you give every layer a unique handle then link back to the previous layer using the handle in brackets at the end:

layer_handle = Layer(params)(prev_layer_handle)

Note that the first layer must be an Input(shape=(x,y)) with no prior connection.

Then when you make your model you need to tell it that it expects multiple inputs with a list:

model = Model(inputs=[in_layer1, in_layer2, ..], outputs=[out_layer1, out_layer2, ..])

Finally when you train it you also need to provide a list of input and output data that corresponds with your definition:

model.fit([x_train1, x_train2, ..], [y_train1, y_train2, ..])

Meanwhile everything else is the same so you just need to combine together the above to give you the network layout that you want:

from keras.models import Model
from keras.layers import Input, Convolution2D, Flatten, Dense, Concatenate

# Note Keras 2.02, channel last dimension ordering

# Model 1
in1 = Input(shape=(28,28,1))
model_one_conv_1 = Convolution2D(32, (3, 3), activation='relu')(in1)
model_one_flat_1 = Flatten()(model_one_conv_1)
model_one_dense_1 = Dense(128, activation='relu')(model_one_flat_1)

# Model 2
in2 = Input(shape=(784, ))
model_two_dense_1 = Dense(128, activation='relu')(in2)
model_two_dense_2 = Dense(128, activation='relu')(model_two_dense_1)

# Model Final
model_final_concat = Concatenate(axis=-1)([model_one_dense_1, model_two_dense_2])
model_final_dense_1 = Dense(10, activation='softmax')(model_final_concat)

model = Model(inputs=[in1, in2], outputs=model_final_dense_1)

model.compile(loss='categorical_crossentropy', #continu together
              optimizer='adam',
              metrics=['accuracy'])

model.fit([X_train_one, X_train_two], Y_train,
          batch_size=32, nb_epoch=10, verbose=1)

Documentation can be found in the Functional Model API. I'd recommend reading around other questions or checking out Keras' repo as well since the documentation currently doesn't have many examples.