multiple softmax classifications (Keras)

Question

I am trying to construct a CNN that will output 2 labels, where each label has 12 possibilities; the input is an image.

In other words, my desired output is A (one out of 12 options) and B (one out of 12 different options).

With each label separately, the go-to is of course softmax, but I couldn't find whether it is possible to do 'multiple softmax' labels like that.

Clearly, I can output 24 neurons, using sigmoid outputs and then normalize manually, but then the network will not intrinsically couple the 12 options within each group.

I'm writing pseudo-pseudo-code of what I would have wanted, if it existed:

model = Sequential()
model.add(Convolution2D(64, kernel_size=3,activation='relu', input_shape=image_shape))
model.add(Flatten())
model.add(Dense(256,activation='relu'))
# pseudo-pseudo-code
model.add(Dense((12,12),activation=('softmax','softmax'))) # <- here is where I would have liked 2 softmax outputs with 12 neurons in each

Any solutions will be welcome (I'm using Keras but will be happy for solutions using any other package, or even code something myself).

Edit: I could also generate 144 outputs representing all combinations, but I am not sure whether this would be a good solution - any comment on that is also very welcome

Answer 1

I would use the functional API with 2 outputs. Guide in https://keras.io/getting-started/functional-api-guide/#multi-input-and-multi-output-models

something on the lines of:

input = Input(input_shape=image_shape)
cnv = Convolution2d(...)(input)
hidden = Dense(256, ...)(Flatten()(cnv))
output1 = Dense(12, activation='softmax')(hidden)
output2 = Dense(12, activation='softmax')(hidden)
model = keras.models.Model(inputs=input, outputs=[output1, output2])
model.compile(optimizer='sgd', loss=['binary_crossentropy', 'binary_crossentropy'],
              loss_weights=[1., 1.])