Neural network for Multiple integer output
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I think the key word you need to know that defines your task is: multi-target classification or regression.

You can find an explanation and some possible techniques at this link.

For neural networks:

The key is to remember that the last layer should have linear activations (i.e. no activation at all).

As per your requirements, the shape of the input layer would be a vector (135,) and the output (132,).

The usual loss function used for regression problems is mean squared error (MSE). Here's an example of multidimensional regression using Keras:

model = Sequential()
model.add(Dense(200, input_dim = (135,)))
model.add(Activation('relu'))
model.add(Dense(200))
model.add(Activation('relu'))
model.add(Dropout(0.3))
model.add(Dense(132))
model.compile(loss='mean_absolute_error', optimizer='Adam')