Multi-dimensional regression with Keras

Question

I want to use Keras to train a neural network for 2-dimensional regression.

My input is a single number, and my output has two numbers:

model = Sequential()
model.add(Dense(16, input_shape=(1,), kernel_initializer=initializers.constant(0.0), bias_initializer=initializers.constant(0.0)))
model.add(Activation('relu'))
model.add(Dense(16, input_shape=(1,), kernel_initializer=initializers.constant(0.0), bias_initializer=initializers.constant(0.0)))
model.add(Activation('relu'))
model.add(Dense(2, kernel_initializer=initializers.constant(0.0), bias_initializer=initializers.constant(0.0)))
adam = Adam(lr=0.001, beta_1=0.9, beta_2=0.999, epsilon=1e-08, decay=0.0)
model.compile(loss='mean_squared_error', optimizer=adam)

I then created some dummy data for training:

inputs = np.zeros((10, 1), dtype=np.float32)
targets = np.zeros((10, 2), dtype=np.float32)

for i in range(10):
    inputs[i] = i / 10.0
    targets[i, 0] = 0.1
    targets[i, 1] = 0.01 * i

And finally, I trained with minibatches in a loop, whilst testing on the training data:

while True:

    loss = model.train_on_batch(inputs, targets)

    test_outputs = model.predict(inputs)

    print test_outputs

The problem is, the outputs printed out are as follows:

[0.1, 0.045]
[0.1, 0.045]
[0.1, 0.045]
.....
.....
.....

So, whilst the first dimension is correct (0.1), the second dimension is not correct. The second dimension should be [0.01, 0.02, 0.03, .....]. So in fact, the output from the network (0.45) is simply the average of what all the values in the second dimension should be.

What am I doing wrong?

Multi-dimensional regression with Keras

1 Answers