# This example demonstrates how to write custom layers for Keras.

We build a custom activation layer called 'Antirectifier', which modifies the shape of the tensor that passes through it. We need to specify two methods: `compute_output_shape` and `call`.

Note that the same result can also be achieved via a Lambda layer.

Because our custom layer is written with primitives from the Keras backend (`K`), our code can run both on TensorFlow and Theano.

    from __future__ import print_function
    import keras
    from keras.models import Sequential
    from keras import layers
    from keras.datasets import mnist
    from keras import backend as K

    class Antirectifier(layers.Layer):
        '''This is the combination of a sample-wise
        L2 normalization with the concatenation of the
        positive part of the input with the negative part
        of the input. The result is a tensor of samples that are
        twice as large as the input samples.

        It can be used in place of a ReLU.

        # Input shape
            2D tensor of shape (samples, n)

        # Output shape
            2D tensor of shape (samples, 2*n)

        # Theoretical justification
            When applying ReLU, assuming that the distribution
            of the previous output is approximately centered around 0.,
            you are discarding half of your input. This is inefficient.

            Antirectifier allows to return all-positive outputs like ReLU,
            without discarding any data.

            Tests on MNIST show that Antirectifier allows to train networks
            with twice less parameters yet with comparable
            classification accuracy as an equivalent ReLU-based network.
        '''

        def compute_output_shape(self, input_shape):
            shape = list(input_shape)
            assert len(shape) == 2  # only valid for 2D tensors
            shape[-1] *= 2
            return tuple(shape)

        def call(self, inputs):
            inputs -= K.mean(inputs, axis=1, keepdims=True)
            inputs = K.l2_normalize(inputs, axis=1)
            pos = K.relu(inputs)
            neg = K.relu(-inputs)
            return K.concatenate([pos, neg], axis=1)

    # global parameters
    batch_size = 128
    num_classes = 10
    epochs = 40

    # the data, split between train and test sets
    (x_train, y_train), (x_test, y_test) = mnist.load_data()

    x_train = x_train.reshape(60000, 784)
    x_test = x_test.reshape(10000, 784)
    x_train = x_train.astype('float32')
    x_test = x_test.astype('float32')
    x_train /= 255
    x_test /= 255
    print(x_train.shape[0], 'train samples')
    print(x_test.shape[0], 'test samples')

    # convert class vectors to binary class matrices
    y_train = keras.utils.to_categorical(y_train, num_classes)
    y_test = keras.utils.to_categorical(y_test, num_classes)

    # build the model
    model = Sequential()
    model.add(layers.Dense(256, input_shape=(784,)))
    model.add(Antirectifier())
    model.add(layers.Dropout(0.1))
    model.add(layers.Dense(256))
    model.add(Antirectifier())
    model.add(layers.Dropout(0.1))
    model.add(layers.Dense(num_classes))
    model.add(layers.Activation('softmax'))

    # compile the model
    model.compile(loss='categorical_crossentropy',
                  optimizer='rmsprop',
                  metrics=['accuracy'])

    # train the model
    model.fit(x_train, y_train,
              batch_size=batch_size,
              epochs=epochs,
              verbose=1,
              validation_data=(x_test, y_test))

    # next, compare with an equivalent network
    # with2x bigger Dense layers and ReLU

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