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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Custom Keras Layer
Idea
Step1:  AntiRectifier Layer
Step2:  Parametrs and Settings
Step3:  Data Preparation
Step4:  Model with Custom Layer
Step5:  Excercise
Compare with an equivalent network that is 2x bigger (in terms of Dense layers) + ReLU)
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Python Code:
from keras.models import Sequential
from keras.layers import Dense, Dropout, Layer, Activation
from keras.datasets import mnist
from keras import backend as K
from keras.utils import np_utils
Explanation: Custom Keras Layer
Idea:
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: get_output_shape_for and call.
Note that the same result can also be achieved via a Lambda layer (keras.layer.core.Lambda).
```python
keras.layers.core.Lambda(function, output_shape=None, arguments=None)
```
Because our custom layer is written with primitives from the Keras backend (K), our code can run both on TensorFlow and Theano.
End of explanation
class Antirectifier(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 get_output_shape_for(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, x, mask=None):
        x -= K.mean(x, axis=1, keepdims=True)
        x = K.l2_normalize(x, axis=1)
        pos = K.relu(x)
        neg = K.relu(-x)
        return K.concatenate([pos, neg], axis=1)
Explanation: AntiRectifier Layer
End of explanation
# global parameters
batch_size = 128
nb_classes = 10
nb_epoch = 40
Explanation: Parametrs and Settings
End of explanation
# the data, shuffled and 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 = np_utils.to_categorical(y_train, nb_classes)
Y_test = np_utils.to_categorical(y_test, nb_classes)
Explanation: Data Preparation
End of explanation
# build the model
model = Sequential()
model.add(Dense(256, input_shape=(784,)))
model.add(Antirectifier())
model.add(Dropout(0.1))
model.add(Dense(256))
model.add(Antirectifier())
model.add(Dropout(0.1))
model.add(Dense(10))
model.add(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, nb_epoch=nb_epoch,
          verbose=1, validation_data=(X_test, Y_test))
Explanation: Model with Custom Layer
End of explanation
## your code here
Explanation: Excercise
Compare with an equivalent network that is 2x bigger (in terms of Dense layers) + ReLU)
End of explanation
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