SELU︱在keras、tensorflow中使用SELU激活函数

arXiv 上公开的一篇 NIPS 投稿论文《Self-Normalizing Neural Networks》引起了圈内极大的关注，它提出了缩放指数型线性单元（SELU）而引进了自归一化属性，该单元主要使用一个函数 g 映射前后两层神经网络的均值和方差以达到归一化的效果。 Shao-Hua Sun 在 Github 上放出了 SELU 与 Relu、Leaky Relu 的对比，机器之心对比较结果进行了翻译介绍，具体的实现过程可参看以下项目地址。

项目地址：shaohua0116/Activation-Visualization-Histogram
来源机器之心：引爆机器学习圈：「自归一化神经网络」提出新型激活函数SELU

keras中使用SELU激活函数

在keras 2.0.6版本之后才可以使用selu激活函数，但是在版本2.0.5还是不行，所以得升级到这个版本。
在全连接层后面接上selu最终收敛会快一些

来看一下，一个介绍非常详细的github：bigsnarfdude/SELU_Keras_Tutorial

具体对比效果：

from __future__ import print_function

import keras
from keras.datasets import mnist
from keras.models import Sequential
from keras.layers.core import Dense, Dropout, Activation
from keras.layers.noise import AlphaDropout
from keras.utils import np_utils
from keras.optimizers import RMSprop, Adam

batch_size = 128
num_classes = 10
epochs = 20
learning_rate = 0.001

# 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 = keras.utils.to_categorical(y_train, num_classes)
y_test = keras.utils.to_categorical(y_test, num_classes)

modelSELU = Sequential()
modelSELU.add(Dense(512, activation='selu', input_shape=(784,)))
modelSELU.add(AlphaDropout(0.1))
modelSELU.add(Dense(512, activation='selu'))
modelSELU.add(AlphaDropout(0.1))
modelSELU.add(Dense(10, activation='softmax'))

modelSELU.summary()

modelSELU.compile(loss='categorical_crossentropy',
              optimizer=RMSprop(),
              metrics=['accuracy'])

historySELU = modelSELU.fit(x_train, y_train,
                    batch_size=batch_size,
                    epochs=epochs,
                    verbose=1,
                    validation_data=(x_test, y_test))
scoreSELU = modelSELU.evaluate(x_test, y_test, verbose=0)
print('Test loss:', scoreSELU[0])
print('Test accuracy:', scoreSELU[1])

tensorflow中使用dropout_selu + SELU

该文作者在tensorflow也加入了selu 和 dropout_selu两个新的激活函数。
可见：https://github.com/bigsnarfdude/SELU_Keras_Tutorial/blob/master/Basic_MLP_combined_comparison.ipynb
定义了两个新函数：SELU 和 dropout_selu

def selu(x):
    with ops.name_scope('elu') as scope:
        alpha = 1.6732632423543772848170429916717
        scale = 1.0507009873554804934193349852946
        return scale*tf.where(x>=0.0, x, alpha*tf.nn.elu(x))

def dropout_selu(x, keep_prob, alpha= -1.7580993408473766, fixedPointMean=0.0, fixedPointVar=1.0,
                 noise_shape=None, seed=None, name=None, training=False):
    """Dropout to a value with rescaling."""

    def dropout_selu_impl(x, rate, alpha, noise_shape, seed, name):
        keep_prob = 1.0 - rate
        x = ops.convert_to_tensor(x, name="x")
        if isinstance(keep_prob, numbers.Real) and not 0 < keep_prob <= 1:
            raise ValueError("keep_prob must be a scalar tensor or a float in the "
                                             "range (0, 1], got %g" % keep_prob)
        keep_prob = ops.convert_to_tensor(keep_prob, dtype=x.dtype, name="keep_prob")
        keep_prob.get_shape().assert_is_compatible_with(tensor_shape.scalar())

        alpha = ops.convert_to_tensor(alpha, dtype=x.dtype, name="alpha")
        keep_prob.get_shape().assert_is_compatible_with(tensor_shape.scalar())

        if tensor_util.constant_value(keep_prob) == 1:
            return x

        noise_shape = noise_shape if noise_shape is not None else array_ops.shape(x)
        random_tensor = keep_prob
        random_tensor += random_ops.random_uniform(noise_shape, seed=seed, dtype=x.dtype)
        binary_tensor = math_ops.floor(random_tensor)
        ret = x * binary_tensor + alpha * (1-binary_tensor)

        a = tf.sqrt(fixedPointVar / (keep_prob *((1-keep_prob) * tf.pow(alpha-fixedPointMean,2) + fixedPointVar)))

        b = fixedPointMean - a * (keep_prob * fixedPointMean + (1 - keep_prob) * alpha)
        ret = a * ret + b
        ret.set_shape(x.get_shape())
        return ret

    with ops.name_scope(name, "dropout", [x]) as name:
        return utils.smart_cond(training,
                                lambda: dropout_selu_impl(x, keep_prob, alpha, noise_shape, seed, name),
                                lambda: array_ops.identity(x))

作者将其使用在以下案例之中：

mnist = input_data.read_data_sets("MNIST_data/", one_hot=True)
# Check out https://www.tensorflow.org/get_started/mnist/beginners for
# more information about the mnist dataset

# parameters
learning_rate = 0.001
training_epochs = 50
batch_size = 100

# input place holders
X = tf.placeholder(tf.float32, [None, 784])
Y = tf.placeholder(tf.float32, [None, 10])

# dropout (keep_prob) rate  0.7 on training, but should be 1 for testing
keep_prob = tf.placeholder(tf.float32)

# weights & bias for nn layers
# http://stackoverflow.com/questions/33640581/how-to-do-xavier-initialization-on-tensorflow
W1 = tf.get_variable("W1", shape=[784, 512],
                     initializer=tf.contrib.layers.xavier_initializer())
b1 = tf.Variable(tf.random_normal([512]))
L1 = selu(tf.matmul(X, W1) + b1)
L1 = dropout_selu(L1, keep_prob=keep_prob)

W2 = tf.get_variable("W2", shape=[512, 512],
                     initializer=tf.contrib.layers.xavier_initializer())
b2 = tf.Variable(tf.random_normal([512]))
L2 = selu(tf.matmul(L1, W2) + b2)
L2 = dropout_selu(L2, keep_prob=keep_prob)

W3 = tf.get_variable("W3", shape=[512, 512],
                     initializer=tf.contrib.layers.xavier_initializer())
b3 = tf.Variable(tf.random_normal([512]))
L3 = selu(tf.matmul(L2, W3) + b3)
L3 = dropout_selu(L3, keep_prob=keep_prob)

W4 = tf.get_variable("W4", shape=[512, 512],
                     initializer=tf.contrib.layers.xavier_initializer())
b4 = tf.Variable(tf.random_normal([512]))
L4 = selu(tf.matmul(L3, W4) + b4)
L4 = dropout_selu(L4, keep_prob=keep_prob)

W5 = tf.get_variable("W5", shape=[512, 10],
                     initializer=tf.contrib.layers.xavier_initializer())
b5 = tf.Variable(tf.random_normal([10]))
hypothesis = tf.matmul(L4, W5) + b5

# define cost/loss & optimizer
cost = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(
    logits=hypothesis, labels=Y))
optimizer = tf.train.AdamOptimizer(learning_rate=learning_rate).minimize(cost)

# initialize
sess = tf.Session()
sess.run(tf.global_variables_initializer())

# train my model
for epoch in range(training_epochs):
    avg_cost = 0
    total_batch = int(mnist.train.num_examples / batch_size)

    for i in range(total_batch):
        batch_xs, batch_ys = mnist.train.next_batch(batch_size)
        feed_dict = {X: batch_xs, Y: batch_ys, keep_prob: 0.7}
        c, _ = sess.run([cost, optimizer], feed_dict=feed_dict)
        avg_cost += c / total_batch

    print('Epoch:', '%04d' % (epoch + 1), 'cost =', '{:.9f}'.format(avg_cost))

print('Learning Finished!')

# Test model and check accuracy
correct_prediction = tf.equal(tf.argmax(hypothesis, 1), tf.argmax(Y, 1))
accuracy = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))

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