【机器学习】DNN训练中的问题与方法

感谢中国人民大学的胡鹤老师，人工智能课程讲的颇有深度，与时俱进

因为深度神经网络（DNN）层数不少，每次训练都是逐层由后至前传递。传递项<1，梯度可能变得很是小趋于0，以此来训练网络几乎不会有什么变化，即vanishing gradients problem；或者>1梯度很是大，以此修正网络会不断震荡，没法造成一个收敛网络。于是DNN的训练中能够造成不少tricks。。

一、初始化权重

起初采用正态分布随机化初始权重，会使得本来单位的variance逐渐变得很是大。例以下图的sigmoid函数，靠近0点的梯度近似线性很敏感，但到了，即很强烈的输入产生木讷的输出。

 

采用Xavier initialization，根据fan-in（输入神经元个数）和fan-out（输出神经元个数）设置权重。

并设计针对不一样激活函数的初始化策略，以下图（左边是均态分布，右边正态分布较为经常使用）

 

二、激活函数

通常使用ReLU，可是不能有小于0的输入（dying ReLUs）

a.Leaky RELU

改进方法Leaky ReLU=max(αx,x)，小于0时保留一点微小特征。

具体应用

 

from tensorflow.examples.tutorials.mnist import input_data
mnist = input_data.read_data_sets("/tmp/data/")

reset_graph()

n_inputs = 28 * 28  # MNIST
n_hidden1 = 300
n_hidden2 = 100
n_outputs = 10
X = tf.placeholder(tf.float32, shape=(None, n_inputs), name="X")
y = tf.placeholder(tf.int64, shape=(None), name="y")

with tf.name_scope("dnn"):
    hidden1 = tf.layers.dense(X, n_hidden1, activation=leaky_relu, name="hidden1")
    hidden2 = tf.layers.dense(hidden1, n_hidden2, activation=leaky_relu, name="hidden2")
    logits = tf.layers.dense(hidden2, n_outputs, name="outputs")

with tf.name_scope("loss"):
    xentropy = tf.nn.sparse_softmax_cross_entropy_with_logits(labels=y, logits=logits)
    loss = tf.reduce_mean(xentropy, name="loss")

learning_rate = 0.01

with tf.name_scope("train"):
    optimizer = tf.train.GradientDescentOptimizer(learning_rate)
    training_op = optimizer.minimize(loss)

with tf.name_scope("eval"):
    correct = tf.nn.in_top_k(logits, y, 1)
    accuracy = tf.reduce_mean(tf.cast(correct, tf.float32))

init = tf.global_variables_initializer()
saver = tf.train.Saver()

n_epochs = 40
batch_size = 50

with tf.Session() as sess:
    init.run()
    for epoch in range(n_epochs):
        for iteration in range(mnist.train.num_examples // batch_size):
            X_batch, y_batch = mnist.train.next_batch(batch_size)
            sess.run(training_op, feed_dict={X: X_batch, y: y_batch})
        if epoch % 5 == 0:
            acc_train = accuracy.eval(feed_dict={X: X_batch, y: y_batch})
            acc_test = accuracy.eval(feed_dict={X: mnist.validation.images, y: mnist.validation.labels})
            print(epoch, "Batch accuracy:", acc_train, "Validation accuracy:", acc_test)

    save_path = saver.save(sess, "./my_model_final.ckpt")

 b. ELU改进

另外一种改进ELU，在神经元小于0时采用指数变化

 

#just specify the activation function when building each layer

X = tf.placeholder(tf.float32, shape=(None, n_inputs), name="X")
hidden1 = tf.layers.dense(X, n_hidden1, activation=tf.nn.elu, name="hidden1")

c. SELU

最新提出的是SELU（仅给出关键代码）

 

with tf.name_scope("dnn"):
    hidden1 = tf.layers.dense(X, n_hidden1, activation=selu, name="hidden1")
    hidden2 = tf.layers.dense(hidden1, n_hidden2, activation=selu, name="hidden2")
    logits = tf.layers.dense(hidden2, n_outputs, name="outputs")

 

# train 过程
means = mnist.train.images.mean(axis=0, keepdims=True)
stds = mnist.train.images.std(axis=0, keepdims=True) + 1e-10

with tf.Session() as sess:
    init.run()
    for epoch in range(n_epochs):
        for iteration in range(mnist.train.num_examples // batch_size):
            X_batch, y_batch = mnist.train.next_batch(batch_size)
            X_batch_scaled = (X_batch - means) / stds
            sess.run(training_op, feed_dict={X: X_batch_scaled, y: y_batch})
        if epoch % 5 == 0:
            acc_train = accuracy.eval(feed_dict={X: X_batch_scaled, y: y_batch})
            X_val_scaled = (mnist.validation.images - means) / stds
            acc_test = accuracy.eval(feed_dict={X: X_val_scaled, y: mnist.validation.labels})
            print(epoch, "Batch accuracy:", acc_train, "Validation accuracy:", acc_test)

    save_path = saver.save(sess, "./my_model_final_selu.ckpt")

三、Batch Normalization

在2015年，有研究者提出，既然使用mini-batch进行操做，对每一批数据也可采用，在调用激活函数以前，先作一下normalization，使得输出数据有一个较好的形状，初始时，超参数scaling（γ）和shifting（β）进行适度缩放平移后传递给activation函数。步骤以下：

 

现今batch normalization已经被TensorFlow实现成一个单独的层，直接调用

测试时，因为没有mini-batch，故训练时直接使用训练时的mean和standard deviation（），实现代码以下

import tensorflow as tf

n_inputs = 28 * 28
n_hidden1 = 300
n_hidden2 = 100
n_outputs = 10

batch_norm_momentum = 0.9

X = tf.placeholder(tf.float32, shape=(None, n_inputs), name="X")
y = tf.placeholder(tf.int64, shape=(None), name="y")
training = tf.placeholder_with_default(False, shape=(), name='training')

with tf.name_scope("dnn"):
    he_init = tf.contrib.layers.variance_scaling_initializer()
    #至关于单独一层
    my_batch_norm_layer = partial(
            tf.layers.batch_normalization,
            training=training,
            momentum=batch_norm_momentum)
    
    my_dense_layer = partial(
            tf.layers.dense,
            kernel_initializer=he_init)

    hidden1 = my_dense_layer(X, n_hidden1, name="hidden1")
    bn1 = tf.nn.elu(my_batch_norm_layer(hidden1))# 激活函数使用ELU
    hidden2 = my_dense_layer(bn1, n_hidden2, name="hidden2")
    bn2 = tf.nn.elu(my_batch_norm_layer(hidden2))
    logits_before_bn = my_dense_layer(bn2, n_outputs, name="outputs")
    logits = my_batch_norm_layer(logits_before_bn)# 输出层也作一个batch normalization

with tf.name_scope("loss"):
    xentropy = tf.nn.sparse_softmax_cross_entropy_with_logits(labels=y, logits=logits)
    loss = tf.reduce_mean(xentropy, name="loss")

with tf.name_scope("train"):
    optimizer = tf.train.GradientDescentOptimizer(learning_rate)
    training_op = optimizer.minimize(loss)

with tf.name_scope("eval"):
    correct = tf.nn.in_top_k(logits, y, 1)
    accuracy = tf.reduce_mean(tf.cast(correct, tf.float32))
    
init = tf.global_variables_initializer()
saver = tf.train.Saver()

n_epochs = 20
batch_size = 200
#须要显示调用训练时得出的方差均值，须要额外调用这些算子
extra_update_ops = tf.get_collection(tf.GraphKeys.UPDATE_OPS)
#在training和testing时不同
with tf.Session() as sess:
    init.run()
    for epoch in range(n_epochs):
        for iteration in range(mnist.train.num_examples // batch_size):
            X_batch, y_batch = mnist.train.next_batch(batch_size)
            sess.run([training_op, extra_update_ops],
                     feed_dict={training: True, X: X_batch, y: y_batch})
        accuracy_val = accuracy.eval(feed_dict={X: mnist.test.images,
                                                y: mnist.test.labels})
        print(epoch, "Test accuracy:", accuracy_val)

    save_path = saver.save(sess, "./my_model_final.ckpt")

四、Gradient Clipp

处理gradient以后日后传，必定程度上解决梯度爆炸问题。（但因为有了batch normalization，此方法用的很少）

threshold = 1.0
optimizer = tf.train.GradientDescentOptimizer(learning_rate)
grads_and_vars = optimizer.compute_gradients(loss)
capped_gvs = [(tf.clip_by_value(grad, -threshold, threshold), var)
                                               for grad, var in grads_and_vars]
training_op = optimizer.apply_gradients(capped_gvs)

五、重用以前训练过的层（Reusing Pretrained Layers）

对以前训练的模型稍加修改，节省时间，在深度模型训练（因为有不少层）中常用。

通常类似问题，分类数等和问题紧密相关的output层与最后一个直接与output相关的隐层不能够直接用，仍需本身训练。

以下图所示，在已训练出一个复杂net后，迁移到相对简单的net时，hidden1和2固定不动，hidden3稍做变化，hidden4和output本身训练。。这在没有本身GPU状况下是很是节省时间的作法。

 

# 只选取须要的操做
X = tf.get_default_graph().get_tensor_by_name("X:0")
y = tf.get_default_graph().get_tensor_by_name("y:0")

accuracy = tf.get_default_graph().get_tensor_by_name("eval/accuracy:0")

training_op = tf.get_default_graph().get_operation_by_name("GradientDescent")

# 若是你是原模型的做者，能够赋给模型一个清楚的名字保存下来
for op in (X, y, accuracy, training_op):
    tf.add_to_collection("my_important_ops", op)
# 若是你要使用这个模型
X, y, accuracy, training_op = tf.get_collection("my_important_ops")

# 训练时
with tf.Session() as sess:
    saver.restore(sess, "./my_model_final.ckpt")

    for epoch in range(n_epochs):
        for iteration in range(mnist.train.num_examples // batch_size):
            X_batch, y_batch = mnist.train.next_batch(batch_size)
            sess.run(training_op, feed_dict={X: X_batch, y: y_batch})
        accuracy_val = accuracy.eval(feed_dict={X: mnist.test.images,
                                                y: mnist.test.labels})
        print(epoch, "Test accuracy:", accuracy_val)

    save_path = saver.save(sess, "./my_new_model_final.ckpt")    

a. Freezing the Lower Layers

训练时固定底层参数，达到Freezing the Lower Layers的目的

 

# 以MINIST为例

n_inputs = 28 * 28  # MNIST
n_hidden1 = 300 # reused
n_hidden2 = 50  # reused
n_hidden3 = 50  # reused
n_hidden4 = 20  # new!
n_outputs = 10  # new!

X = tf.placeholder(tf.float32, shape=(None, n_inputs), name="X")
y = tf.placeholder(tf.int64, shape=(None), name="y")

 

with tf.name_scope("dnn"):
    hidden1 = tf.layers.dense(X, n_hidden1, activation=tf.nn.relu,
                              name="hidden1") # reused frozen
    hidden2 = tf.layers.dense(hidden1, n_hidden2, activation=tf.nn.relu,
                              name="hidden2") # reused frozen
    hidden2_stop = tf.stop_gradient(hidden2)
    hidden3 = tf.layers.dense(hidden2_stop, n_hidden3, activation=tf.nn.relu,
                              name="hidden3") # reused, not frozen
    hidden4 = tf.layers.dense(hidden3, n_hidden4, activation=tf.nn.relu,
                              name="hidden4") # new!
    logits = tf.layers.dense(hidden4, n_outputs, name="outputs") # new!

with tf.name_scope("loss"):
    xentropy = tf.nn.sparse_softmax_cross_entropy_with_logits(labels=y, logits=logits)
    loss = tf.reduce_mean(xentropy, name="loss")

with tf.name_scope("eval"):
    correct = tf.nn.in_top_k(logits, y, 1)
    accuracy = tf.reduce_mean(tf.cast(correct, tf.float32), name="accuracy")

with tf.name_scope("train"):
    optimizer = tf.train.GradientDescentOptimizer(learning_rate)
    training_op = optimizer.minimize(loss)

reuse_vars = tf.get_collection(tf.GraphKeys.GLOBAL_VARIABLES,
                               scope="hidden[123]") # regular expression
reuse_vars_dict = dict([(var.op.name, var) for var in reuse_vars])
restore_saver = tf.train.Saver(reuse_vars_dict) # to restore layers 1-3

init = tf.global_variables_initializer()
saver = tf.train.Saver()

with tf.Session() as sess:
    init.run()
    restore_saver.restore(sess, "./my_model_final.ckpt")

    for epoch in range(n_epochs):
        for iteration in range(mnist.train.num_examples // batch_size):
            X_batch, y_batch = mnist.train.next_batch(batch_size)
            sess.run(training_op, feed_dict={X: X_batch, y: y_batch})
        accuracy_val = accuracy.eval(feed_dict={X: mnist.test.images,
                                                y: mnist.test.labels})
        print(epoch, "Test accuracy:", accuracy_val)

    save_path = saver.save(sess, "./my_new_model_final.ckpt")

b. Catching the Frozen Layers

训练时直接从lock层以后的层开始训练，Catching the Frozen Layers

 

# 以MINIST为例

n_inputs = 28 * 28  # MNIST
n_hidden1 = 300 # reused
n_hidden2 = 50  # reused
n_hidden3 = 50  # reused
n_hidden4 = 20  # new!
n_outputs = 10  # new!

X = tf.placeholder(tf.float32, shape=(None, n_inputs), name="X")
y = tf.placeholder(tf.int64, shape=(None), name="y")

with tf.name_scope("dnn"):
    hidden1 = tf.layers.dense(X, n_hidden1, activation=tf.nn.relu,
                              name="hidden1") # reused frozen
    hidden2 = tf.layers.dense(hidden1, n_hidden2, activation=tf.nn.relu,
                              name="hidden2") # reused frozen & cached
    hidden2_stop = tf.stop_gradient(hidden2)
    hidden3 = tf.layers.dense(hidden2_stop, n_hidden3, activation=tf.nn.relu,
                              name="hidden3") # reused, not frozen
    hidden4 = tf.layers.dense(hidden3, n_hidden4, activation=tf.nn.relu,
                              name="hidden4") # new!
    logits = tf.layers.dense(hidden4, n_outputs, name="outputs") # new!

with tf.name_scope("loss"):
    xentropy = tf.nn.sparse_softmax_cross_entropy_with_logits(labels=y, logits=logits)
    loss = tf.reduce_mean(xentropy, name="loss")

with tf.name_scope("eval"):
    correct = tf.nn.in_top_k(logits, y, 1)
    accuracy = tf.reduce_mean(tf.cast(correct, tf.float32), name="accuracy")

with tf.name_scope("train"):
    optimizer = tf.train.GradientDescentOptimizer(learning_rate)
    training_op = optimizer.minimize(loss)

 

reuse_vars = tf.get_collection(tf.GraphKeys.GLOBAL_VARIABLES,
                               scope="hidden[123]") # regular expression
reuse_vars_dict = dict([(var.op.name, var) for var in reuse_vars])
restore_saver = tf.train.Saver(reuse_vars_dict) # to restore layers 1-3

init = tf.global_variables_initializer()
saver = tf.train.Saver()

import numpy as np

n_batches = mnist.train.num_examples // batch_size

with tf.Session() as sess:
    init.run()
    restore_saver.restore(sess, "./my_model_final.ckpt")
    
    h2_cache = sess.run(hidden2, feed_dict={X: mnist.train.images})
    h2_cache_test = sess.run(hidden2, feed_dict={X: mnist.test.images}) # not shown in the book

    for epoch in range(n_epochs):
        shuffled_idx = np.random.permutation(mnist.train.num_examples)
        hidden2_batches = np.array_split(h2_cache[shuffled_idx], n_batches)
        y_batches = np.array_split(mnist.train.labels[shuffled_idx], n_batches)
        for hidden2_batch, y_batch in zip(hidden2_batches, y_batches):
            sess.run(training_op, feed_dict={hidden2:hidden2_batch, y:y_batch})

        accuracy_val = accuracy.eval(feed_dict={hidden2: h2_cache_test, # not shown
                                                y: mnist.test.labels})  # not shown
        print(epoch, "Test accuracy:", accuracy_val)                    # not shown

    save_path = saver.save(sess, "./my_new_model_final.ckpt")

六、Unsupervised Pretraining

该方法的提出，让人们对深度学习网络的训练有了一个新的认识，能够利用不那么昂贵的未标注数据，训练数据时没有标注的数据先作一个Pretraining训练出一个差很少的网络，再使用带label的数据作正式的训练进行反向传递，增进深度模型可用性

也能够在类似模型中作pretraining

七、Faster Optimizers

在传统的SGD上提出改进

有Momentum optimization（最先提出，利用惯性冲量），Nesterov Accelerated Gradient，AdaGrad（adaptive gradient每层降低不同），RMSProp，Adam optimization（结合adagrad和momentum，用的最多，是缺省的optimizer）

a. momentum optimization

记住以前算出的gradient方向，做为惯性加到当前梯度上。至关于下山时，SGD是静止的之判断当前最陡的是哪里，而momentum至关于在跑的过程当中不断修正方向，显然更加有效。

b. Nesterov Accelerated Gradient 

只计算当前这点的梯度，超前一步，再往前跑一点计算会更准一些。

c. AdaGrad

各个维度计算梯度做为分母，加到当前梯度上，不一样维度梯度降低不一样。以下图所示，横轴比纵轴平缓不少，传统gradient仅仅单纯沿法线方向移动，而AdaGrad平缓的θ1走的慢点，陡的θ2走的快点，效果较好。

但也有必定缺陷，s不断积累，分母愈来愈大，可能致使最后走不动。

d. RMSProp（Adadelta）

只加一部分，加一个衰减系数只选取相关的最近几步相关系数

 

e. Adam Optimization

目前用的最多效果最好的方法，结合AdaGrad和Momentum的优势

# TensorFlow中调用方法
optimizer = tf.train.MomentumOptimizer(learning_rate=learning_rate,momentum=0.9)

optimizer = tf.train.MomentumOptimizer(learning_rate=learning_rate,momentum=0.9, use_nesterov=True)

optimizer = tf.train.RMSPropOptimizer(learning_rate=learning_rate,momentum=0.9, decay=0.9, epsilon=1e-10)
# 能够看出AdamOptimizer最省心了
optimizer = tf.train.AdamOptimizer(learning_rate=learning_rate)

八、learning rate scheduling

learning rate的设置也很重要，以下图所示，太大不会收敛到全局最优，过小收敛效果最差。最理想状况是都必定状况缩小learning rate，先大后小

a. Exponential Scheduling

指数级降低学习率

initial_learning_rate = 0.1
decay_steps = 10000
decay_rate = 1/10
global_step = tf.Variable(0, trainable=False)
learning_rate = tf.train.exponential_decay(initial_learning_rate, global_step, decay_steps, decay_rate)
optimizer = tf.train.MomentumOptimizer(learning_rate, momentum=0.9)
training_op = optimizer.minimize(loss, global_step=global_step)

九、Avoiding Overfitting Through Regularization 

解决深度模型过拟合问题

a. Early Stopping

训练集上错误率开始上升时中止

b. l1和l2正则化

# construct the neural network
base_loss = tf.reduce_mean(xentropy, name="avg_xentropy")
reg_losses = tf.reduce_sum(tf.abs(weights1)) + tf.reduce_sum(tf.abs(weights2))
loss = tf.add(base_loss, scale * reg_losses, name="loss")

with arg_scope( [fully_connected], weights_regularizer=tf.contrib.layers.l1_regularizer(scale=0.01)):
    hidden1 = fully_connected(X, n_hidden1, scope="hidden1")
    hidden2 = fully_connected(hidden1, n_hidden2, scope="hidden2")
    logits = fully_connected(hidden2, n_outputs, activation_fn=None,scope="out")

reg_losses = tf.get_collection(tf.GraphKeys.REGULARIZATION_LOSSES)
loss = tf.add_n([base_loss] + reg_losses, name="loss")

c. dropout

 一种新的正则化方法，随机生成一个几率，大于某个阈值就扔掉，随机扔掉一些神经元节点，结果代表dropout很能解决过拟合问题。可强迫现有神经元不会集中太多特征，下降网络复杂度，鲁棒性加强。

 加入dropout后，training和test的准确率会很接近，必定程度解决overfit问题

training = tf.placeholder_with_default(False, shape=(), name='training')

dropout_rate = 0.5  # == 1 - keep_prob
X_drop = tf.layers.dropout(X, dropout_rate, training=training)

with tf.name_scope("dnn"):
    hidden1 = tf.layers.dense(X_drop, n_hidden1, activation=tf.nn.relu,
                              name="hidden1")
    hidden1_drop = tf.layers.dropout(hidden1, dropout_rate, training=training)
    hidden2 = tf.layers.dense(hidden1_drop, n_hidden2, activation=tf.nn.relu,
                              name="hidden2")
    hidden2_drop = tf.layers.dropout(hidden2, dropout_rate, training=training)
    logits = tf.layers.dense(hidden2_drop, n_outputs, name="outputs")

 

d. Max-Norm Regularization

 能够把超出threshold的权重截取掉，必定程度上让网络更加稳定

def max_norm_regularizer(threshold, axes=1, name="max_norm",
                                                   collection="max_norm"):
    def max_norm(weights):
        clipped = tf.clip_by_norm(weights, clip_norm=threshold, axes=axes)
        clip_weights = tf.assign(weights, clipped, name=name)
        tf.add_to_collection(collection, clip_weights)
        return None # there is no regularization loss term
    return max_norm

max_norm_reg = max_norm_regularizer(threshold=1.0)
hidden1 = fully_connected(X, n_hidden1, scope="hidden1",
                                                  weights_regularizer=max_norm_reg)

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e. Date Augmentation

 深度学习网络是一个数据饥渴模型，须要不少的数据。扩大数据集，例如图片左右镜像翻转，随机截取，倾斜随机角度，变换敏感度，改变色调等方法，扩大数据量，减小overfit可能性

十、default DNN configuration