【機器學習】DNN訓練中的問題與方法

感謝中國人民大學的胡鶴老師，人工智能課程講的頗有深度，與時俱進

因爲深度神經網絡（DNN）層數不少，每次訓練都是逐層由後至前傳遞。傳遞項<1，梯度可能變得很是小趨於0，以此來訓練網絡幾乎不會有什麼變化，即vanishing gradients problem；或者>1梯度很是大，以此修正網絡會不斷震盪，沒法造成一個收斂網絡。於是DNN的訓練中能夠造成不少tricks。。

一、初始化權重

起初採用正態分佈隨機化初始權重，會使得本來單位的variance逐漸變得很是大。例以下圖的sigmoid函數，靠近0點的梯度近似線性很敏感，但到了，即很強烈的輸入產生木訥的輸出。

 

採用Xavier initialization，根據fan-in（輸入神經元個數）和fan-out（輸出神經元個數）設置權重。

並設計針對不一樣激活函數的初始化策略，以下圖（左邊是均態分佈，右邊正態分佈較爲經常使用）

 

二、激活函數

通常使用ReLU，可是不能有小於0的輸入（dying ReLUs）

a.Leaky RELU

改進方法Leaky ReLU=max(αx,x)，小於0時保留一點微小特徵。

具體應用

 

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改進

另外一種改進ELU，在神經元小於0時採用指數變化

 

#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（僅給出關鍵代碼）

 

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 過程
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進行操做，對每一批數據也可採用，在調用激活函數以前，先作一下normalization，使得輸出數據有一個較好的形狀，初始時，超參數scaling（γ）和shifting（β）進行適度縮放平移後傳遞給activation函數。步驟以下：

 

現今batch normalization已經被TensorFlow實現成一個單獨的層，直接調用

測試時，因爲沒有mini-batch，故訓練時直接使用訓練時的mean和standard deviation（），實現代碼以下

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()
    #至關於單獨一層
    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))# 激活函數使用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)# 輸出層也作一個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
#須要顯示調用訓練時得出的方差均值，須要額外調用這些算子
extra_update_ops = tf.get_collection(tf.GraphKeys.UPDATE_OPS)
#在training和testing時不同
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

處理gradient以後日後傳，必定程度上解決梯度爆炸問題。（但因爲有了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、重用以前訓練過的層（Reusing Pretrained Layers）

對以前訓練的模型稍加修改，節省時間，在深度模型訓練（因爲有不少層）中常用。

通常類似問題，分類數等和問題緊密相關的output層與最後一個直接與output相關的隱層不能夠直接用，仍需本身訓練。

以下圖所示，在已訓練出一個複雜net後，遷移到相對簡單的net時，hidden1和2固定不動，hidden3稍做變化，hidden4和output本身訓練。。這在沒有本身GPU狀況下是很是節省時間的作法。

 

# 只選取須要的操做
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，能夠賦給模型一個清楚的名字保存下來
for op in (X, y, accuracy, training_op):
    tf.add_to_collection("my_important_ops", op)
# 若是你要使用這個模型
X, y, accuracy, training_op = tf.get_collection("my_important_ops")

# 訓練時
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

訓練時固定底層參數，達到Freezing the Lower Layers的目的

 

# 以MINIST爲例

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

訓練時直接從lock層以後的層開始訓練，Catching the Frozen Layers

 

# 以MINIST爲例

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

該方法的提出，讓人們對深度學習網絡的訓練有了一個新的認識，能夠利用不那麼昂貴的未標註數據，訓練數據時沒有標註的數據先作一個Pretraining訓練出一個差很少的網絡，再使用帶label的數據作正式的訓練進行反向傳遞，增進深度模型可用性

也能夠在類似模型中作pretraining

七、Faster Optimizers

在傳統的SGD上提出改進

有Momentum optimization（最先提出，利用慣性衝量），Nesterov Accelerated Gradient，AdaGrad（adaptive gradient每層降低不同），RMSProp，Adam optimization（結合adagrad和momentum，用的最多，是缺省的optimizer）

a. momentum optimization

記住以前算出的gradient方向，做爲慣性加到當前梯度上。至關於下山時，SGD是靜止的之判斷當前最陡的是哪裏，而momentum至關於在跑的過程當中不斷修正方向，顯然更加有效。

b. Nesterov Accelerated Gradient 

只計算當前這點的梯度，超前一步，再往前跑一點計算會更準一些。

c. AdaGrad

各個維度計算梯度做爲分母，加到當前梯度上，不一樣維度梯度降低不一樣。以下圖所示，橫軸比縱軸平緩不少，傳統gradient僅僅單純沿法線方向移動，而AdaGrad平緩的θ1走的慢點，陡的θ2走的快點，效果較好。

但也有必定缺陷，s不斷積累，分母愈來愈大，可能致使最後走不動。

d. RMSProp（Adadelta）

只加一部分，加一個衰減係數只選取相關的最近幾步相關係數

 

e. Adam Optimization

目前用的最多效果最好的方法，結合AdaGrad和Momentum的優勢

# TensorFlow中調用方法
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)
# 能夠看出AdamOptimizer最省心了
optimizer = tf.train.AdamOptimizer(learning_rate=learning_rate)

八、learning rate scheduling

learning rate的設置也很重要，以下圖所示，太大不會收斂到全局最優，過小收斂效果最差。最理想狀況是都必定狀況縮小learning rate，先大後小

a. Exponential Scheduling

指數級降低學習率

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 

解決深度模型過擬合問題

a. Early Stopping

訓練集上錯誤率開始上升時中止

b. l1和l2正則化

# 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

 一種新的正則化方法，隨機生成一個機率，大於某個閾值就扔掉，隨機扔掉一些神經元節點，結果代表dropout很能解決過擬合問題。可強迫現有神經元不會集中太多特徵，下降網絡複雜度，魯棒性加強。

 加入dropout後，training和test的準確率會很接近，必定程度解決overfit問題

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

 能夠把超出threshold的權重截取掉，必定程度上讓網絡更加穩定

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

 深度學習網絡是一個數據飢渴模型，須要不少的數據。擴大數據集，例如圖片左右鏡像翻轉，隨機截取，傾斜隨機角度，變換敏感度，改變色調等方法，擴大數據量，減小overfit可能性

十、default DNN configuration