由于深度神經網絡（DNN）層數很多，每次訓練都是逐層由后至前傳遞。傳遞項<1，梯度可能變得非常小趨于0，以此來訓練網絡幾乎不會有什么變化，即vanishing gradients problem；或者>1梯度非常大，以此修正網絡會不斷震蕩，無法形成一個收斂網絡。因而DNN的訓練中可以形成很多tricks。。

1、初始化權重

起初采用正態分布隨機化初始權重，會使得原本單位的variance逐漸變得非常大。例如下圖的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。

采用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。

并設計針對不同激活函數的初始化策略，如下圖（左邊是均態分布，右邊正態分布較為常用）

2、激活函數

一般使用ReLU，但是不能有小于0的輸入（dying ReLUs）

a.Leaky RELU

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

具體應用

from tensorflow.examples.tutorials.mnist import input_datamnist = input_data.read_data_sets("/tmp/data/")reset_graph()n_inputs =28*28# MNISTn_hidden1 =300n_hidden2 =100n_outputs =10X=tf.placeholder(tf.float32, shape=(None, n_inputs), name="X")y=tf.placeholder(tf.int64, shape=(None), name="y")withtf.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")withtf.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 =0.01withtf.name_scope("train"): optimizer =tf.train.GradientDescentOptimizer(learning_rate) training_op = optimizer.minimize(loss)withtf.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 =40batch_size =50withtf.Session()assess: init.run() forepoch inrange(n_epochs): foriteration inrange(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}) ifepoch %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

另一種改進ELU，在神經元小于0時采用指數變化

#just specify the activation function when building each layerX= 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）

withtf.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-10withtf.Session()assess: init.run() forepoch inrange(n_epochs): foriteration inrange(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}) ifepoch %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")3、Batch Normalization

在2015年，有研究者提出，既然使用mini-batch進行操作，對每一批數據也可采用，在調用激活函數之前，先做一下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）進行適度縮放平移后傳遞給activation函數。步驟如下：

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

測試時，由于沒有mini-batch，故訓練時直接使用訓練時的mean和standard deviation（），實現代碼如下

import tensorflowastfn_inputs =28*28n_hidden1 =300n_hidden2 =100n_outputs =10batch_norm_momentum =0.9X=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')withtf.name_scope("dnn"): he_init =tf.contrib.layers.variance_scaling_initializer() #相當于單獨一層 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)# 輸出層也做一個batch normalizationwithtf.name_scope("loss"): xentropy =tf.nn.sparse_softmax_cross_entropy_with_logits(labels=y, logits=logits) loss =tf.reduce_mean(xentropy, name="loss")withtf.name_scope("train"): optimizer =tf.train.GradientDescentOptimizer(learning_rate) training_op = optimizer.minimize(loss)withtf.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 =20batch_size =200#需要顯示調用訓練時得出的方差均值，需要額外調用這些算子extra_update_ops =tf.get_collection(tf.GraphKeys.UPDATE_OPS)#在training和testing時不一樣withtf.Session()assess: init.run() forepoch inrange(n_epochs): foriteration inrange(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")4、Gradient Clipp

處理gradient之后往后傳，一定程度上解決梯度爆炸問題。（但由于有了batch normalization，此方法用的不多）

threshold =1.0optimizer = tf.train.GradientDescentOptimizer(learning_rate)grads_and_vars = optimizer.compute_gradients(loss)capped_gvs = [(tf.clip_by_value(grad, -threshold, threshold),var) forgrad,varingrads_and_vars]training_op = optimizer.apply_gradients(capped_gvs)5、重用之前訓練過的層

（Reusing Pretrained Layers）

對之前訓練的模型稍加修改，節省時間，在深度模型訓練（由于有很多層）中經常使用。

一般相似問題，分類數等和問題緊密相關的output層與最后一個直接與output相關的隱層不可以直接用，仍需自己訓練。

如下圖所示，在已訓練出一個復雜net后，遷移到相對簡單的net時，hidden1和2固定不動，hidden3稍作變化，hidden4和output自己訓練。。這在沒有自己GPU情況下是非常節省時間的做法。

# 只選取需要的操作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")# 如果你是原模型的作者，可以賦給模型一個清楚的名字保存下來forop in (X,y, accuracy, training_op): tf.add_to_collection("my_important_ops", op)# 如果你要使用這個模型X,y, accuracy, training_op =tf.get_collection("my_important_ops")# 訓練時withtf.Session()assess: saver.restore(sess,"./my_model_final.ckpt") forepoch inrange(n_epochs): foriteration inrange(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為例n_inputs=28*28# MNISTn_hidden1=300# reusedn_hidden2=50# reusedn_hidden3=50# reusedn_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")withtf.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!withtf.name_scope("loss"): xentropy =tf.nn.sparse_softmax_cross_entropy_with_logits(labels=y, logits=logits) loss =tf.reduce_mean(xentropy, name="loss")withtf.name_scope("eval"): correct =tf.nn.in_top_k(logits,y,1) accuracy =tf.reduce_mean(tf.cast(correct,tf.float32), name="accuracy")withtf.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 expressionreuse_vars_dict = dict([(var.op.name, var)forvar in reuse_vars])restore_saver =tf.train.Saver(reuse_vars_dict) #torestore layers1-3init =tf.global_variables_initializer()saver =tf.train.Saver()withtf.Session()assess: init.run() restore_saver.restore(sess,"./my_model_final.ckpt") forepoch inrange(n_epochs): foriteration inrange(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層之后的層開始訓練，Catching the Frozen Layers

# 以MINIST為例n_inputs =28*28# MNISTn_hidden1 =300# reusedn_hidden2 =50# reusedn_hidden3 =50# reusedn_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")withtf.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!withtf.name_scope("loss"): xentropy =tf.nn.sparse_softmax_cross_entropy_with_logits(labels=y, logits=logits) loss =tf.reduce_mean(xentropy, name="loss")withtf.name_scope("eval"): correct =tf.nn.in_top_k(logits,y,1) accuracy =tf.reduce_mean(tf.cast(correct,tf.float32), name="accuracy")withtf.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 expressionreuse_vars_dict = dict([(var.op.name, var)forvar in reuse_vars])restore_saver =tf.train.Saver(reuse_vars_dict) #torestore layers1-3init =tf.global_variables_initializer()saver =tf.train.Saver()importnumpyasnpn_batches = mnist.train.num_examples // batch_sizewithtf.Session()assess: 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 forepochinrange(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) forhidden2_batch, y_batchinzip(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")6、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，可以利用不那么昂貴的未標注數據，訓練數據時沒有標注的數據先做一個Pretraining訓練出一個差不多的網絡，再使用帶label的數據做正式的訓練進行反向傳遞，增進深度模型可用性

也可以在相似模型中做pretraining

7、Faster Optimizers

在傳統的SGD上提出改進

有Momentum optimization（最早提出，利用慣性沖量），Nesterov Accelerated Gradient，AdaGrad（adaptive gradient每層下降不一樣），RMSProp，Adam optimization（結合adagrad和momentum，用的最多，是缺省的optimizer）

a. momentum optimization

記住之前算出的gradient方向，作為慣性加到當前梯度上。相當于下山時，SGD是靜止的之判斷當前最陡的是哪里，而momentum相當于在跑的過程中不斷修正方向，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

各個維度計算梯度作為分母，加到當前梯度上，不同維度梯度下降不同。如下圖所示，橫軸比縱軸平緩很多，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。

但也有一定缺陷，s不斷積累，分母越來越大，可能導致最后走不動。

d. RMSProp（Adadelta）

只加一部分，加一個衰減系數只選取相關的最近幾步相關系數

e. Adam Optimization

目前用的最多效果最好的方法，結合AdaGrad和Momentum的優點

# 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)# 可以看出AdamOptimizer最省心了optimizer= tf.train.AdamOptimizer(learning_rate=learning_rate)8、learning rate scheduling

learning rate的設置也很重要，如下圖所示，太大不會收斂到全局最優，太小收斂效果最差。最理想情況是都一定情況縮小learning rate，先大后小

a. Exponential Scheduling

指數級下降學習率

initial_learning_rate=0.1decay_steps=10000decay_rate=1/10global_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)9、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停止

b. l1和l2正則化

# construct the neural networkbase_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，隨機生成一個概率，大于某個閾值就扔掉，隨機扔掉一些神經元節點，結果表明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征，降低網絡復雜度，魯棒性增強。

加入dropout后，training和test的準確率會很接近，一定程度解決overfit問題

training =tf.placeholder_with_default(False, shape=(), name='training')dropout_rate =0.5# ==1- keep_probX_drop =tf.layers.dropout(X, dropout_rate, training=training)withtf.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

可以把超出threshold的權重截取掉，一定程度上讓網絡更加穩定

defmax_norm_regularizer(threshold, axes=1, name="max_norm", collection="max_norm"): defmax_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) returnNone# there is no regularization loss term returnmax_normmax_norm_reg = max_norm_regularizer(threshold=1.0)hidden1 = fully_connected(X, n_hidden1, scope="hidden1", weights_regularizer=max_norm_reg)

e. Date Augmentation

深度學習網絡是一個數據饑渴模型，需要很多的數據。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，減少overfit可能性

10、default DNN configuration