【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，人工智能课程讲的很有深度，与时俱进
由于深度神经网络（DNN）层数很多，每次训练都是逐层由后至前传递。传递项<1，梯度可能变得非常小趋于0，以此来训练网络几乎不会有什么变化，即vanishing gradients problem；或者>1梯度非常大，以此修正网络会不断震荡，无法形成一个收敛网络。因而DNN的训练中可以形成很多tricks。。
1、初始化权重
起初采用正态分布随机化初始权重，会使得原本单位的variance逐渐变得非常大。例如下图的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。
并设计针对不同激活函数的初始化策略，如下图（左边是均态分布，右边正态分布较为常用）
2、激活函数
一般使用ReLU，但是不能有小于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")
3、Batch Normalization
在2015年，有研究者提出，既然使用mini-batch进行操作，对每一批数据也可采用，在调用激活函数之前，先做一下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。步骤如下：
现今batch normalization已经被TensorFlow实现成一个单独的层，直接调用
测试时，由于没有mini-batch，故训练时直接使用训练时的mean和standard deviation（），实现代码如下
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() #相当于单独一层 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)# 输出层也做一个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 #需要显示调用训练时得出的方差均值，需要额外调用这些算子 extra_update_ops = tf.get_collection(tf.GraphKeys.UPDATE_OPS) #在training和testing时不一样 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")
4、Gradient Clipp
处理gradient之后往后传，一定程度上解决梯度爆炸问题。（但由于有了batch normalization，此方法用的不多）
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)
5、重用之前训练过的层（Reusing Pretrained Layers）
对之前训练的模型稍加修改，节省时间，在深度模型训练（由于有很多层）中经常使用。
一般相似问题，分类数等和问题紧密相关的output层与最后一个直接与output相关的隐层不可以直接用，仍需自己训练。
如下图所示，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稍作变化，hidden4和output自己训练。。这在没有自己GPU情况下是非常节省时间的做法。
# 只选取需要的操作 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) # 如果你要使用这个模型 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层之后的层开始训练，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")
6、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，可以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做一个Pretraining训练出一个差不多的网络，再使用带label的数据做正式的训练进行反向传递，增进深度模型可用性
也可以在相似模型中做pretraining
7、Faster Optimizers
在传统的SGD上提出改进
有Momentum optimization（最早提出，利用惯性冲量），Nesterov Accelerated Gradient，AdaGrad（adaptive gradient每层下降不一样），RMSProp，Adam optimization（结合adagrad和momentum，用的最多，是缺省的optimizer）
a. momentum optimization
记住之前算出的gradient方向，作为惯性加到当前梯度上。相当于下山时，SGD是静止的之判断当前最陡的是哪里，而momentum相当于在跑的过程中不断修正方向，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
各个维度计算梯度作为分母，加到当前梯度上，不同维度梯度下降不同。如下图所示，横轴比纵轴平缓很多，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。
但也有一定缺陷，s不断积累，分母越来越大，可能导致最后走不动。
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的优点
# 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) # 可以看出AdamOptimizer最省心了 optimizer = tf.train.AdamOptimizer(learning_rate=learning_rate)
8、learning rate scheduling
learning rate的设置也很重要，如下图所示，太大不会收敛到全局最优，太小收敛效果最差。最理想情况是都一定情况缩小learning rate，先大后小
a. Exponential Scheduling
指数级下降学习率
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)
9、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停止
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，随机生成一个概率，大于某个阈值就扔掉，随机扔掉一些神经元节点，结果表明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，降低网络复杂度，鲁棒性增强。
加入dropout后，training和test的准确率会很接近，一定程度解决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
可以把超出threshold的权重截取掉，一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)
e. Date Augmentation
深度学习网络是一个数据饥渴模型，需要很多的数据。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，减少overfit可能性
10、default DNN configuration
