TensorFlow-具有L2损失的正则化,如何应用于所有权重,而不仅仅是最后一个?
deep-learning
machine-learning
neural-network
tensorflow
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0

我正在玩ANN,它是Udacity DeepLearning课程的一部分。

我的一项作业涉及使用L2损耗将具有一层隐藏ReLU层的网络引入一般化。我想知道如何正确地引入它,以便所有权重都受到惩罚,而不仅仅是输出层的权重。

无需底部概括的网络代码位于该帖子的底部(实际运行培训的代码不在问题范围内)。

引入L2的一种明显方法是将损失计算替换为以下内容(如果beta为0.01):

loss = tf.reduce_mean( tf.nn.softmax_cross_entropy_with_logits(out_layer, tf_train_labels) + 0.01*tf.nn.l2_loss(out_weights))

但是在这种情况下,它将考虑输出层权重的值。我不确定,我们如何适当地惩罚进入隐藏的ReLU层的权重。是根本需要还是对输出层进行惩罚会以某种方式控制隐藏的权重?

#some importing
from __future__ import print_function
import numpy as np
import tensorflow as tf
from six.moves import cPickle as pickle
from six.moves import range

#loading data
pickle_file = '/home/maxkhk/Documents/Udacity/DeepLearningCourse/SourceCode/tensorflow/examples/udacity/notMNIST.pickle'

with open(pickle_file, 'rb') as f:
  save = pickle.load(f)
  train_dataset = save['train_dataset']
  train_labels = save['train_labels']
  valid_dataset = save['valid_dataset']
  valid_labels = save['valid_labels']
  test_dataset = save['test_dataset']
  test_labels = save['test_labels']
  del save  # hint to help gc free up memory
  print('Training set', train_dataset.shape, train_labels.shape)
  print('Validation set', valid_dataset.shape, valid_labels.shape)
  print('Test set', test_dataset.shape, test_labels.shape)


#prepare data to have right format for tensorflow
#i.e. data is flat matrix, labels are onehot

image_size = 28
num_labels = 10

def reformat(dataset, labels):
  dataset = dataset.reshape((-1, image_size * image_size)).astype(np.float32)
  # Map 0 to [1.0, 0.0, 0.0 ...], 1 to [0.0, 1.0, 0.0 ...]
  labels = (np.arange(num_labels) == labels[:,None]).astype(np.float32)
  return dataset, labels
train_dataset, train_labels = reformat(train_dataset, train_labels)
valid_dataset, valid_labels = reformat(valid_dataset, valid_labels)
test_dataset, test_labels = reformat(test_dataset, test_labels)
print('Training set', train_dataset.shape, train_labels.shape)
print('Validation set', valid_dataset.shape, valid_labels.shape)
print('Test set', test_dataset.shape, test_labels.shape)


#now is the interesting part - we are building a network with
#one hidden ReLU layer and out usual output linear layer

#we are going to use SGD so here is our size of batch
batch_size = 128

#building tensorflow graph
graph = tf.Graph()
with graph.as_default():
      # Input data. For the training data, we use a placeholder that will be fed
  # at run time with a training minibatch.
  tf_train_dataset = tf.placeholder(tf.float32,
                                    shape=(batch_size, image_size * image_size))
  tf_train_labels = tf.placeholder(tf.float32, shape=(batch_size, num_labels))
  tf_valid_dataset = tf.constant(valid_dataset)
  tf_test_dataset = tf.constant(test_dataset)

  #now let's build our new hidden layer
  #that's how many hidden neurons we want
  num_hidden_neurons = 1024
  #its weights
  hidden_weights = tf.Variable(
    tf.truncated_normal([image_size * image_size, num_hidden_neurons]))
  hidden_biases = tf.Variable(tf.zeros([num_hidden_neurons]))

  #now the layer itself. It multiplies data by weights, adds biases
  #and takes ReLU over result
  hidden_layer = tf.nn.relu(tf.matmul(tf_train_dataset, hidden_weights) + hidden_biases)

  #time to go for output linear layer
  #out weights connect hidden neurons to output labels
  #biases are added to output labels  
  out_weights = tf.Variable(
    tf.truncated_normal([num_hidden_neurons, num_labels]))  

  out_biases = tf.Variable(tf.zeros([num_labels]))  

  #compute output  
  out_layer = tf.matmul(hidden_layer,out_weights) + out_biases
  #our real output is a softmax of prior result
  #and we also compute its cross-entropy to get our loss
  loss = tf.reduce_mean( tf.nn.softmax_cross_entropy_with_logits(out_layer, tf_train_labels))

  #now we just minimize this loss to actually train the network
  optimizer = tf.train.GradientDescentOptimizer(0.5).minimize(loss)

  #nice, now let's calculate the predictions on each dataset for evaluating the
  #performance so far
  # Predictions for the training, validation, and test data.
  train_prediction = tf.nn.softmax(out_layer)
  valid_relu = tf.nn.relu(  tf.matmul(tf_valid_dataset, hidden_weights) + hidden_biases)
  valid_prediction = tf.nn.softmax( tf.matmul(valid_relu, out_weights) + out_biases) 

  test_relu = tf.nn.relu( tf.matmul( tf_test_dataset, hidden_weights) + hidden_biases)
  test_prediction = tf.nn.softmax(tf.matmul(test_relu, out_weights) + out_biases)
参考资料:
Stack Overflow
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共 3 个回答
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一种更短且可扩展的方法是;

vars   = tf.trainable_variables() 
lossL2 = tf.add_n([ tf.nn.l2_loss(v) for v in vars ]) * 0.001

这基本上将所有可训练变量的l2_loss相加。您也可以制作一个字典,在其中仅指定要添加到成本中的变量,然后使用上面的第二行。然后,您可以将lossL2与softmax交叉熵值相加,以计算总损耗。

编辑 :正如Piotr Dabkowski所提到的, 上面的代码还将规范偏差 。可以通过在第二行中添加if语句来避免这种情况;

lossL2 = tf.add_n([ tf.nn.l2_loss(v) for v in vars
                    if 'bias' not in v.name ]) * 0.001

这可以用来排除其他变量。

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hidden_weightshidden_biasesout_weightsout_biases都是要创建的模型参数。您可以将L2正则化添加到所有这些参数,如下所示:

loss = (tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(
    logits=out_layer, labels=tf_train_labels)) +
    0.01*tf.nn.l2_loss(hidden_weights) +
    0.01*tf.nn.l2_loss(hidden_biases) +
    0.01*tf.nn.l2_loss(out_weights) +
    0.01*tf.nn.l2_loss(out_biases))
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实际上,我们通常不对偏差项(拦截)进行正则化。所以,我追求:

loss = (tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(
    logits=out_layer, labels=tf_train_labels)) +
    0.01*tf.nn.l2_loss(hidden_weights) +
    0.01*tf.nn.l2_loss(out_weights))

通过对截距项进行惩罚,当将截距添加到y值时,将导致更改y值,从而为截距添加常数c。拥有或不拥有它不会改变结果,但是需要一些计算

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