深度学习实践系列（2）- 搭建notMNIST的深度神经网络

如果你希望系统性的了解神经网络，请参考零基础入门深度学习系列 ，下面我会粗略的介绍一下本文中实现神经网络需要了解的知识。

什么是深度神经网络？

 

神经网络包含三层：输入层（X）、隐藏层和输出层：f(x)

每层之间每个节点都是完全连接的，其中包含权重（W）。每层都存在一个偏移值（b）。

 

每一层节点的计算方式如下：

其中g()代表激活函数，o()代表softmax输出函数。

 

使用Flow Graph的方式来表达如何正向推导神经网络，可以表达如下：

x: 输入值

a(x)：表示每个隐藏层的pre-activation的数据，由前一个隐藏层数据(h)、权重(w)和偏移值(b)计算而来

h(x)：表示每个隐藏层的数据

f(x)：表示输出层数据

 

激活函数ReLUs

激活函数有很多种类，例如sigmoid、tanh、ReLUs，对于深度神经网络而言，目前最流行的是ReLUs。

关于几种激活函数的对比可以参见：常用激活函数的总结与比较

ReLUs函数如下：

 

反向传播

现在，我们需要知道一个神经网络的每个连接上的权值是如何得到的。我们可以说神经网络是一个模型，那么这些权值就是模型的参数，也就是模型要学习的东西。然而，一个神经网络的连接方式、网络的层数、每层的节点数这些参数，则不是学习出来的，而是人为事先设置的。对于这些人为设置的参数，我们称之为超参数(Hyper-Parameters)。

接下来，我们将要介绍神经网络的训练算法：反向传播算法。

具体内容请参考：零基础入门深度学习(3) - 神经网络和反向传播算法

 

SGD

梯度下降算法是一种不断调整参数值从而达到减少Loss function的方法，通过不断迭代而获得最佳的权重值。梯度下降传统上是每次迭代都使用全部训练数据来进行参数调整，随机梯度下降则是使用少量训练数据来进行调整。

关于GD和SGD的区别可以参考：GD(梯度下降)和SGD(随机梯度下降)

 

正则化和Dropout

正则化和Dropout都是一些防止过度拟合的方法，详细介绍可以参考：正则化方法：L1和L2 regularization、数据集扩增、dropout

正则化：通过在Loss function中加入对权重(w)的惩罚，可以限制权重值变得非常大

Dropout: 通过随机抛弃一些节点，使得神经网络更加多样性，然后组合起来获得的结果更加通用。

 

好吧，基本的概念大概介绍了一遍，开始撸代码啦。

请先参考深度学习实践系列（1）- 从零搭建notMNIST逻辑回归模型，获得notMNIST.pickle的训练数据。

1. 引用第三方库

# These are all the modules we'll be using later. Make sure you can import them# before proceeding further.from __future__ import print_functionimport numpy as npimport tensorflow as tffrom six.moves import cPickle as picklefrom six.moves import range

2. 读取数据

pickle_file = '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)

Training set (200000, 28, 28) (200000,)Validation set (10000, 28, 28) (10000,)Test set (10000, 28, 28) (10000,)

3. 调整数据格式以便后续训练

image_size = 28num_labels = 10def 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, labelstrain_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)

Training set (200000, 784) (200000, 10)Validation set (10000, 784) (10000, 10)Test set (10000, 784) (10000, 10)

4. 定义神经网络

# With gradient descent training, even this much data is prohibitive.# Subset the training data for faster turnaround.train_subset = 10000graph = tf.Graph()with graph.as_default():  # Input data.  # Load the training, validation and test data into constants that are  # attached to the graph.  tf_train_dataset = tf.constant(train_dataset[:train_subset, :])  tf_train_labels = tf.constant(train_labels[:train_subset])  tf_valid_dataset = tf.constant(valid_dataset)  tf_test_dataset = tf.constant(test_dataset)    # Variables.  # These are the parameters that we are going to be training. The weight  # matrix will be initialized using random values following a (truncated)  # normal distribution. The biases get initialized to zero.  weights = tf.Variable(    tf.truncated_normal([image_size * image_size, num_labels]))  biases = tf.Variable(tf.zeros([num_labels]))    # Training computation.  # We multiply the inputs with the weight matrix, and add biases. We compute  # the softmax and cross-entropy (it's one operation in TensorFlow, because  # it's very common, and it can be optimized). We take the average of this  # cross-entropy across all training examples: that's our loss.  logits = tf.matmul(tf_train_dataset, weights) + biases  loss = tf.reduce_mean(    tf.nn.softmax_cross_entropy_with_logits(labels=tf_train_labels, logits=logits))    # Optimizer.  # We are going to find the minimum of this loss using gradient descent.  optimizer = tf.train.GradientDescentOptimizer(0.5).minimize(loss)    # Predictions for the training, validation, and test data.  # These are not part of training, but merely here so that we can report  # accuracy figures as we train.  train_prediction = tf.nn.softmax(logits)  valid_prediction = tf.nn.softmax(    tf.matmul(tf_valid_dataset, weights) + biases)  test_prediction = tf.nn.softmax(tf.matmul(tf_test_dataset, weights) + biases)

 

5. 使用梯度下降（GD）训练神经网络

num_steps = 801def accuracy(predictions, labels):  return (100.0 * np.sum(np.argmax(predictions, 1) == np.argmax(labels, 1))          / predictions.shape[0])with tf.Session(graph=graph) as session:  # This is a one-time operation which ensures the parameters get initialized as  # we described in the graph: random weights for the matrix, zeros for the  # biases.   tf.global_variables_initializer().run()  print('Initialized')  for step in range(num_steps):    # Run the computations. We tell .run() that we want to run the optimizer,    # and get the loss value and the training predictions returned as numpy    # arrays.    _, l, predictions = session.run([optimizer, loss, train_prediction])    if (step % 100 == 0):      print('Loss at step %d: %f' % (step, l))      print('Training accuracy: %.1f%%' % accuracy(        predictions, train_labels[:train_subset, :]))      # Calling .eval() on valid_prediction is basically like calling run(), but      # just to get that one numpy array. Note that it recomputes all its graph      # dependencies.      print('Validation accuracy: %.1f%%' % accuracy(        valid_prediction.eval(), valid_labels))  print('Test accuracy: %.1f%%' % accuracy(test_prediction.eval(), test_labels))

InitializedLoss at step 0: 16.516306Training accuracy: 11.4%Validation accuracy: 11.7%Loss at step 100: 2.269041Training accuracy: 71.8%Validation accuracy: 70.2%Loss at step 200: 1.816886Training accuracy: 74.8%Validation accuracy: 72.6%Loss at step 300: 1.574824Training accuracy: 76.0%Validation accuracy: 73.6%Loss at step 400: 1.415523Training accuracy: 77.1%Validation accuracy: 73.9%Loss at step 500: 1.299691Training accuracy: 78.0%Validation accuracy: 74.4%Loss at step 600: 1.209450Training accuracy: 78.6%Validation accuracy: 74.6%Loss at step 700: 1.135888Training accuracy: 79.0%Validation accuracy: 74.9%Loss at step 800: 1.074228Training accuracy: 79.5%Validation accuracy: 75.0%Test accuracy: 82.3%

6. 使用随机梯度下降（SGD）算法

batch_size = 128graph = 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)    # Variables.  weights = tf.Variable(    tf.truncated_normal([image_size * image_size, num_labels]))  biases = tf.Variable(tf.zeros([num_labels]))    # Training computation.  logits = tf.matmul(tf_train_dataset, weights) + biases  loss = tf.reduce_mean(    tf.nn.softmax_cross_entropy_with_logits(labels=tf_train_labels, logits=logits))    # Optimizer.  optimizer = tf.train.GradientDescentOptimizer(0.5).minimize(loss)    # Predictions for the training, validation, and test data.  train_prediction = tf.nn.softmax(logits)  valid_prediction = tf.nn.softmax(    tf.matmul(tf_valid_dataset, weights) + biases)  test_prediction = tf.nn.softmax(tf.matmul(tf_test_dataset, weights) + biases)num_steps = 3001with tf.Session(graph=graph) as session:  tf.global_variables_initializer().run()  print("Initialized")  for step in range(num_steps):    # Pick an offset within the training data, which has been randomized.    # Note: we could use better randomization across epochs.    offset = (step * batch_size) % (train_labels.shape[0] - batch_size)    # Generate a minibatch.    batch_data = train_dataset[offset:(offset + batch_size), :]    batch_labels = train_labels[offset:(offset + batch_size), :]    # Prepare a dictionary telling the session where to feed the minibatch.    # The key of the dictionary is the placeholder node of the graph to be fed,    # and the value is the numpy array to feed to it.    feed_dict = {tf_train_dataset : batch_data, tf_train_labels : batch_labels}    _, l, predictions = session.run(      [optimizer, loss, train_prediction], feed_dict=feed_dict)    if (step % 500 == 0):      print("Minibatch loss at step %d: %f" % (step, l))      print("Minibatch accuracy: %.1f%%" % accuracy(predictions, batch_labels))      print("Validation accuracy: %.1f%%" % accuracy(        valid_prediction.eval(), valid_labels))  print("Test accuracy: %.1f%%" % accuracy(test_prediction.eval(), test_labels))

InitializedMinibatch loss at step 0: 18.121506Minibatch accuracy: 11.7%Validation accuracy: 15.0%Minibatch loss at step 500: 1.192153Minibatch accuracy: 80.5%Validation accuracy: 76.1%Minibatch loss at step 1000: 1.309419Minibatch accuracy: 75.8%Validation accuracy: 76.8%Minibatch loss at step 1500: 0.739157Minibatch accuracy: 83.6%Validation accuracy: 77.3%Minibatch loss at step 2000: 0.854160Minibatch accuracy: 85.2%Validation accuracy: 77.5%Minibatch loss at step 2500: 1.045702Minibatch accuracy: 76.6%Validation accuracy: 78.8%Minibatch loss at step 3000: 0.940078Minibatch accuracy: 79.7%Validation accuracy: 78.8%Test accuracy: 85.8%

7. 使用ReLUs激活函数

batch_size = 128hidden_layer_size = 1024graph = 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)    # Variables.        # Hidden layer (RELU magic)        weights_hidden = tf.Variable(        tf.truncated_normal([image_size * image_size, hidden_layer_size]))    biases_hidden = tf.Variable(tf.zeros([hidden_layer_size]))    hidden = tf.nn.relu(tf.matmul(tf_train_dataset, weights_hidden) + biases_hidden)    # Output layer    weights_output = tf.Variable(        tf.truncated_normal([hidden_layer_size, num_labels]))    biases_output = tf.Variable(tf.zeros([num_labels]))        # Training computation.        logits = tf.matmul(hidden, weights_output) + biases_output        loss = tf.reduce_mean(        tf.nn.softmax_cross_entropy_with_logits(labels=tf_train_labels, logits=logits))      # Optimizer.    optimizer = tf.train.GradientDescentOptimizer(0.5).minimize(loss)      # Predictions for the training, validation, and test data.    # Creation of hidden layer of RELU for the validation and testing process            train_prediction = tf.nn.softmax(logits)        hidden_validation = tf.nn.relu(tf.matmul(tf_valid_dataset, weights_hidden) + biases_hidden)    valid_prediction = tf.nn.softmax(    tf.matmul(hidden_validation, weights_output) + biases_output)        hidden_prediction = tf.nn.relu(tf.matmul(tf_test_dataset, weights_hidden) + biases_hidden)    test_prediction = tf.nn.softmax(tf.matmul(hidden_prediction, weights_output) + biases_output)num_steps = 3001def accuracy(predictions, labels):  return (100.0 * np.sum(np.argmax(predictions, 1) == np.argmax(labels, 1))          / predictions.shape[0])with tf.Session(graph=graph) as session:  tf.initialize_all_variables().run()  print("Initialized")  for step in range(num_steps):    # Pick an offset within the training data, which has been randomized.    # Note: we could use better randomization across epochs.    offset = (step * batch_size) % (train_labels.shape[0] - batch_size)    # Generate a minibatch.    batch_data = train_dataset[offset:(offset + batch_size), :]    batch_labels = train_labels[offset:(offset + batch_size), :]    # Prepare a dictionary telling the session where to feed the minibatch.    # The key of the dictionary is the placeholder node of the graph to be fed,    # and the value is the numpy array to feed to it.    feed_dict = {tf_train_dataset : batch_data, tf_train_labels : batch_labels}    _, l, predictions = session.run(      [optimizer, loss, train_prediction], feed_dict=feed_dict)    if (step % 500 == 0):      print("Minibatch loss at step %d: %f" % (step, l))      print("Minibatch accuracy: %.1f%%" % accuracy(predictions, batch_labels))      print("Validation accuracy: %.1f%%" % accuracy(        valid_prediction.eval(), valid_labels))  print("Test accuracy: %.1f%%" % accuracy(test_prediction.eval(), test_labels))

InitializedMinibatch loss at step 0: 282.291931Minibatch accuracy: 14.1%Validation accuracy: 32.1%Minibatch loss at step 500: 18.090569Minibatch accuracy: 82.0%Validation accuracy: 79.7%Minibatch loss at step 1000: 15.504422Minibatch accuracy: 75.0%Validation accuracy: 80.8%Minibatch loss at step 1500: 5.314545Minibatch accuracy: 87.5%Validation accuracy: 80.6%Minibatch loss at step 2000: 3.442260Minibatch accuracy: 86.7%Validation accuracy: 81.5%Minibatch loss at step 2500: 2.226066Minibatch accuracy: 83.6%Validation accuracy: 82.6%Minibatch loss at step 3000: 2.228517Minibatch accuracy: 83.6%Validation accuracy: 82.5%Test accuracy: 89.6%

8. 正则化

import mathbatch_size = 128hidden_layer_size = 1024 # Doubled because half of the results are discardedregularization_beta = 5e-4graph = 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)    # Variables.        # Hidden layer (RELU magic)        weights_hidden_1 = tf.Variable(        tf.truncated_normal([image_size * image_size, hidden_layer_size],                            stddev=1 / math.sqrt(float(image_size * image_size))))    biases_hidden_1 = tf.Variable(tf.zeros([hidden_layer_size]))    hidden_1 = tf.nn.relu(tf.matmul(tf_train_dataset, weights_hidden_1) + biases_hidden_1)    weights_hidden_2 = tf.Variable(tf.truncated_normal([hidden_layer_size, hidden_layer_size],                                                      stddev=1 / math.sqrt(float(image_size * image_size))))    biases_hidden_2 = tf.Variable(tf.zeros([hidden_layer_size]))    hidden_2 = tf.nn.relu(tf.matmul(hidden_1, weights_hidden_2) + biases_hidden_2)        # Output layer    weights_output = tf.Variable(        tf.truncated_normal([hidden_layer_size, num_labels],                           stddev=1 / math.sqrt(float(image_size * image_size))))    biases_output = tf.Variable(tf.zeros([num_labels]))        # Training computation.        logits = tf.matmul(hidden_2, weights_output) + biases_output        loss = tf.reduce_mean(        tf.nn.softmax_cross_entropy_with_logits(labels=tf_train_labels, logits=logits))      # L2 regularization on hidden and output weights and biases        regularizers = (tf.nn.l2_loss(weights_hidden_1) + tf.nn.l2_loss(biases_hidden_1) +                     tf.nn.l2_loss(weights_hidden_2) + tf.nn.l2_loss(biases_hidden_2) +                    tf.nn.l2_loss(weights_output) + tf.nn.l2_loss(biases_output))    loss = loss + regularization_beta * regularizers        # Optimizer.    optimizer = tf.train.GradientDescentOptimizer(0.5).minimize(loss)      # Predictions for the training, validation, and test data.    # Creation of hidden layer of RELU for the validation and testing process            train_prediction = tf.nn.softmax(logits)        hidden_validation_1 = tf.nn.relu(tf.matmul(tf_valid_dataset, weights_hidden_1) + biases_hidden_1)    hidden_validation_2 = tf.nn.relu(tf.matmul(hidden_validation_1, weights_hidden_2) + biases_hidden_2)    valid_prediction = tf.nn.softmax(    tf.matmul(hidden_validation_2, weights_output) + biases_output)        hidden_prediction_1 = tf.nn.relu(tf.matmul(tf_test_dataset, weights_hidden_1) + biases_hidden_1)    hidden_prediction_2 = tf.nn.relu(tf.matmul(hidden_prediction_1, weights_hidden_2) + biases_hidden_2)    test_prediction = tf.nn.softmax(tf.matmul(hidden_prediction_2, weights_output) + biases_output)num_steps = 3001def accuracy(predictions, labels):  return (100.0 * np.sum(np.argmax(predictions, 1) == np.argmax(labels, 1))          / predictions.shape[0])with tf.Session(graph=graph) as session:  tf.initialize_all_variables().run()  print("Initialized")  for step in range(num_steps):    # Pick an offset within the training data, which has been randomized.    # Note: we could use better randomization across epochs.    offset = (step * batch_size) % (train_labels.shape[0] - batch_size)    # Generate a minibatch.    batch_data = train_dataset[offset:(offset + batch_size), :]    batch_labels = train_labels[offset:(offset + batch_size), :]    # Prepare a dictionary telling the session where to feed the minibatch.    # The key of the dictionary is the placeholder node of the graph to be fed,    # and the value is the numpy array to feed to it.    feed_dict = {tf_train_dataset : batch_data, tf_train_labels : batch_labels}    _, l, predictions = session.run(      [optimizer, loss, train_prediction], feed_dict=feed_dict)    if (step % 500 == 0):      print("Minibatch loss at step %d: %f" % (step, l))      print("Minibatch accuracy: %.1f%%" % accuracy(predictions, batch_labels))      print("Validation accuracy: %.1f%%" % accuracy(        valid_prediction.eval(), valid_labels))  print("Test accuracy: %.1f%%" % accuracy(test_prediction.eval(), test_labels))

InitializedMinibatch loss at step 0: 2.769384Minibatch accuracy: 8.6%Validation accuracy: 34.8%Minibatch loss at step 500: 0.735681Minibatch accuracy: 89.1%Validation accuracy: 86.2%Minibatch loss at step 1000: 0.791112Minibatch accuracy: 85.9%Validation accuracy: 86.9%Minibatch loss at step 1500: 0.523572Minibatch accuracy: 93.0%Validation accuracy: 88.1%Minibatch loss at step 2000: 0.487140Minibatch accuracy: 95.3%Validation accuracy: 88.5%Minibatch loss at step 2500: 0.529468Minibatch accuracy: 89.8%Validation accuracy: 88.4%Minibatch loss at step 3000: 0.531258Minibatch accuracy: 86.7%Validation accuracy: 88.9%Test accuracy: 94.7%

9. Dropout

import mathbatch_size = 128hidden_layer_size = 2048 # Doubled because half of the results are discardedregularization_beta = 5e-4graph = 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)    # Variables.        # Hidden layer (RELU magic)        weights_hidden_1 = tf.Variable(        tf.truncated_normal([image_size * image_size, hidden_layer_size],                            stddev=1 / math.sqrt(float(image_size * image_size))))    biases_hidden_1 = tf.Variable(tf.zeros([hidden_layer_size]))    hidden_1 = tf.nn.relu(tf.matmul(tf_train_dataset, weights_hidden_1) + biases_hidden_1)    weights_hidden_2 = tf.Variable(tf.truncated_normal([hidden_layer_size, hidden_layer_size],                                                      stddev=1 / math.sqrt(float(image_size * image_size))))    biases_hidden_2 = tf.Variable(tf.zeros([hidden_layer_size]))    hidden_2 = tf.nn.relu(tf.matmul(tf.nn.dropout(hidden_1, 0.5), weights_hidden_2) + biases_hidden_2)        # Output layer    weights_output = tf.Variable(        tf.truncated_normal([hidden_layer_size, num_labels],                           stddev=1 / math.sqrt(float(image_size * image_size))))    biases_output = tf.Variable(tf.zeros([num_labels]))        # Training computation.        logits = tf.matmul(tf.nn.dropout(hidden_2, 0.5), weights_output) + biases_output        loss = tf.reduce_mean(        tf.nn.softmax_cross_entropy_with_logits(labels=tf_train_labels, logits=logits))      # L2 regularization on hidden and output weights and biases        regularizers = (tf.nn.l2_loss(weights_hidden_1) + tf.nn.l2_loss(biases_hidden_1) +                     tf.nn.l2_loss(weights_hidden_2) + tf.nn.l2_loss(biases_hidden_2) +                    tf.nn.l2_loss(weights_output) + tf.nn.l2_loss(biases_output))    loss = loss + regularization_beta * regularizers        # Optimizer.    optimizer = tf.train.GradientDescentOptimizer(0.5).minimize(loss)      # Predictions for the training, validation, and test data.    # Creation of hidden layer of RELU for the validation and testing process            train_prediction = tf.nn.softmax(logits)        hidden_validation_1 = tf.nn.relu(tf.matmul(tf_valid_dataset, weights_hidden_1) + biases_hidden_1)    hidden_validation_2 = tf.nn.relu(tf.matmul(hidden_validation_1, weights_hidden_2) + biases_hidden_2)    valid_prediction = tf.nn.softmax(    tf.matmul(hidden_validation_2, weights_output) + biases_output)        hidden_prediction_1 = tf.nn.relu(tf.matmul(tf_test_dataset, weights_hidden_1) + biases_hidden_1)    hidden_prediction_2 = tf.nn.relu(tf.matmul(hidden_prediction_1, weights_hidden_2) + biases_hidden_2)    test_prediction = tf.nn.softmax(tf.matmul(hidden_prediction_2, weights_output) + biases_output)num_steps = 5001def accuracy(predictions, labels):  return (100.0 * np.sum(np.argmax(predictions, 1) == np.argmax(labels, 1))          / predictions.shape[0])with tf.Session(graph=graph) as session:  tf.initialize_all_variables().run()  print("Initialized")  for step in range(num_steps):    # Pick an offset within the training data, which has been randomized.    # Note: we could use better randomization across epochs.    offset = (step * batch_size) % (train_labels.shape[0] - batch_size)    # Generate a minibatch.    batch_data = train_dataset[offset:(offset + batch_size), :]    batch_labels = train_labels[offset:(offset + batch_size), :]    # Prepare a dictionary telling the session where to feed the minibatch.    # The key of the dictionary is the placeholder node of the graph to be fed,    # and the value is the numpy array to feed to it.    feed_dict = {tf_train_dataset : batch_data, tf_train_labels : batch_labels}    _, l, predictions = session.run(      [optimizer, loss, train_prediction], feed_dict=feed_dict)    if (step % 500 == 0):      print("Minibatch loss at step %d: %f" % (step, l))      print("Minibatch accuracy: %.1f%%" % accuracy(predictions, batch_labels))      print("Validation accuracy: %.1f%%" % accuracy(        valid_prediction.eval(), valid_labels))  print("Test accuracy: %.1f%%" % accuracy(test_prediction.eval(), test_labels))

WARNING:tensorflow:From <ipython-input-12-3684c7218154>:8: initialize_all_variables (from tensorflow.python.ops.variables) is deprecated and will be removed after 2017-03-02.Instructions for updating:Use `tf.global_variables_initializer` instead.InitializedMinibatch loss at step 0: 4.059163Minibatch accuracy: 7.8%Validation accuracy: 31.5%Minibatch loss at step 500: 1.626858Minibatch accuracy: 86.7%Validation accuracy: 84.8%Minibatch loss at step 1000: 1.492026Minibatch accuracy: 82.0%Validation accuracy: 85.8%Minibatch loss at step 1500: 1.139689Minibatch accuracy: 92.2%Validation accuracy: 87.1%Minibatch loss at step 2000: 0.970064Minibatch accuracy: 93.0%Validation accuracy: 87.1%Minibatch loss at step 2500: 0.963178Minibatch accuracy: 87.5%Validation accuracy: 87.6%Minibatch loss at step 3000: 0.870884Minibatch accuracy: 87.5%Validation accuracy: 87.6%Minibatch loss at step 3500: 0.898399Minibatch accuracy: 85.2%Validation accuracy: 87.7%Minibatch loss at step 4000: 0.737084Minibatch accuracy: 91.4%Validation accuracy: 88.0%Minibatch loss at step 4500: 0.646125Minibatch accuracy: 88.3%Validation accuracy: 87.7%Minibatch loss at step 5000: 0.685591Minibatch accuracy: 88.3%Validation accuracy: 88.6%Test accuracy: 94.4%

最后总结一下各种算法的训练表现，可以看出使用正则化和Dropout后训练效果明显变好，最后趋近于95%的准确率了。