深度学习实践系列（2）- 搭建notMNIST的深度神经网络

2023年4月11日上午2:41 • 深度学习

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。

深度学习实践系列（2）- 搭建notMNIST的深度神经网络

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：

深度学习实践系列（2）- 搭建notMNIST的深度神经网络

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

深度学习实践系列（2）- 搭建notMNIST的深度神经网络

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：

深度学习实践系列（2）- 搭建notMNIST的深度神经网络

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。

：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

深度学习实践系列（2）- 搭建notMNIST的深度神经网络

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。

深度学习实践系列（2）- 搭建notMNIST的深度神经网络

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_function
import numpy as np
import tensorflow as tf
from six.moves import cPickle as pickle
from 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 = 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)

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 = 10000

graph = 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 = 801

def 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))

Initialized
Loss at step 0: 16.516306
Training accuracy: 11.4%
Validation accuracy: 11.7%
Loss at step 100: 2.269041
Training accuracy: 71.8%
Validation accuracy: 70.2%
Loss at step 200: 1.816886
Training accuracy: 74.8%
Validation accuracy: 72.6%
Loss at step 300: 1.574824
Training accuracy: 76.0%
Validation accuracy: 73.6%
Loss at step 400: 1.415523
Training accuracy: 77.1%
Validation accuracy: 73.9%
Loss at step 500: 1.299691
Training accuracy: 78.0%
Validation accuracy: 74.4%
Loss at step 600: 1.209450
Training accuracy: 78.6%
Validation accuracy: 74.6%
Loss at step 700: 1.135888
Training accuracy: 79.0%
Validation accuracy: 74.9%
Loss at step 800: 1.074228
Training 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 = 128

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)
  
  # 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 = 3001

with 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))

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

7. 使用ReLUs激活函数

batch_size = 128
hidden_layer_size = 1024

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)

    # 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 = 3001

def 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))

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

8. 正则化

import math
batch_size = 128
hidden_layer_size = 1024 # Doubled because half of the results are discarded
regularization_beta = 5e-4

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)

    # 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 = 3001

def 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))

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

9. Dropout

import math
batch_size = 128
hidden_layer_size = 2048 # Doubled because half of the results are discarded
regularization_beta = 5e-4

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)

    # 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 = 5001

def 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.
Initialized
Minibatch loss at step 0: 4.059163
Minibatch accuracy: 7.8%
Validation accuracy: 31.5%
Minibatch loss at step 500: 1.626858
Minibatch accuracy: 86.7%
Validation accuracy: 84.8%
Minibatch loss at step 1000: 1.492026
Minibatch accuracy: 82.0%
Validation accuracy: 85.8%
Minibatch loss at step 1500: 1.139689
Minibatch accuracy: 92.2%
Validation accuracy: 87.1%
Minibatch loss at step 2000: 0.970064
Minibatch accuracy: 93.0%
Validation accuracy: 87.1%
Minibatch loss at step 2500: 0.963178
Minibatch accuracy: 87.5%
Validation accuracy: 87.6%
Minibatch loss at step 3000: 0.870884
Minibatch accuracy: 87.5%
Validation accuracy: 87.6%
Minibatch loss at step 3500: 0.898399
Minibatch accuracy: 85.2%
Validation accuracy: 87.7%
Minibatch loss at step 4000: 0.737084
Minibatch accuracy: 91.4%
Validation accuracy: 88.0%
Minibatch loss at step 4500: 0.646125
Minibatch accuracy: 88.3%
Validation accuracy: 87.7%
Minibatch loss at step 5000: 0.685591
Minibatch 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。

深度学习实践系列（2）- 搭建notMNIST的深度神经网络

本站文章如无特殊说明，均为本站原创，如若转载，请注明出处：深度学习实践系列（2）- 搭建notMNIST的深度神经网络 - Python技术站

深度学习

0 0 打赏

微信扫一扫

支付宝扫一扫

深度学习_遇到的错误信息汇总

上一篇 2023年4月11日

深度学习导论 – 读李宏毅《1天搞懂深度学习》

下一篇 2023年4月11日

NLP

用于NLP的7大免费数据集！

在开始为自然语言处理任务进行深度学习时，您需要练习数据集。最好使用可以快速下载的小型数据集，并且不会花费太长时间来拟合模型。此外，使用易于理解和广泛使用的标准数据集也很有帮助，这样您就可以比较您的结果以查看您是否正在取得进展。在这篇文章中，您将发现一套用于自然语言处理任务的标准数据集，您可以在开始使用深度学习时使用它们。概述这篇文章分为7个部分，根据…

2023年2月12日
000
UFLDL深度学习笔记（五）自编码线性解码器

1. 基本问题在第一篇 UFLDL深度学习笔记（一）基本知识与稀疏自编码中讨论了激活函数为$sigmoid$函数的系数自编码网络，本文要讨论“UFLDL 线性解码器”，区别在于输出层去掉了$sigmoid$，将计算值$z$直接作为输出。线性输出的原因是为了避免对输入范围的缩放： S 型激励函数输出范围是 [0,1]，当$ f(z^{(3)})…

深度学习 2023年4月13日
000
神经网络与深度学习[邱锡鹏] 第七章习题解析

明显地，埃尔法和K成正比 7-2 7-3 7-4 7-5 7-6 7-7 从再参数化的角度来分析批量归一化中缩放和平移的意义在此公式中，r和b表示缩放和平移参数向量。通过r和b，能够有效适应不同的激活函数。例如：通过r和b，可以自动调整输入分布，防止ReLU死亡问题。有了b的存在，仿射变换不再需要偏置参数。逐层归一化可以提高效率，并且作为一种隐形的正则…

深度学习 2023年4月11日
000
重磅！神经网络浅讲：从神经元到深度学习

http://www.open-open.com/lib/view/open1452752687042.html 图1 人脑神经网络神经网络是一门重要的机器学习技术。它是目前最为火热的研究方向–深度学习的基础。学习神经网络不仅可以让你掌握一门强大的机器学习方法，同时也可以更好地帮助你理解深度学习技术。本文以一种简单的，循序的方式讲解神经网络。适合对神…

深度学习 2023年4月13日
000
深度学习

深度学习训练数据打标签过程

为了获取大量的图片训练数据，在采集数据的过程中常用视频的方式采集数据，但对于深度学习，训练的过程需要很多的有有标签的数据，这篇文章主要是解决视频文件转换成图片文件，并加标签，最后把数据存储到pkl文件中，为后续深度学习提供数据。 1. video to image 这个应用，主要是把视频切分成图片，并保存到本地，可以自定义切分的时间间隔；在深度学习中，由于…

2023年4月9日
000
Tensorflow%20实战Google深度学习框架 4.2.2 自定义损失函数源代码

import os import tab import tensorflow as tf from numpy.random import RandomState print “hello tensorflow 4.1” batch_size = 8 x = tf.placeholder(tf.float32,shape=(None,2),name=\’x-…

深度学习 2023年4月12日
000
深度学习与中文短文本分析总结与梳理

感谢原著，原文出处：https://www.cnblogs.com/wangyaning/p/7853879.html 过去几年，深度神经网络在模式识别中占绝对主流。它们在许多计算机视觉任务中完爆之前的顶尖算法。在语音识别上也有这个趋势了。而中文文本处理，以及中文自然语言处理上，似乎没有太厉害的成果？尤其是中文短文本处理的问题上，尚且没有太成功的应用于分布式…

深度学习 2023年4月13日
000
深度学习

基于图像的三维物体重建：在深度学习时代的最新技术和趋势综述之三维曲面解码

作者：Longway 来源：公众号@3D视觉工坊链接：基于图像的三维物体重建：在深度学习时代的最新技术和趋势综述之三维曲面解码 1.三维曲面解码基于体积表示的方法在计算上非常浪费，因为信息只在三维形状的表面或其附近丰富。直接处理曲面时的主要挑战是，网格或点云等常见表示没有规则的结构，因此，它们不容易适应深度学习体系结构，特别是使用CNN的体系结构。本节…

2023年4月10日
000

深度学习实践系列（2）- 搭建notMNIST的深度神经网络

激活函数ReLUs

反向传播

SGD

正则化和Dropout

相关文章