CNN最大的特點在于卷積的權值共享結構，可以大幅減少神經網絡的參數量，防止過擬合的同時又降低了神經網絡模型的復雜度。在CNN中，第一個卷積層會直接接受圖像像素級的輸入，每一個卷積操作只處理一小塊圖像，進行卷積變化后再傳到后面的網絡，每一層卷積都會提取數據中最有效的特征。這種方法可以提取到圖像中最基礎的特征，比如不同方向的邊或者拐角，而后再進行組合和抽象形成更高階的特征。

一般的卷積神經網絡由多個卷積層構成，每個卷積層中通常會進行如下幾個操作：

總結一下，CNN的要點是局部連接（local Connection）、權值共享（Weight Sharing）和池化層（Pooling）中的降采樣（Down-Sampling）。

本文將使用Tensorflow實現一個簡單的卷積神經網絡，使用的數據集是MNIST，網絡結構：兩個卷積層加一個全連接層。

from tensorflow.examples.tutorials.mnist import input_dataimport tensorflow as tf# 載入MNIST數據集，并創建默認的Interactive Session。mnist = input_data.read_data_sets("MNIST_data/", one_hot=True)sess = tf.InteractiveSession()# 創建權重和偏置，以便重復使用。我們需要給權重制造一些隨機的噪聲來打破完全對稱，比如截斷的正態分布噪聲，標準差設為0.1def weight_variable(shape): initial = tf.truncated_normal(shape, stddev=0.1) return tf.Variable(initial)def bias_variable(shape): initial = tf.constant(0.1, shape=shape) return tf.Variable(initial)# 創建卷積層、池化層，以便重復使用def conv2d(x, W): return tf.nn.conv2d(x, W, strides=[1, 1, 1, 1], padding='SAME')def max_pool(x): return tf.nn.max_pool(x, ksize=[1, 2, 2, 1], strides=[1, 2, 2, 1], padding='SAME')# 定義輸入的placeholderx = tf.placeholder(tf.float32, [None, 784])y_ = tf.placeholder(tf.float32, [None, 10])x_image = tf.reshape(x, [-1, 28, 28, 1])# 定義第一個卷積層W_conv1 = weight_variable([5, 5, 1, 32])b_conv1 = bias_variable([32])h_conv1 = tf.nn.relu(conv2d(x_image, W_conv1) + b_conv1)h_pool1 = max_pool(h_conv1)# 定義第二個卷積層W_conv2 = weight_variable([5, 5, 32, 64])b_conv2 = bias_variable([64])h_conv2 = tf.nn.relu(conv2d(h_pool1, W_conv2) + b_conv2)h_pool2 = max_pool(h_conv2)# 定義全連接層。由于第二個卷積層輸出的tensor是7*7*64，我們使用tf.reshape函數對其進行變形W_fc1 = weight_variable([7*7*64, 1024])b_fc1 = bias_variable([1024])h_pool2_flat = tf.reshape(h_pool2, [-1, 7*7*64])h_fc1 = tf.nn.relu(tf.matmul(h_pool2_flat, W_fc1) + b_fc1)# 為了減輕過擬合，下面使用一個Dropout層。通過一個placeholder傳入keep_prob比率來控制的。在訓練時，我們隨機丟棄一部分節點# 的數據來減輕過擬合，預測時則保留全部數據來追求最好的預測性能。keep_prob = tf.placeholder(dtype=tf.float32)h_fc1_drop = tf.nn.dropout(h_fc1, keep_prob)# 最后我們將Dropout層的輸出連接一個Softmax層，得到最后的概率輸出W_fc2 = weight_variable([1024, 10])b_fc2 = bias_variable([10])y_conv = tf.nn.softmax(tf.matmul(h_fc1_drop, W_fc2) + b_fc2)# 定義損失函數為cross entropy和優化器cross_entropy = tf.reduce_mean(-tf.reduce_sum(y_ * tf.log(y_conv), reduction_indices=[1]))train_step = tf.train.AdamOptimizer(1e-4).minimize(cross_entropy)# 定義評測準確率的操作correct_prediction = tf.equal(tf.argmax(y_conv, 1), tf.argmax(y_, 1))accuracy = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))# 下面開始訓練tf.global_variables_initializer().run()for i in range(20000): batch = mnist.train.next_batch(50) if i % 100 == 0:  train_accuracy = accuracy.eval(feed_dict={x: batch[0], y_: batch[1], keep_prob: 1.0})  print("Step %d, training accuracy %g" % (i, train_accuracy)) train_step.run(feed_dict={x: batch[0], y_: batch[1], keep_prob: 0.5})print("test accuracy %g" % accuracy.eval(feed_dict={x: mnist.test.images, y_: mnist.test.labels, keep_prob: 1.0}))# 載入MNIST數據集，并創建默認的Interactive Session。mnist = input_data.read_data_sets("MNIST_data/", one_hot=True)sess = tf.InteractiveSession()# 創建權重和偏置，以便重復使用。我們需要給權重制造一些隨機的噪聲來打破完全對稱，比如截斷的正態分布噪聲，標準差設為0.1def weight_variable(shape): initial = tf.truncated_normal(shape, stddev=0.1) return tf.Variable(initial)def bias_variable(shape): initial = tf.constant(0.1, shape=shape) return tf.Variable(initial)# 創建卷積層、池化層，以便重復使用def conv2d(x, W): return tf.nn.conv2d(x, W, strides=[1, 1, 1, 1], padding='SAME')def max_pool(x): return tf.nn.max_pool(x, ksize=[1, 2, 2, 1], strides=[1, 2, 2, 1], padding='SAME')# 定義輸入的placeholderx = tf.placeholder(tf.float32, [None, 784])y_ = tf.placeholder(tf.float32, [None, 10])x_image = tf.reshape(x, [-1, 28, 28, 1])# 定義第一個卷積層W_conv1 = weight_variable([5, 5, 1, 32])b_conv1 = bias_variable([32])h_conv1 = tf.nn.relu(conv2d(x_image, W_conv1) + b_conv1)h_pool1 = max_pool(h_conv1)# 定義第二個卷積層W_conv2 = weight_variable([5, 5, 32, 64])b_conv2 = bias_variable([64])h_conv2 = tf.nn.relu(conv2d(h_pool1, W_conv2) + b_conv2)h_pool2 = max_pool(h_conv2)# 定義全連接層。由于第二個卷積層輸出的tensor是7*7*64，我們使用tf.reshape函數對其進行變形W_fc1 = weight_variable([7*7*64, 1024])b_fc1 = bias_variable([1024])h_pool2_flat = tf.reshape(h_pool2, [-1, 7*7*64])h_fc1 = tf.nn.relu(tf.matmul(h_pool2_flat, W_fc1) + b_fc1)# 為了減輕過擬合，下面使用一個Dropout層。通過一個placeholder傳入keep_prob比率來控制的。在訓練時，我們隨機丟棄一部分節點# 的數據來減輕過擬合，預測時則保留全部數據來追求最好的預測性能。keep_prob = tf.placeholder(dtype=tf.float32)h_fc1_drop = tf.nn.dropout(h_fc1, keep_prob)# 最后我們將Dropout層的輸出連接一個Softmax層，得到最后的概率輸出W_fc2 = weight_variable([1024, 10])b_fc2 = bias_variable([10])y_conv = tf.nn.softmax(tf.matmul(h_fc1_drop, W_fc2) + b_fc2)# 定義損失函數為cross entropy和優化器cross_entropy = tf.reduce_mean(-tf.reduce_sum(y_ * tf.log(y_conv), reduction_indices=[1]))train_step = tf.train.AdamOptimizer(1e-4).minimize(cross_entropy)# 定義評測準確率的操作correct_prediction = tf.equal(tf.argmax(y_conv, 1), tf.argmax(y_, 1))accuracy = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))# 下面開始訓練tf.global_variables_initializer().run()for i in range(20000): batch = mnist.train.next_batch(50) if i % 100 == 0:  train_accuracy = accuracy.eval(feed_dict={x: batch[0], y_: batch[1], keep_prob: 1.0})  print("Step %d, training accuracy %g" % (i, train_accuracy)) train_step.run(feed_dict={x: batch[0], y_: batch[1], keep_prob: 0.5})print("test accuracy %g" % accuracy.eval(feed_dict={x: mnist.test.images, y_: mnist.test.labels, keep_prob: 1.0}))