在《数字识别-softmax 回归》和《数字识别-rnn 算法》两篇博文中分别介绍了使用 softmax 和 rnn 算法来对数字进行识别，并且 rnn 算法相对于 softmax 回归的基础得到了很大的提升，而在图片分类中，cnn 算法一直是主导，本篇博文将介绍使用 rnn 算法来进行数字识别。

import tensorflow as tf 
from tensorflow.examples.tutorials.mnist import input_data
mnist = input_data.read_data_sets('data/mnist', one_hot=True)


X = tf.placeholder(tf.float32, [None, 784])
y = tf.placeholder(tf.float32, [None, 10])


def weight_variable(shape):
    return tf.Variable(tf.truncated_normal(shape, stddev=0.1))

def bias_variable(shape):
    return tf.Variable(tf.constant(0.1, shape=shape))

def conv2d(X,W):
    return tf.nn.conv2d(X, W, strides=[1, 1, 1, 1], padding='SAME')

def max_pool_2x2(X):
    return tf.nn.max_pool(X, ksize=[1, 2, 2, 1], strides=[1, 2, 2, 1], padding='SAME’)

X_image = tf.reshape(X, [-1, 28, 28, 1])

# 第一个卷积层
# patch_size: 5*5 input channels: 1 output channels:32 
W_conv1 = weight_variable([5, 5, 1, 32])
b_conv1 = bias_variable([32])
# 第一个池化层
h_conv1 = tf.nn.relu(conv2d(X_image, W_conv1) + b_conv1)
h_pool1 = max_pool_2x2(h_conv1)

# 第二个卷积层
W_conv2 = weight_variable([5, 5, 32, 64])
b_conv2 = bias_variable([64])

# 第二个池化层
h_conv2 = tf.nn.relu(conv2d(h_pool1, W_conv2) + b_conv2)
h_pool2 = max_pool_2x2(h_conv2)

# 第一个全连接层
# image_size:7*7
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)

keep_prob = tf.placeholder(tf.float32)
h_fc1_drop = tf.nn.dropout(h_fc1, keep_prob)

# 第二个全连接层
W_fc2 = weight_variable([1024, 10])
b_fc2 = bias_variable([10])

y_conv = tf.matmul(h_fc1_drop, W_fc2) + b_fc2

# 计算损失函数
cross_entropy = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(labels=y, logits=y_conv))

#adam 算法优化
train_step = tf.train.AdamOptimizer(1e-4).minimize(cross_entropy)

# 正确预测数目
correct_prediction = tf.equal(tf.argmax(y, 1),tf.argmax(y_conv, 1))

#计算准确率
accuracy = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))

sess = tf.InteractiveSession()
sess.run(tf.global_variables_initializer())

for i in range(1001):
    xs, ys= mnist.train.next_batch(64)
    if i%100 == 0:
        train_accuracy = accuracy.eval(feed_dict={X: xs, y: ys, keep_prob: 1.0})
        print('step %d, training accuracy %g' % (i, train_accuracy))
    train_step.run(feed_dict={X: xs, y: ys, keep_prob: 0.5})

  正确率为98%左右。