本文是在Softmax Regression的基础上增加了一个隐含层，实现了Multilayer Perceptron的一个模型，Multilayer Perceptron是深度学习模型的基础，对于Softmax Regression的TensorFlow实现，可以参见博文“TensorFlow实践——Softmax Regression”。对于Multilayer Perceptron的基本原理，可以参见以下的文章：

• 深度学习算法原理——神经网络的基本原理
• 利用Theano理解深度学习——Multilayer Perceptron

下面的代码是利用TensorFlow的基本API实现的Softmax Regression：

'''
@author:zhaozhiyong
@date:20170821
Multilayer Perceptron
'''

import tensorflow as tf

from tensorflow.examples.tutorials.mnist import input_data

mnist = input_data.read_data_sets("./MNIST_data", one_hot=True)

learning_rate = 0.05
training_epochs = 1000
batch_size = 100
display_step = 50

n_input = 784
n_hidden = 256
n_classes = 10

x = tf.placeholder("float", [None, n_input])
y = tf.placeholder("float", [None, n_classes])

w1 = tf.Variable(tf.random_normal([n_input, n_hidden]))
b1 = tf.Variable(tf.random_normal([n_hidden]))

hidden = tf.add(tf.matmul(x, w1), b1)
hidden = tf.nn.relu(hidden)
#hidden = tf.nn.sigmoid(hidden)

w2 = tf.Variable(tf.random_normal([n_hidden, n_classes]))
b2 = tf.Variable(tf.random_normal([n_classes]))

pred = tf.add(tf.matmul(hidden, w2), b2)

cost = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(logits=pred, labels=y))
optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate).minimize(cost)

init = tf.global_variables_initializer()

with tf.Session() as sess:
	sess.run(init)
	for epoch in range(training_epochs):
		avg_cost = 0
		total_batch = int(mnist.train.num_examples/batch_size)
		for i in range(total_batch):
			batch_x, batch_y = mnist.train.next_batch(batch_size)
			_, c = sess.run([optimizer, cost], feed_dict={x: batch_x, y: batch_y})
			avg_cost += c / total_batch
		if epoch % display_step == 0:
			print "Epoch:", '%04d' % (epoch+1), "cost=", "{:.9f}".format(avg_cost)
	print "Optimization Finished!"

	print "Get test data:"    	
	correct_prediction = tf.equal(tf.argmax(pred, 1), tf.argmax(y, 1))
    	accuracy = tf.reduce_mean(tf.cast(correct_prediction, "float"))
    	print "Accuracy:", accuracy.eval({x: mnist.test.images, y: mnist.test.labels})

上述实现的运行结果如下所示：

参考文献

1. [03]tensorflow实现softmax回归（softmax regression）