通常神经层都包括输入层、隐藏层和输出层。大致结构是这样的：

神经层

在 Tensorflow 里定义一个添加层的函数可以很容易的添加神经层,为之后的添加省下不少时间.

神经层里常见的参数通常有weights、biases和激励函数。

当activation_function——激励函数为None时，输出就是当前的预测值——Wx_plus_b，不为None时，就把Wx_plus_b传到activation_function()函数中得到输出。

def add_layer(inputs, in_size, out_size, activation_function=None):
    Weights = tf.Variable(tf.random_normal([in_size, out_size]))
    biases = tf.Variable(tf.zeros([1, out_size]) + 0.1)
    Wx_plus_b = tf.matmul(inputs, Weights) + biases
    if activation_function is None:
        outputs = Wx_plus_b
    else:
        outputs = activation_function(Wx_plus_b)
    return outputs

完整代码

import numpy as np
import tensorflow.compat.v1 as tf
tf.disable_v2_behavior()

# 隐藏层核心代码
def add_layer(inputs, in_size, out_size, activation_function=None):
    Weights = tf.Variable(tf.random_normal([in_size, out_size]))
    biases = tf.Variable(tf.zeros([1, out_size]) + 0.1)
    Wx_plus_b = tf.matmul(inputs, Weights) + biases
    if activation_function is None:
        outputs = Wx_plus_b
    else:
        outputs = activation_function(Wx_plus_b)
    return outputs

# 一元二次函数，加上噪声，模拟真实的数据
x_data = np.linspace(-1,1,300, dtype=np.float32)[:, np.newaxis]
noise = np.random.normal(0, 0.05, x_data.shape).astype(np.float32)
y_data = np.square(x_data) - 0.5 + noise

# 输入层
xs = tf.placeholder(tf.float32, [None, 1])
ys = tf.placeholder(tf.float32, [None, 1])

# 隐藏层
l1 = add_layer(xs, 1, 10, activation_function=tf.nn.relu)

# 输出层
prediction = add_layer(l1, 10, 1, activation_function=None)

# 计算误差
loss = tf.reduce_mean(tf.reduce_sum(tf.square(ys - prediction),
                     reduction_indices=[1]))

# 训练，减小误差
train_step = tf.train.GradientDescentOptimizer(0.1).minimize(loss)

# init = tf.initialize_all_variables() # tf 马上就要废弃这种写法
init = tf.global_variables_initializer()  # 替换成这样就好

sess = tf.Session()
sess.run(init)

for i in range(1000):
    # training
    sess.run(train_step, feed_dict={xs: x_data, ys: y_data})
    if i % 50 == 0:
        # to see the step improvement
        print(sess.run(loss, feed_dict={xs: x_data, ys: y_data}))

运行结果：

0.3283323
0.0139856115
0.010608546
0.008023611
0.006943002
0.006471345
0.00616818
0.0059153
0.005697193
0.005496873
0.005304386
0.0051179132
0.004955535
0.004783967
0.004625158
0.0044726464
0.0043255114
0.004189127
0.0040659993
0.00395698

可以看出，误差在逐渐减小，这说明机器学习是有积极的效果的。

可视化

构建图形，用散点图描述真实数据之间的关系。

# plot the real data
fig = plt.figure()
ax = fig.add_subplot(1,1,1)
ax.scatter(x_data, y_data)
plt.ion()#本次运行请注释，全局运行不要注释
plt.show()

接下来，我们来显示预测数据。

每隔50次训练刷新一次图形，用红色、宽度为5的线来显示我们的预测数据和输入之间的关系，并暂停0.1s。

import numpy as np
import matplotlib.pyplot as plt
import tensorflow.compat.v1 as tf
tf.disable_v2_behavior()

def add_layer(inputs, in_size, out_size, activation_function=None):
    Weights = tf.Variable(tf.random_normal([in_size, out_size]))
    biases = tf.Variable(tf.zeros([1, out_size]) + 0.1)
    Wx_plus_b = tf.matmul(inputs, Weights) + biases
    if activation_function is None:
        outputs = Wx_plus_b
    else:
        outputs = activation_function(Wx_plus_b)
    return outputs

# 一元二次函数，加上噪声，模拟真实的数据
x_data = np.linspace(-1,1,300, dtype=np.float32)[:, np.newaxis]
noise = np.random.normal(0, 0.05, x_data.shape).astype(np.float32)
y_data = np.square(x_data) - 0.5 + noise

# 输入层
xs = tf.placeholder(tf.float32, [None, 1])
ys = tf.placeholder(tf.float32, [None, 1])

# 隐藏层
l1 = add_layer(xs, 1, 10, activation_function=tf.nn.relu)

# 输出层
prediction = add_layer(l1, 10, 1, activation_function=None)

# 计算误差
loss = tf.reduce_mean(tf.reduce_sum(tf.square(ys - prediction),
                     reduction_indices=[1]))

# 训练，减小误差
train_step = tf.train.GradientDescentOptimizer(0.1).minimize(loss)

# init = tf.initialize_all_variables() # tf 马上就要废弃这种写法
init = tf.global_variables_initializer()  # 替换成这样就好

sess = tf.Session()
sess.run(init)

# plot the real data
fig = plt.figure()
ax = fig.add_subplot(1,1,1)
ax.scatter(x_data, y_data)
plt.ion()#本次运行请注释，全局运行不要注释
plt.show()

for i in range(1000):
    # training
    sess.run(train_step, feed_dict={xs: x_data, ys: y_data})
    if i % 50 == 0:
        # to visualize the result and improvement
        try:
            ax.lines.remove(lines[0])
        except Exception:
            pass
        prediction_value = sess.run(prediction, feed_dict={xs: x_data})
        # plot the prediction
        lines = ax.plot(x_data, prediction_value, 'r-', lw=5)
        plt.pause(0.1)

效果：