梯度下降：代码

梯度下降：代码

之前我们看到一个权重的计算是：

Δw​i​​=ηδx​i​​

这里 error term δ 是指

δ=(y−​y​^​​)f​′​​(h)=(y−​y​^​​)f​′​​(∑w​i​​x​i​​)

记住，上面公式中 (y−​y​^​​) 是输出误差，f​′​​(h) 是激活函数 f(h) 的导函数，我们把这个导函数称做输出的梯度。

现在假设只有一个输出，我来把这个写成代码。我们还是用 sigmoid 来作为激活函数 f(h)。import numpy as np

def sigmoid(x):
"""
Calculate sigmoid
"""
return 1/(1+np.exp(-x))

def sigmoid_prime(x):
"""
# Derivative of the sigmoid function
"""
return sigmoid(x) * (1 - sigmoid(x))

learnrate = 0.5
x = np.array([1, 2, 3, 4])
y = np.array(0.5)

# Initial weights
w = np.array([0.5, -0.5, 0.3, 0.1])

### Calculate one gradient descent step for each weight
### Note: Some steps have been consilated, so there are
### fewer variable names than in the above sample code

# TODO: Calculate the node's linear combination of inputs and weights
h = np.dot(x, w)

# TODO: Calculate output of neural network
nn_output = sigmoid(h)

# TODO: Calculate error of neural network
error = y - nn_output

# TODO: Calculate the error term
# Remember, this requires the output gradient, which we haven't
# specifically added a variable for.
error_term = error * sigmoid_prime(h)

# TODO: Calculate change in weights
del_w = learnrate * error_term * x

print('Neural Network output:')
print(nn_output)
print('Amount of Error:')
print(error)
print('Change in Weights:')
print(del_w)