反向传播&梯度下降 的直观理解程序(numpy)

import numpy as np
import math
import matplotlib.pyplot as plt

# Create random input and output data
x = np.linspace(-math.pi, math.pi, 2000)
y = np.sin(x)
plt.scatter(x,y)
plt.show()

# Randomly initialize weights
a = np.random.randn()
b = np.random.randn()
c = np.random.randn()
d = np.random.randn()
learning_rate = 1e-6

for t in range(4000):
    # Forward pass: compute predicted y
    # y = a + b x + c x^2 + d x^3
    y_pred = a + b * x + c * x**2 + d * x**3

    # Compute and print loss
    loss = np.square(y_pred - y).sum()

    if t % 100 == 99:
        print(t, loss)

    # Backprop to compute gradients of a, b, c, d with respect to loss
    grad_y_pred = 2.0 * (y_pred - y)
    grad_a = grad_y_pred.sum()
    grad_b = (grad_y_pred * x).sum()
    grad_c = (grad_y_pred * x**2).sum()
    grad_d = (grad_y_pred * x**3).sum()

    # Update weights
    a -= learning_rate * grad_a
    b -= learning_rate * grad_b
    c -= learning_rate * grad_c
    d -= learning_rate * grad_d

print(f'Result: y = {a} + {b} x + {c} x^2 + {d} x^3')
           

首先记住，权重w更新是 减去 损失函数L 对权重w的求导，即αL/αw

这里a,b,c,d都是权重