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import numpy as npimport mathimport matplotlib.pyplot as plt# Create random input and output datax = np.linspace(-math.pi, math.pi, 2000)y = np.sin(x)plt.scatter(x,y)plt.show()# Randomly initialize weightsa = np.random.randn()b = np.random.randn()c = np.random.randn()d = np.random.randn()learning_rate = 1e-6for 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_dprint(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

 

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