手动推导线性模型y=w*x,损失函数loss=(ŷ-y)²下,当数据集x=2,y=4的时候,反向传播的过程.

手动推导线性模型 y=w*x+b,损失函数loss=(ŷ-y)²下,当数据集x=1,y=2的时候,反向传播的过程.

线性模型y=w*x,损失函数loss=(ŷ-y)²下,当数据集x=2,y=4的时候,反向传播代码实现

注意：w.grad.data不会自动清0,Manual cleaning required0

代码如下：

import torch

x_data = [1.0, 2.0, 3.0]
y_data = [2.0, 4.0, 6.0]

w = torch.Tensor([1.0])  # w的初值为1.0
w.requires_grad = True  # 需要计算梯度

learning_rate=0.05      #学习率

def forward(x):
    return x * w  # w是一个Tensor


def loss(x, y):
    y_pred = forward(x)
    return (y_pred - y) *(y_pred - y)


print("predict (before training)", 4, forward(4).item())

for epoch in range(100):
    for x, y in zip(x_data, y_data):
        l = loss(x, y)  # l是一个张量,tensor主要是在建立计算图 forward, compute the loss
        l.backward()  # backward,compute grad for Tensor whose requires_grad set to True
        print('\tgrad:', x, y, w.grad.item())
        w.data = w.data - learning_rate * w.grad.data  # 权重更新时,注意grad也是一个tensor

        w.grad.data.zero_()  # after update, remember set the grad to zero

    print('progress:', epoch, l.item())  # 取出loss使用l.item,不要直接使用l（l是tensor会构建计算图）

print("predict (after training)", 4, forward(4).item())

运行结果：

predict (before training) 4 4.0
	grad: 1.0 2.0 -2.0
	grad: 2.0 4.0 -7.520000457763672
	grad: 3.0 6.0 -12.859201431274414
progress: 0 4.593307018280029
	grad: 1.0 2.0 -0.6572480201721191
	grad: 2.0 4.0 -2.47125244140625
	grad: 3.0 6.0 -4.225842475891113
progress: 1 0.4960484504699707
	grad: 1.0 2.0 -0.2159874439239502
	grad: 2.0 4.0 -0.8121128082275391
	grad: 3.0 6.0 -1.388711929321289
progress: 2 0.05357002466917038
	grad: 1.0 2.0 -0.07097864151000977
	grad: 2.0 4.0 -0.2668800354003906
	grad: 3.0 6.0 -0.45636463165283203
....................
progress: 13 9.094947017729282e-13
	grad: 1.0 2.0 -4.76837158203125e-07
	grad: 2.0 4.0 -1.9073486328125e-06
	grad: 3.0 6.0 -5.7220458984375e-06
progress: 14 9.094947017729282e-13
	grad: 1.0 2.0 -2.384185791015625e-07
	grad: 2.0 4.0 -9.5367431640625e-07
	grad: 3.0 6.0 -2.86102294921875e-06
progress: 15 2.2737367544323206e-13
	grad: 1.0 2.0 0.0
	grad: 2.0 4.0 0.0
	grad: 3.0 6.0 0.0
progress: 16 0.0
	grad: 1.0 2.0 0.0
	grad: 2.0 4.0 0.0
	grad: 3.0 6.0 0.0
.....................
progress: 97 0.0
	grad: 1.0 2.0 0.0
	grad: 2.0 4.0 0.0
	grad: 3.0 6.0 0.0
progress: 98 0.0
	grad: 1.0 2.0 0.0
	grad: 2.0 4.0 0.0
	grad: 3.0 6.0 0.0
progress: 99 0.0
predict (after training) 4 8.0