反向传播back propagation代码

再简单模型中，按照下图的神经网络来完成模型的训练

在复杂的模型当中，输入，权重，隐藏层的数量都是很多的，例如下图中，输入x有5个神经元，第一层隐藏层h中有6个神经元，则中间不同的权重矩阵w有30个

这时候需要反向传播利用链式法则，将其中的梯度求出来

假设在一个两层的神经网络中，做以下的运算

在全连接网络第一层中

重复操作构成第二层

我们需要在每一全连接层中添加一层非线性变化函数（激活函数）

我们来看一个关于最简单的线性模型的反向传播过程

下面我们进行代码的解析

这里采用了torch包，定义训练集和权重w，这里需要requires_grad保留来计算梯度

定义模型，把x转换成tensor类型与w进行乘法，得到相应的输出，也需要计算梯度

定义损失函数，每次运行loss函数都是在构造一个计算图

训练过程：

• 前馈计算loss

• 反馈过程，用backward（）自动的把计算图上所有需要梯度的地方都求出梯度，把梯度存到w中，之后计算图被释放，下一次进行forward后重新创建计算图

• 获取梯度

• 想要获取梯度的标量我们用

• 当我们想要计算总和时，不能直接加上损失值l，tensor在计算时会构造计算图，会造成计算图越来越大，可以加上标量

sum += l.item()

• 在计算完需要清零

我们来看一下整个计算图

前向传播：权重的处置是随机的

反向传播：计算权重的导数，更新权重

下面我们来看完整代码

import torch
import matplotlib.pyplot as plt

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
epoch_list = []
loss_list = []


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


def loss(x, y):
    y_pred = forward(x)
    return (y_pred - y) ** 2


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 - 0.01 * 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
    epoch_list.append(epoch)
    loss_list.append(l.item())
    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())


plt.plot(epoch_list, loss_list)
plt.ylabel('Loss')
plt.xlabel('Epoch')
plt.show()

运行结果：

predict(before training) 4 4.0
  grad: 1.0 2.0 -2.0
  grad: 2.0 4.0 -7.840000152587891
  grad: 3.0 6.0 -16.228801727294922
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progress: 98 9.094947017729282e-13
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progress: 99 9.094947017729282e-13
predict(after training) 4 7.999998569488525

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