loss = 0.5 / X2.shape[0] * (R ** 2).sum() G_loss = - 1.0 / X.shape[0] * X2.T @ R

这段代码看起来像是计算神经网络中的损失函数和梯度，其中X2是模型的预测结果，R是真实标签，loss计算的是均方误差(MSE)损失函数，G_loss计算的是MSE损失函数对模型参数的梯度。具体来说，loss计算的是预测值与真实值之间的差距，而G_loss计算的是这个差距对模型参数的影响，用于更新模型参数以使得模型更加准确地预测输出。

相关问题

对loss = 0.5 / X2.shape[0] * (R ** 2).sum() 求导

根据链式法则，我们需要先求出 $\frac{\partial L}{\partial R}$，然后再根据 $R$ 的定义求出 $\frac{\partial R}{\partial w}$，最后将两部分结果相乘即可得到 $\frac{\partial L}{\partial w}$。

首先，对 $\frac{1}{2} R^2$ 求导得到 $R$，即：

$$
\frac{\partial}{\partial R} \left(\frac{1}{2} R^2\right) = R
$$

因此，

$$
\frac{\partial L}{\partial R} = \frac{\partial}{\partial R} \left(\frac{0.5}{X_2.shape[0]} (R^2).sum() \right) = \frac{1}{X_2.shape[0]} R
$$

接下来，对 $R$ 的定义 $R = X_2W - X_1$ 求导，得到：

$$
\frac{\partial R}{\partial W} = X_2^T
$$

最后，将两部分结果相乘，得到：

$$
\frac{\partial L}{\partial W} = \frac{\partial L}{\partial R} \cdot \frac{\partial R}{\partial W} = \frac{1}{X_2.shape[0]} X_2^T R
$$

将 $R$ 的定义代入上式，得到：

$$
\frac{\partial L}{\partial W} = \frac{1}{X_2.shape[0]} X_2^T (X_2W - X_1)
$$

这就是最终的梯度公式。

#encoding=utf8 import torch import torch.nn as nn from torch.autograd import Variable import torch.utils.data as Data import torchvision import os if os.path.exists('/data/workspace/course/step3/cnn.pkl'): os.remove('/data/workspace/course/step3/cnn.pkl') #加载数据 train_data = torchvision.datasets.MNIST( root='/data/workspace/course/step3/mnist', train=True, # this is training data transform=torchvision.transforms.ToTensor(), # Converts a PIL.Image or numpy.ndarray to download=False, ) #取6000个样本为训练集 train_data_tiny = [] for i in range(6000): train_data_tiny.append(train_data[i]) train_data = train_data_tiny #********* Begin *********# #********* End *********# #保存模型 torch.save(cnn.state_dict(), '/data/workspace/course/step3/cnn.pkl') 帮我补全begin-end区域代码

# 定义卷积神经网络模型
class CNN(nn.Module):
def __init__(self):
super(CNN, self).__init__()
self.conv1 = nn.Sequential( # input shape (1, 28, 28)
nn.Conv2d(
in_channels=1, # input height
out_channels=16, # n_filters
kernel_size=5, # filter size
stride=1, # filter movement/step
padding=2,
), # output shape (16, 28, 28)
nn.ReLU(), # activation
nn.MaxPool2d(kernel_size=2), # choose max value in 2x2 area, output shape (16, 14, 14)
)
self.conv2 = nn.Sequential( # input shape (16, 14, 14)
nn.Conv2d(16, 32, 5, 1, 2), # output shape (32, 14, 14)
nn.ReLU(), # activation
nn.MaxPool2d(2), # output shape (32, 7, 7)
)
self.out = nn.Linear(32 * 7 * 7, 10) # fully connected layer, output 10 classes

def forward(self, x):
x = self.conv1(x)
x = self.conv2(x)
x = x.view(x.size(0), -1) # flatten the output of conv2 to (batch_size, 32 * 7 * 7)
output = self.out(x)
return output

# 实例化卷积神经网络模型
cnn = CNN()

# 定义损失函数和优化器
loss_func = nn.CrossEntropyLoss()
optimizer = torch.optim.Adam(cnn.parameters(), lr=0.001)

# 定义数据集和数据加载器
train_loader = Data.DataLoader(dataset=train_data, batch_size=64, shuffle=True)

# 训练模型
for epoch in range(1):
for step, (x, y) in enumerate(train_loader):
b_x = Variable(x) # batch x
b_y = Variable(y) # batch y
output = cnn(b_x)
loss = loss_func(output, b_y)
optimizer.zero_grad()
loss.backward()
optimizer.step()
if step % 100 == 0:
test_output = cnn(torch.unsqueeze(train_data_tiny[0][0], dim=0))
pred_y = torch.max(test_output, 1)[1].data.squeeze()
accuracy = sum(pred_y == train_data_tiny[0][1]) / float(train_data_tiny[0][1].size)
print('Epoch:', epoch, '| train loss: %.4f' % loss.data.numpy(), '| test accuracy: %.2f' % accuracy)

# 保存模型
torch.save(cnn.state_dict(), '/data/workspace/course/step3/cnn.pkl')