首先不妨假设最简单的一种情况：

假设$G$和$D$的损失函数：

那么计算梯度有：

 

 

 

第一种正确的方式：

import torch
from torch import nn


def set_requires_grad(net: nn.Module, mode=True):
    for p in net.parameters():
        p.requires_grad_(mode)


print(f"Pytorch version: {torch.__version__} \n")

X = torch.ones(size=[1, 1, 1, 1]).requires_grad_(False)

G = nn.Conv2d(1, 1, kernel_size=1, stride=1, padding=0, bias=False)
G.weight.data.fill_(0.5)
G_optim = torch.optim.SGD(G.parameters(), lr=1.0)

D = nn.Conv2d(1, 1, kernel_size=1, stride=1, padding=0, bias=False)
D.weight.data.fill_(0.7)
D_optim = torch.optim.SGD(D.parameters(), lr=1.0)print(f"Init grad: {G.weight.grad} {D.weight.grad}")
print(f"Init weight: {G.weight.detach()} {D.weight.detach()} \n")

# Zero gradient of 2 layers.
G_optim.zero_grad()
D_optim.zero_grad()

# Forward pass.
Y = G(X)

# Calculate D loss.
D_loss = D(Y.detach()) ** 2

# Calculate G loss.
G_loss = D(Y) ** 2

# Backward D loss.
D_loss.backward(retain_graph=True)

print(f"Checkpoint 1 grad: {G.weight.grad} {D.weight.grad}")
print(f"Checkpoint 1 weight: {G.weight.detach()} {D.weight.detach()} \n")

# Backward G loss.
set_requires_grad(D, False)  # Turn off D's grad to avoid redundant gradient accumulation on D.
G_loss.backward()
set_requires_grad(D, True)

print(f"Checkpoint 2 grad: {G.weight.grad} {D.weight.grad}")
print(f"Checkpoint 2 weight: {G.weight.detach()} {D.weight.detach()} \n")

# Update G.
G_optim.step()

print(f"Checkpoint 3 grad: {G.weight.grad} {D.weight.grad}")
print(f"Checkpoint 3 weight: {G.weight.detach()} {D.weight.detach()} \n")

# Update D.
D_optim.step()

print(f"Checkpoint 4 grad: {G.weight.grad} {D.weight.grad}")
print(f"Checkpoint 4 weight: {G.weight.detach()} {D.weight.detach()} \n")

 

运行结果：

Pytorch version: 1.9.0 

Init grad: None None
Init weight: tensor([[[[0.5000]]]]) tensor([[[[0.7000]]]]) 

Checkpoint 1 grad: None tensor([[[[0.3500]]]])
Checkpoint 1 weight: tensor([[[[0.5000]]]]) tensor([[[[0.7000]]]]) 

Checkpoint 2 grad: tensor([[[[0.4900]]]]) tensor([[[[0.3500]]]])
Checkpoint 2 weight: tensor([[[[0.5000]]]]) tensor([[[[0.7000]]]]) 

Checkpoint 3 grad: tensor([[[[0.4900]]]]) tensor([[[[0.3500]]]])
Checkpoint 3 weight: tensor([[[[0.0100]]]]) tensor([[[[0.7000]]]]) 

Checkpoint 4 grad: tensor([[[[0.4900]]]]) tensor([[[[0.3500]]]])
Checkpoint 4 weight: tensor([[[[0.0100]]]]) tensor([[[[0.3500]]]]) 

 

分析：

此时，$x = 1.0, y = 0.5, z = 0.7, \theta_G = 0.5, \theta_D = 0.7$，

首先checkpoint 1处，D loss的梯度反传到D网络上得到了 $2 y^2 \cdot \theta_D = 2 \times 0.25 \times 0.7 = 0.35$，没有反传到G网络。

其次checkpoint 2处，G loss的梯度反传，D网络梯度不受影响（因为所有网络参数的requires_grad := False），在G网络上得到了 $2 \times 0.5 \times 0.7^2 \times 1.0 = 0.49$。注意，这里的D网络参数 $\theta_D = 0.7$，因为尽管此时D loss已经反传，但是没有D optimizer的step()就还没有更新D网络。

最后checkpoint 3和4处，就是两个optimizer的step()分别更新G网络和D网络，这两个step()之间的先后顺序对最终的网络更新结果没什么影响。

 

注意，这种做法更新G网络时，对应的是更新前的D网络。

 

在Pytorch 1.2上的结果：

Pytorch version: 1.2.0 

Init grad: None None
Init weight: tensor([[[[0.5000]]]]) tensor([[[[0.7000]]]]) 

Checkpoint 1 grad: None tensor([[[[0.3500]]]])
Checkpoint 1 weight: tensor([[[[0.5000]]]]) tensor([[[[0.7000]]]]) 

Checkpoint 2 grad: tensor([[[[0.4900]]]]) tensor([[[[0.3500]]]])
Checkpoint 2 weight: tensor([[[[0.5000]]]]) tensor([[[[0.7000]]]]) 

Checkpoint 3 grad: tensor([[[[0.4900]]]]) tensor([[[[0.3500]]]])
Checkpoint 3 weight: tensor([[[[0.0100]]]]) tensor([[[[0.7000]]]]) 

Checkpoint 4 grad: tensor([[[[0.4900]]]]) tensor([[[[0.3500]]]])
Checkpoint 4 weight: tensor([[[[0.0100]]]]) tensor([[[[0.3500]]]]) 

可以看到，也是一样的。

 

错误的做法：

在 G_loss.backward() 前后不进行对D网络的网络参数的requires_grad的关和开，使得G loss反传了多余的梯度到D网络上。

 

---

 

第二种正确的方式：

import torch
from torch import nn


print(f"Pytorch version: {torch.__version__} \n")

X = torch.ones(size=[1, 1, 1, 1]).requires_grad_(False)

G = nn.Conv2d(1, 1, kernel_size=1, stride=1, padding=0, bias=False)
G.weight.data.fill_(0.5)
G_optim = torch.optim.SGD(G.parameters(), lr=1.0)

D = nn.Conv2d(1, 1, kernel_size=1, stride=1, padding=0, bias=False)
D.weight.data.fill_(0.7)
D_optim = torch.optim.SGD(D.parameters(), lr=1.0)

print(f"Init grad: {G.weight.grad} {D.weight.grad}")
print(f"Init weight: {G.weight.detach()} {D.weight.detach()} \n")

# Forward pass.
Y = G(X)

# Zero gradient of D.
D_optim.zero_grad()

# Calculate D loss.
D_loss = D(Y.detach()) ** 2

# Backward D loss.
D_loss.backward()

# Update D.
D_optim.step()

print(f"Checkpoint 1 grad: {G.weight.grad} {D.weight.grad}")
print(f"Checkpoint 1 weight: {G.weight.detach()} {D.weight.detach()} \n")

# Zero gradient of G.
G_optim.zero_grad()

# Calculate G loss.
G_loss = D(Y) ** 2

# Backward G loss.
G_loss.backward()

# Update G.
G_optim.step()

print(f"Checkpoint 2 grad: {G.weight.grad} {D.weight.grad}")
print(f"Checkpoint 2 weight: {G.weight.detach()} {D.weight.detach()} \n")

 

分析：

这种方式就很明了，更新D网络和更新G网络完全分开。

此时，$x = 1.0, y = 0.5, z = 0.7, \theta_G = 0.5, \theta_D = 0.7$，

首先checkpoint 1处，D loss的梯度反传到D网络上得到了 $2 y^2 \cdot \theta_D = 2 \times 0.25 \times 0.7 = 0.35$，没有反传到G网络。

其次checkpoint 2处，G loss的梯度同时反传到了G网络和D网络上，但是由于只更新G网络，D网络上的梯度会在下一个iteration中被zero_grad()清零。G网络上的梯度是 $2 \times 0.5 \times 0.35^2 \times 1.0 = 0.1225$，注意此时的D网络参数已经从 $0.7$ 更新为 $0.7 - 1.0 \times 0.35 = 0.35$（梯度下降：原参数减去学习率乘梯度，得新参数）。

 

注意，这种做法更新G网络时，对应的是已经更新后的D网络。事实上，我认为这种做法更正确，同时在逻辑上也更加清晰、更好理解。

 

运行结果：

Pytorch version: 1.9.0 

Init grad: None None
Init weight: tensor([[[[0.5000]]]]) tensor([[[[0.7000]]]]) 

Checkpoint 1 grad: None tensor([[[[0.3500]]]])
Checkpoint 1 weight: tensor([[[[0.5000]]]]) tensor([[[[0.3500]]]]) 

Checkpoint 2 grad: tensor([[[[0.1225]]]]) tensor([[[[0.5250]]]])
Checkpoint 2 weight: tensor([[[[0.3775]]]]) tensor([[[[0.3500]]]]) 

Pytorch version: 1.2.0 

Init grad: None None
Init weight: tensor([[[[0.5000]]]]) tensor([[[[0.7000]]]]) 

Checkpoint 1 grad: None tensor([[[[0.3500]]]])
Checkpoint 1 weight: tensor([[[[0.5000]]]]) tensor([[[[0.3500]]]]) 

Checkpoint 2 grad: tensor([[[[0.1225]]]]) tensor([[[[0.5250]]]])
Checkpoint 2 weight: tensor([[[[0.3775]]]]) tensor([[[[0.3500]]]]) 

 

---

 

 

一种错误的方式：

import torch
from torch import nn


print(f"Pytorch version: {torch.__version__} \n")

X = torch.ones(size=[1, 1, 1, 1]).requires_grad_(False)

G = nn.Conv2d(1, 1, kernel_size=1, stride=1, padding=0, bias=False)
G.weight.data.fill_(0.5)
G_optim = torch.optim.SGD(G.parameters(), lr=1.0)

D = nn.Conv2d(1, 1, kernel_size=1, stride=1, padding=0, bias=False)
D.weight.data.fill_(0.7)
D_optim = torch.optim.SGD(D.parameters(), lr=1.0)

print(f"Init grad: {G.weight.grad} {D.weight.grad}")
print(f"Init weight: {G.weight.detach()} {D.weight.detach()} \n")

# Forward pass.
Y = G(X)

# Zero gradient of G & D.
G_optim.zero_grad()
D_optim.zero_grad()

# Calculate D loss.
D_loss = D(Y.detach()) ** 2

# Calculate G loss.
G_loss = D(Y) ** 2

# Backward D loss.
D_loss.backward()

# Update D.
D_optim.step()

print(f"Checkpoint 1 grad: {G.weight.grad} {D.weight.grad}")
print(f"Checkpoint 1 weight: {G.weight.detach()} {D.weight.detach()} \n")

# Backward G loss.
G_loss.backward()

# Update G.
G_optim.step()

print(f"Checkpoint 2 grad: {G.weight.grad} {D.weight.grad}")
print(f"Checkpoint 2 weight: {G.weight.detach()} {D.weight.detach()} \n")

 

运行结果：

Pytorch version: 1.2.0 

Init grad: None None
Init weight: tensor([[[[0.5000]]]]) tensor([[[[0.7000]]]]) 

Checkpoint 1 grad: None tensor([[[[0.3500]]]])
Checkpoint 1 weight: tensor([[[[0.5000]]]]) tensor([[[[0.3500]]]]) 

Checkpoint 2 grad: tensor([[[[0.2450]]]]) tensor([[[[0.7000]]]])
Checkpoint 2 weight: tensor([[[[0.2550]]]]) tensor([[[[0.3500]]]]) 

Pytorch version: 1.9.0 

Init grad: None None
Init weight: tensor([[[[0.5000]]]]) tensor([[[[0.7000]]]]) 

Checkpoint 1 grad: None tensor([[[[0.3500]]]])
Checkpoint 1 weight: tensor([[[[0.5000]]]]) tensor([[[[0.3500]]]]) 

Traceback (most recent call last):
  File "D:/Program/PycharmProjects/Test/test.py", line 65, in <module>
    G_loss.backward()
  File "D:\Program\Anaconda\envs\py38_torch19\lib\site-packages\torch\_tensor.py", line 255, in backward
    torch.autograd.backward(self, gradient, retain_graph, create_graph, inputs=inputs)
  File "D:\Program\Anaconda\envs\py38_torch19\lib\site-packages\torch\autograd\__init__.py", line 147, in backward
    Variable._execution_engine.run_backward(
RuntimeError: one of the variables needed for gradient computation has been modified by an inplace operation: [torch.FloatTensor [1, 1, 1, 1]] is at version 2; expected version 1 instead. Hint: enable anomaly detection to find the operation that failed to compute its gradient, with torch.autograd.set_detect_anomaly(True).

 

分析：

这种做法的错误核心就在于，你在计算G loss时（前向传播时）使用的是更新前的D网络，但是你在G loss反向传播时D网络已经变成了更新后的，

这个错误在较低版本（1.2.0）的Pytorch上并没有报错，我们可以看到它在计算G网络的梯度时，似乎用了更新前后的 $\theta_D$ 相乘 $2 \times 0.5 \times (0.7 \times 0.35) \times 1.0 = 0.245$，而非单纯更新前的 ${\theta_D}^2 = 0.7^2$，或者单纯更新后的 ${\theta_D}^2 = 0.35^2$.

至于在较高版本（1.9.0）的Pytorch上则直接报错了，估计是因为step()更新了D网络之后，G loss对应的计算图被破坏了，因此直接报了一个 "inplace operation" 错误。

 

因此，使用低版本的Pytorch时千万一定要注意这种比较隐蔽的错误写法！！！！