MSE是mean squared error的缩写，即平均平方误差，简称均方误差。
MSE是逐元素计算的，计算公式为：
旧版的nn.MSELoss()函数有reduce、size_average两个参数，新版的只有一个reduction参数了，功能是一样的。reduction的意思是维度要不要缩减，以及怎么缩减，有三个选项：
- 'none': no reduction will be applied.
- 'mean': the sum of the output will be divided by the number of elements in the output.
- 'sum': the output will be summed.
如果不设置reduction参数，默认是'mean'。
程序示例：
import torch
import torch.nn as nn
a = torch.tensor([[1, 2], [3, 4]], dtype=torch.float)
b = torch.tensor([[3, 5], [8, 6]], dtype=torch.float)
loss_fn1 = torch.nn.MSELoss(reduction='none')
loss1 = loss_fn1(a.float(), b.float())
print(loss1) # 输出结果：tensor([[ 4., 9.],
# [25., 4.]])
loss_fn2 = torch.nn.MSELoss(reduction='sum')
loss2 = loss_fn2(a.float(), b.float())
print(loss2) # 输出结果：tensor(42.)
loss_fn3 = torch.nn.MSELoss(reduction='mean')
loss3 = loss_fn3(a.float(), b.float())
print(loss3) # 输出结果：tensor(10.5000)
对于三维的输入也是一样的：
a = torch.randint(0, 9, (2, 2, 3)).float()
b = torch.randint(0, 9, (2, 2, 3)).float()
print('a:
', a)
print('b:
', b)
loss_fn1 = torch.nn.MSELoss(reduction='none')
loss1 = loss_fn1(a.float(), b.float())
print('loss_none:
', loss1)
loss_fn2 = torch.nn.MSELoss(reduction='sum')
loss2 = loss_fn2(a.float(), b.float())
print('loss_sum:
', loss2)
loss_fn3 = torch.nn.MSELoss(reduction='mean')
loss3 = loss_fn3(a.float(), b.float())
print('loss_mean:
', loss3)
运行结果：
参考资料：