MSE是mean squared error的縮寫，即平均平方誤差，簡稱均方誤差。
MSE是逐元素計算的，計算公式為：
舊版的nn.MSELoss()函數有reduce、size_average兩個參數，新版的只有一個reduction參數了，功能是一樣的。reduction的意思是維度要不要縮減，以及怎么縮減，有三個選項：
- '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.
如果不設置reduction參數，默認是'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) # 輸出結果：tensor([[ 4., 9.],
# [25., 4.]])
loss_fn2 = torch.nn.MSELoss(reduction='sum')
loss2 = loss_fn2(a.float(), b.float())
print(loss2) # 輸出結果：tensor(42.)
loss_fn3 = torch.nn.MSELoss(reduction='mean')
loss3 = loss_fn3(a.float(), b.float())
print(loss3) # 輸出結果：tensor(10.5000)
對於三維的輸入也是一樣的：
a = torch.randint(0, 9, (2, 2, 3)).float()
b = torch.randint(0, 9, (2, 2, 3)).float()
print('a:\n', a)
print('b:\n', b)
loss_fn1 = torch.nn.MSELoss(reduction='none')
loss1 = loss_fn1(a.float(), b.float())
print('loss_none:\n', loss1)
loss_fn2 = torch.nn.MSELoss(reduction='sum')
loss2 = loss_fn2(a.float(), b.float())
print('loss_sum:\n', loss2)
loss_fn3 = torch.nn.MSELoss(reduction='mean')
loss3 = loss_fn3(a.float(), b.float())
print('loss_mean:\n', loss3)
運行結果：
參考資料：