L1Loss and MSELoss in PyTorch

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*Memos:

• My post explains L1 Loss(MAE), L2 Loss(MSE).
• My post explains HuberLoss().

L1Loss() can get the 0D or more D tensor of the zero or more values(float) computed by L1 Loss(MAE) from the 0D or more D tensor of zero or more elements as shown below:

*Memos:

• There is reduction argument for initialization(Optional-Default:'mean'-Type:str). *'none', 'mean' or 'sum' can be selected.
• There are size_average and reduce argument for initialization but they are deprecated.
• The 1st argument is input(Required-Type:tensor of float or complex).
• The 2nd argument is target(Required-Type:tensor of float or complex).
• input and target should be the same size otherwise there is a warning.
• Even complex type of input and target tensors return a float tensor.
• The empty 1D or more D input and target tensor with reduction='mean' return nan.
• The empty 1D or more D input and target tensor with reduction='sum' return 0..

import torch
from torch import nn

tensor1 = torch.tensor([ 8., -3., 0.,  1.,  5., -2., -1., 4.])
tensor2 = torch.tensor([-3.,  7., 4., -2., -9.,  6., -8., 5.])
                      # |x-y|
                      # |8.-(-3.)| = 11.
                      # ↓↓
                      # 11.+ 10.+ 4. + 3.+ 14. + 8. + 7.+ 1. = 58.
                      # 58. / 8 = 7.25
l1loss = nn.L1Loss()
l1loss(input=tensor1, target=tensor2)
# tensor(7.2500)

l1loss
# L1Loss()

l1loss.reduction
# 'mean'

l1loss = nn.L1Loss(reduction='mean')
l1loss(input=tensor1, target=tensor2)
# tensor(7.2500)

l1loss = nn.L1Loss(reduction='sum')
l1loss(input=tensor1, target=tensor2)
# tensor(58.)

l1loss = nn.L1Loss(reduction='none')
l1loss(input=tensor1, target=tensor2)
# tensor([11., 10., 4., 3., 14., 8., 7., 1.])

tensor1 = torch.tensor([[8., -3., 0., 1.], [5., -2., -1., 4.]])
tensor2 = torch.tensor([[-3., 7., 4., -2.], [-9., 6., -8., 5.]])

l1loss = nn.L1Loss()
l1loss(input=tensor1, target=tensor2)
# tensor(7.2500)

tensor1 = torch.tensor([[[8., -3.], [0., 1.]], [[5., -2.], [-1., 4.]]])
tensor2 = torch.tensor([[[-3., 7.], [4., -2.]], [[-9., 6.], [-8., 5.]]])

l1loss = nn.L1Loss()
l1loss(input=tensor1, target=tensor2)
# tensor(7.2500)

tensor1 = torch.tensor([[[8.+0.j, -3.+0.j], [0.+0.j, 1.+0.j]],
                        [[5.+0.j, -2.+0.j], [-1.+0.j, 4.+0.j]]])
tensor2 = torch.tensor([[[-3.+0.j, 7.+0.j], [4.+0.j, -2.+0.j]],
                        [[-9.+0.j, 6.+0.j], [-8.+0.j, 5.+0.j]]])
l1loss = nn.L1Loss()
l1loss(input=tensor1, target=tensor2)
# tensor(7.2500)

tensor1 = torch.tensor([])
tensor2 = torch.tensor([])

l1loss = nn.L1Loss(reduction='mean')
l1loss(input=tensor1, target=tensor2)
# tensor(nan)

l1loss = nn.L1Loss(reduction='sum')
l1loss(input=tensor1, target=tensor2)
# tensor(0.)

MSELoss() can get the 0D or more D tensor of the zero or more values(float) computed by L2 Loss(MSE) from the 0D or more D tensor of zero or more elements as shown below:

*Memos:

• There is reduction argument for initialization(Optional-Default:'mean'-Type:str). *'none', 'mean' or 'sum' can be selected.
• There are size_average and reduce argument for initialization but they are deprecated.
• The 1st argument is input(Required-Type:tensor of float).
• The 2nd argument is target(Required-Type:tensor of float).
• input and target should be the same size otherwise there is a warning.
• The empty 1D or more D input and target tensor with reduction='mean' return nan.
• The empty 1D or more D input and target tensor with reduction='sum' return 0..

import torch
from torch import nn

tensor1 = torch.tensor([ 8., -3., 0.,  1.,  5., -2., -1., 4.])
tensor2 = torch.tensor([-3.,  7., 4., -2., -9.,  6., -8., 5.])
                     # (x-y)^2
                     # (8.-(-3.))^2 = 121.
                     # ↓↓↓
                     # 121. 100. 16.   9. 196.  64.  49.  1. = 556.
                     # 556. / 8 = 69.5
mseloss = nn.MSELoss()
mseloss(input=tensor1, target=tensor2)
# tensor(69.5000)

mseloss
# MSELoss()

mseloss.reduction
# 'mean'

mseloss = nn.MSELoss(reduction='mean')
mseloss(input=tensor1, target=tensor2)
# tensor(69.5000)

mseloss = nn.MSELoss(reduction='sum')
mseloss(input=tensor1, target=tensor2)
# tensor(556.)

mseloss = nn.MSELoss(reduction='none')
mseloss(input=tensor1, target=tensor2)
# tensor([121., 100., 16., 9., 196., 64., 49., 1.])

tensor1 = torch.tensor([[8., -3., 0., 1.], [5., -2., -1., 4.]])
tensor2 = torch.tensor([[-3., 7., 4., -2.], [-9., 6., -8., 5.]])

mseloss = nn.MSELoss()
mseloss(input=tensor1, target=tensor2)
# tensor(69.5000)

tensor1 = torch.tensor([[[8., -3.], [0., 1.]], [[5., -2.], [-1., 4.]]])
tensor2 = torch.tensor([[[-3., 7.], [4., -2.]], [[-9., 6.], [-8., 5.]]])

mseloss = nn.MSELoss()
mseloss(input=tensor1, target=tensor2)
# tensor(69.5000)

tensor1 = torch.tensor([])
tensor2 = torch.tensor([])

mseloss = nn.MSELoss(reduction='mean')
mseloss(input=tensor1, target=tensor2)
# tensor(nan)

mseloss = nn.MSELoss(reduction='sum')
mseloss(input=tensor1, target=tensor2)
# tensor(0.)