L1Loss() and MSELoss() in PyTorch

#pytorch #l1loss #mseloss #lossfunction

*Memos:

My post explains L1 Loss(MAE), L2 Loss(MSE), Huber Loss, BCE and Cross Entropy Loss.
My post explains HuberLoss().
My post explains BCELoss().
My post explains CrossEntropyLoss().

L1Loss() can get the 0D or more D tensor of the zero or more values(float) computed by L1Loss(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 L2Loss(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.)

DEV Community

L1Loss() and MSELoss() in PyTorch

Top comments (0)

Read next

Contract Substitution Principle (Design by Interface)

Provide storage for a public website

Ned's Declassified Git Survival Guide 📚

How Outliers Affect the Mean: An Analogy with Leadership in a Company