BCEWithLogitsLoss in PyTorch

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*Memos:

• My post explains BCE(Binary Cross Entropy) Loss. *My post explains BCELoss().
• My post explains Sigmoid. *My post explains Sigmoid().
• My post explains CrossEntropyLoss().

BCEWithLogitsLoss() can get the 0D or more D tensor of the zero or more values(float) computed by BCE Loss and Sigmoid from the 0D or more D tensor of zero or more elements as shown below:

*Memos:

• The 1st argument for initialization is weight(Optional-Default:None-Type:tensor of int, float or bool): *Memos:
  • If it's not given, it's 1.
  • It must be the 0D or more D tensor of zero or more elements.
• There is reduction argument for initialization(Optional-Default:'mean'-Type:str). *'none', 'mean' or 'sum' can be selected.
• There is pos_weight argument for initialization(Optional-Default:None-Type:tensor of int or float): *Memos:
  • If it's not given, it's 1.
  • It must be the 0D or more D tensor of zero or more elements.
• There are size_average and reduce argument for initialization but they are deprecated.
• The 1st argument is input(Required-Type:tensor of float). *It must be the 0D or more D tensor of zero or more elements.
• The 2nd argument is target(Required-Type:tensor of float). *It must be the 0D or more D tensor of zero or more elements.
• input and target must be the same size otherwise there is error.
• 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..
• BCEWithLogitsLoss() is the combination of Sigmoid and BCE Loss.

import torch
from torch import nn

tensor1 = torch.tensor([ 8., -3., 0.,  1.,  5., -2.])
tensor2 = torch.tensor([-3.,  7., 4., -2., -9.,  6.])
       # -w*(p*y*log(1/(1+exp(-x))+(1-y)*log(1-(1/1+exp(-x))))
       # -1*(1*(-3)*log(1/(1+exp(-8)))+(1-(-3))*log(1-(1/(1+exp(-8)))))
       # ↓↓↓↓↓↓↓
       # 32.0003 + 21.0486 + 0.6931 + 3.3133 + 50.0067 + 50.0067 = 82.8423
       # 119.1890 / 6 = 19.8648
bcelogits = nn.BCEWithLogitsLoss()
bcelogits(input=tensor1, target=tensor2)
# tensor(19.8648)

bcelogits
# BCEWithLogitsLoss()

print(bcelogits.weight)
# None

bcelogits.reduction
# 'mean'

bcelogits = nn.BCEWithLogitsLoss(weight=None,
                                 reduction='mean',
                                 pos_weight=None)
bcelogits(input=tensor1, target=tensor2)
# tensor(19.8648)

bcelogits = nn.BCEWithLogitsLoss(reduction='sum')
bcelogits(input=tensor1, target=tensor2)
# tensor(119.1890)

bcelogits = nn.BCEWithLogitsLoss(reduction='none')
bcelogits(input=tensor1, target=tensor2)
# tensor([32.0003, 21.0486, 0.6931, 3.3133, 50.0067, 12.1269])

bcelogits = nn.BCEWithLogitsLoss(weight=torch.tensor([0., 1., 2., 3., 4., 5.]))
bcelogits(input=tensor1, target=tensor2)
# tensor(48.8394)

bcelogits = nn.BCEWithLogitsLoss(
                pos_weight=torch.tensor([0., 1., 2., 3., 4., 5.])
            )
bcelogits(input=tensor1, target=tensor2)
# tensor(28.5957)

bcelogits = nn.BCEWithLogitsLoss(weight=torch.tensor(0.))
bcelogits(input=tensor1, target=tensor2)
# tensor(0.)

bcelogits = nn.BCEWithLogitsLoss(pos_weight=torch.tensor(0.))
bcelogits(input=tensor1, target=tensor2)
# tensor(13.8338)

bcelogits = nn.BCEWithLogitsLoss(weight=torch.tensor([0, 1, 2, 3, 4, 5]))
bcelogits(input=tensor1, target=tensor2)
# tensor(48.8394)

bcelogits = nn.BCEWithLogitsLoss(pos_weight=torch.tensor([0, 1, 2, 3, 4, 5]))
bcelogits(input=tensor1, target=tensor2)
# tensor(28.5957)

bcelogits = nn.BCEWithLogitsLoss(weight=torch.tensor(0))
bcelogits(input=tensor1, target=tensor2)
# tensor(0.)

bcelogits = nn.BCEWithLogitsLoss(pos_weight=torch.tensor(0))
bcelogits(input=tensor1, target=tensor2)
# tensor(13.8338)

bcelogits = nn.BCEWithLogitsLoss(
              weight=torch.tensor([True, False, True, False, True, False])
          )
bcelogits(input=tensor1, target=tensor2)
# tensor(13.7834)

bcelogits = nn.BCEWithLogitsLoss(weight=torch.tensor([False]))
bcelogits(input=tensor1, target=tensor2)
# tensor(0.)

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

bcelogits = nn.BCEWithLogitsLoss()
bcelogits(input=tensor1, target=tensor2)
# tensor(19.8648)

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

bcelogits = nn.BCEWithLogitsLoss()
bcelogits(input=tensor1, target=tensor2)
# tensor(19.8648)

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

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

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

BCEWithLogitsLoss() and BCELoss() with Sigmoid() or torch.sigmoid() for input argument can get the same results as shown below. *BCEWithLogitsLoss() can accept the values out of 0<=y<=1 for input and target argument while BCELoss() cannot:

import torch
from torch import nn

tensor1 = torch.tensor([0.4, 0.8, 0.6, 0.3, 0.0, 0.5])
tensor2 = torch.tensor([0.2, 0.9, 0.4, 0.1, 0.8, 0.5])

bcelogits = nn.BCEWithLogitsLoss()
bcelogits(input=tensor1, target=tensor2)
# tensor(0.7205)

sigmoid = nn.Sigmoid()

bceloss = nn.BCELoss()
bceloss(input=sigmoid(input=tensor1), target=tensor2)
# tensor(0.7205)

bceloss = nn.BCELoss()
bceloss(input=torch.sigmoid(input=tensor1), target=tensor2)
# tensor(0.7205)