So I was going through the documentation of the cross entropy loss and I noticed that while taking the probabilities they have performed softmax , but softmax is internally performed again in cross entropy loss so confused why its is mentioned again in the Example of target with class probabilities

```
>>> # Example of target with class indices
>>> loss = nn.CrossEntropyLoss()
>>> input = torch.randn(3, 5, requires_grad=True)
>>> target = torch.empty(3, dtype=torch.long).random_(5)
>>> output = loss(input, target)
>>> output.backward()
>>>
>>> # Example of target with class probabilities
>>> input = torch.randn(3, 5, requires_grad=True)
>>> target = torch.randn(3, 5).softmax(dim=1)
>>> output = loss(input, target)
>>> output.backward()
```

Moreover in this following example shouldnt the loss be the same in the first two cases

```
import torch.nn as nn
import torch
from torch.nn import Softmax as softmax
target_tensor = torch.tensor([1, 1, 0, 1])
target_tensor_prob = torch.tensor([[1.0, 0.0],
[1.0, 0.0],
[0.0, 1.0],
[1.0, 0.0]])
input_tensor = torch.randn(4, 2)
loss = nn.CrossEntropyLoss(reduction='mean')
with torch.no_grad():
output = loss(input_tensor, target_tensor )
print(output)
output2 = loss(input_tensor, target_tensor_prob)
print(output2)
output3 = loss(input_tensor, target_tensor_prob.softmax(dim=1))
print(output3)
```

It gives the following ouput

tensor(0.7072)

tensor(0.9613)

tensor(0.8930)

According to my understanding the first 2 should be the same.