Cross entropy loss, also known as negative log likelihood loss, measures the dissimilarity between the predicted probability distribution and the true distribution. It is commonly used in classification problems and is implemented in PyTorch using the torch.nn.CrossEntropyLoss() function.

In a classification problem, the goal is to predict the class of a given input. The predicted class is represented by a probability distribution, also known as a softmax function, over all possible classes. The true class is represented by a one-hot vector, where the element corresponding to the true class is 1 and all other elements are 0.

The cross entropy loss is calculated as the negative sum of the true class element multiplied by the corresponding predicted class element in the softmax probability distribution. The negative sign is added to ensure that the loss is a minimization problem.

Here is an example of how to implement cross entropy loss in PyTorch:

```
import torch
import torch.nn as nn
# Define a simple neural network
class Net(nn.Module):
def __init__(self):
super(Net, self).__init__()
self.fc = nn.Linear(10, 3)
def forward(self, x):
x = self.fc(x)
return x
# Instantiate the network
net = Net()
# Define the criterion (loss function)
criterion = nn.CrossEntropyLoss()
# Generate some input data and corresponding target labels
inputs = torch.randn(3, 10)
targets = torch.tensor([1, 2, 0], dtype=torch.long)
# Forward pass
outputs = net(inputs)
# Compute the loss
loss = criterion(outputs, targets)
print(loss)
```

In the above example, we define a simple neural network with a single fully connected layer and 10 input units and 3 output units. We then instantiate the network and define the criterion (loss function) as the cross entropy loss. Finally, we generate some random input data and corresponding target labels, perform a forward pass through the network, and compute the loss.

It's important to note that the CrossEntropyLoss() function in PyTorch combines both the softmax and the cross entropy loss in one function, so it is not necessary to apply a softmax function to the output of the neural network before computing the loss.

It is also important to note that the targets passed to the criterion must be in the form of LongTensor and not Tensor, otherwise it will raise an error.

In conclusion, cross entropy loss is a popular choice for classification problems and is easily implemented in PyTorch using the torch.nn.CrossEntropyLoss() function. It measures the dissimilarity between the predicted probability distribution and the true distribution, and is commonly used in deep learning to train neural networks.

In addition to cross entropy loss, there are several other commonly used loss functions in deep learning. One popular choice is mean squared error (MSE) loss, which is commonly used in regression problems. It measures the average squared difference between the predicted value and the true value. MSE is implemented in PyTorch using the torch.nn.MSELoss() function.

Another popular loss function is hinge loss, which is commonly used in support vector machines (SVMs) for binary classification. It is implemented in PyTorch using the torch.nn.HingeEmbeddingLoss() function.

In addition to the loss function, the optimizer is also an important component of the training process. The optimizer is responsible for updating the model parameters based on the gradients computed during the backward pass.

A very popular optimization algorithm is Stochastic Gradient Descent (SGD) which is used in many deep learning models. Pytorch provides the torch.optim.SGD() function for implementing SGD.

One of the more recent optimization algorithm is Adam optimizer, which is a combination of RMSprop and SGD with momentum. Adam is computationally efficient, and it also adapts the learning rates of all parameters. Pytorch provides the torch.optim.Adam() function for implementing Adam optimizer.

To train a neural network using PyTorch, we typically loop through the training dataset, perform a forward pass through the network, compute the loss, perform a backward pass to calculate the gradients, and update the model parameters using the optimizer. This process is known as one training iteration, or one epoch. The number of training iterations is typically chosen based on the specific task and the size of the dataset.

In conclusion, cross entropy loss is a popular choice for classification problems, but there are other loss functions that are commonly used in deep learning such as MSE, hinge loss and etc. The optimizer is also an important component of the training process, and it is responsible for updating the model parameters based on the gradients computed during the backward pass. Popular optimizers include SGD, Adam and etc. Training a neural network in PyTorch involves looping through the training dataset, performing forward and backward passes, and updating the model parameters using the optimizer.

## Popular questions

- What is cross entropy loss used for in deep learning?

- Cross entropy loss is commonly used in classification problems to measure the dissimilarity between the predicted probability distribution and the true distribution.

- How is cross entropy loss implemented in PyTorch?

- Cross entropy loss is implemented in PyTorch using the torch.nn.CrossEntropyLoss() function.

- Is it necessary to apply a softmax function to the output of the neural network before computing the cross entropy loss in PyTorch?

- No, it is not necessary to apply a softmax function to the output of the neural network before computing the cross entropy loss in PyTorch. The CrossEntropyLoss() function in PyTorch combines both the softmax and the cross entropy loss in one function.

- What is the difference between cross entropy loss and mean squared error (MSE) loss?

- Cross entropy loss is commonly used in classification problems to measure the dissimilarity between the predicted probability distribution and the true distribution, while mean squared error (MSE) loss is commonly used in regression problems to measure the average squared difference between the predicted value and the true value.

- What are other commonly used loss functions and optimizers in deep learning besides cross entropy loss and SGD?

- Other commonly used loss functions in deep learning include mean squared error (MSE) loss, hinge loss, etc. Popular optimizers include Adam, RMSprop and etc.

### Tag

Classification.