What is the reason for using the average of cross-entropy loss instead of its sum when training models like neural networks?

The cross-entropy loss is a commonly used loss function in machine learning for classification problems. It measures the difference between the predicted probability distribution and the true probability distribution of the classes. In training a model like a neural network, we use the cross-entropy loss to update the model's parameters such that it learns to better predict the correct class for each input sample.

When training a neural network, we typically use a batch of samples to update the model's parameters. The sum of the cross-entropy loss across all the samples in the batch would be proportional to the size of the batch. Therefore, using the sum of the cross-entropy loss would make the gradient update dependent on the batch size, which can be problematic for training the model on different batch sizes.

Instead, we use the average of the cross-entropy loss, which is obtained by dividing the sum of the cross-entropy loss by the number of samples in the batch. This way, the gradient update is not dependent on the batch size and the model can be trained on different batch sizes without changing the learning rate. Using the average of the cross-entropy loss also makes the loss value comparable across different batch sizes, which is useful for monitoring the training progress and evaluating the model's performance.