Why can cross entropy loss be used to characterize loss

This paper is mainly about why the cross entropy loss can be used to calculate the cost , Mainly write ideas , Don't explain in detail .
1. The amount of information -log(p)----> Information entropy -plog(p) （ The amount of information expected ）
    There is only one distribution
2. Further introduce KL The divergence , At this time, there are two distributions , Use at this time p Represents the true distribution ,q Represents the distribution of the forecast
      plog(p/q)

      KL Divergence is the distance between two distributions

3. In machine learning and deep learning , What we want is the distribution learned by the model Pmodel As close to the real distribution of data as possible Preal.

So according to KL The divergence , We minimize Pmodel and Ptraining Of KL Divergence is enough .

And then we went to KL Make a change in divergence as follows , In the formula p It means Ptraining,q It means the distribution of model learning derivatives Pmodel.

In the machine （ depth ） I am learning , Distribution of training data p(x) It has been fixed , that   Is a fixed value , So we minimize KL The divergence , It is approximately equal to minimizing cross entropy .