machine learning - Model Compression why it works very well? Explanation please -

model compression: let me explain in simple terms.

lets x_train (features), y_train (target) training data.

x_train, y_train ------> m1 (example: decision tree)  x_train --------> m1 ----> y_pred (predicted y x_train) 

now

case 1:     x_train, y_pred -----------> m2 (example: model not decision tree)      x_train ---------------> m2  ----------> y_pred1   case 2:     x_train, y_train -----------> m2 (example: model not decision tree)      x_train ---------------> m2  ----------> y_pred2 

now compute auc score m2.

case 1:  auc (y_pred, y_pred1) case 2:   auc (y_train, y_pred2) 

case 1 auc higher case 2 auc. case 1 called model compression. intuition behind it. of course auc calculated probabilities.

the intuition behind result conditional entropy of y_pred given x_train zero. m2 can learn x_train-> y_pred more in second case.