I must tell you that your intuitions are not wrong.
Many language models do predict.
In this case, they either try to predict what the next word (or character, or sub-character in case of Chinese, Japanese, etc.- this is totally the decision of the DS) is , or what some "masked" word are.
w_i becomes w_(i-1) in the sequence
where w_i is the last word generated
The ones that are trained to be able to predict the next word are the ones that are good generators.
Many language models do predict.
In this case, they either try to predict what the next word (or character, or sub-character in case of Chinese, Japanese, etc.- this is totally the decision of the DS) is , or what some "masked" word are.
The ones that are trained to be able to predict the next word are the ones that are good generators.