Statistical Learning Theory
The field proving generalization bounds on how far true error can exceed training error — too loose to use directly, but explaining why data and capacity both matter.
PAC learning frames generalization as a probabilistic guarantee, and VC dimension measures a model class's raw capacity to fit arbitrary labelings. The resulting bound's numeric value is almost always too loose to act on, since it has to hold for every possible data distribution at once.
What survives practically is the shape of the argument: more data narrows the gap between training and true performance, more capacity widens it, and a held-out test set is never optional.