One of the key issues in machine learning is the characterization of the learnability of a problem. In some cases the learning is under-fitting, in other cases the learning is over-fitting. In both cases the dedicated generative AI may fail. We introduce a theoretical fitting indicator which, when negative, shows that the learning is over-fitting and when positive, indicates that the learning is under-fitting.
We analyze the variations of the indicator with classic logistic regression and quantum tomography. We show that when the source problem belongs to the learning class, the learning is over-fitting (but the indicator remains bounded), and when the problem does not belong to the learning class, the learning is under-fitting with an indicator increasing with the learning set.