Avoiding Coding Tricks by Hyperrobust Learning

The present work introduces and justiies the notion of hy-perrobust learning where one xed learner has to learn all functions in a given class plus their images under primitive recursive operators. The following is shown: This notion of learnability does not change if the class of primitive recursive operators is replaced by a larger enumerable class of operators. A class is hyperrobustly Ex-learnable ii it is a subclass of a recursively enumerable family of total functions. So, the notion of hyperrobust learning overcomes a problem of the traditional deenitions of robustness which either do not preserve learning by enumeration or still permit topological coding tricks for the learning criterion Ex. Hy-perrobust BC-learning as well as the hyperrobust version of Ex-learning by teams are more powerful than hyperrobust Ex-learning. The notion of bounded totally reliable BC-learning is properly between hyperrobust Ex-learning and hyperrobust BC-learning. Furthermore, the bounded totally reliably BC-learnable classes are characterized in terms of inn-nite branches of certain enumerable families of bounded recursive trees. A class of innnite branches of a further family of trees separates hyper-robust BC-learning from totally reliable BC-learning.