Learning all subfunctions of a function

Abstract

Sublearning, a model for learning of subconcepts of a concept, is presented. Sublearning a class of total recursive functions informally means to learn all functions from that class together with all of their subfunctions. While in language learning it is known to be impossible to learn any infinite language together with all of its sublanguages, the situation changes for sublearning of functions. Several types of sublearning are defined and compared to each other as well as to other learning types. For example, in some cases, sublearning coincides with robust learning. Furthermore, whereas in usual function learning there are classes that cannot be learned consistently, all sublearnable classes of some natural types can be learned consistently. Moreover, the power of sublearning is characterized in several terms, thereby establishing a close connection to measurable classes and variants of this notion. As a consequence, there are rich classes which do not need any self-referential coding for sublearning them.