Recursively Enumerably Representable Classes and Computable Versions of the Fundamental Theorem of Statistical Learning

A recent study published on arXiv investigates computable probably approximately correct (CPAC) learning and reveals that the classical Fundamental Theorem of Statistical Learning does not hold in this computable setting. This finding challenges the direct applicability of the theorem when restricted to computable functions. However, subsequent research has developed adaptations of the theorem tailored for computable functions, thereby extending its relevance. These advancements provide new insights into PAC learnability under computability constraints, enriching the theoretical understanding of learning processes in computational contexts. The study and related work collectively highlight the nuanced relationship between classical statistical learning theory and computability considerations. This evolving perspective may influence future research directions in machine learning theory, particularly in areas where algorithmic computability is a critical factor.