The present work explores the theoretical limits of Machine Learning (ML) within the framework of Kolmogorov's theory of Algorithmic Probability, which clarifies the notion of entropy as Expected Kolmogorov Complexity and formalizes other fundamental concepts such as Occam's razor via Levin's Universal Distribution. As a fundamental application, we develop Maximum Entropy methods that allow us to derive the Erd\H{o}s--Kac Law in Probabilistic Number Theory, and establish the impossibility of discovering a formula for primes using Machine Learning via the Prime Coding Theorem.

翻译：本研究在科尔莫戈罗夫算法概率理论框架下探讨了机器学习的理论极限，该理论阐明了熵作为期望科尔莫戈罗夫复杂度的概念，并通过莱文通用分布形式化了奥卡姆剃刀等基本法则。作为核心应用，我们发展了最大熵方法，由此推导出概率数论中的厄尔多斯-卡克定律，并通过素数编码定理确立了利用机器学习发现素数公式的不可能性。