标题： 可学习性可以独立于ZFC公理：解释与启示 显示英文标题

标题： Learnability Can Be Independent of ZFC Axioms: Explanations and Implications

摘要： 在本-戴维等人发表的《可学习性可能是不可判定的》一文中，他们证明了理论机器学习领域的一个独立性结果。 特别是，他们定义了一种新的学习类型，称为估计最大值（EMX）学习。 他们认为这种学习类型与其他概念，如 PAC 学习、Vapnik 的统计学习框架以及其他一般学习设置相一致。 然而，使用一些集合论技术，他们表明 EMX 设置中的某些学习问题与 ZFC（策梅洛-弗兰克尔集合论公理系统）独立。 具体来说，他们证明了 ZFC 无法证明或否定 [0,1] 区间上有限子集的 EMX 学习能力。 此外，他们证明的方式表明，EMX 不可能存在特征维度；因此，一般学习设置也不存在特征维度。 在这里，我将解释他们的发现，讨论这些发现的一些局限性，并提出一些如何消除这种不可判定性的建议。 第 2-3 部分将解释论文的结果，第 4-5 部分将讨论一些局限性和下一步工作，第 6 部分我将总结。 显示英文摘要

摘要： In Ben-David et al.'s "Learnability Can Be Undecidable," they prove an independence result in theoretical machine learning. In particular, they define a new type of learnability, called Estimating The Maximum (EMX) learnability. They argue that this type of learnability fits in with other notions such as PAC learnability, Vapnik's statistical learning setting, and other general learning settings. However, using some set-theoretic techniques, they show that some learning problems in the EMX setting are independent of ZFC. Specifically they prove that ZFC cannot prove or disprove EMX learnability of the finite subsets on the [0,1] interval. Moreover, the way they prove it shows that there can be no characteristic dimension for EMX; and, hence, for general learning settings. Here, I will explain their findings, discuss some limitations on those findings, and offer some suggestions about how to excise that undecidability. Parts 2-3 will explain the results of the paper, part 4-5 will discuss some limitations and next steps, and I will conclude in part 6.