English(EN) A Borel Concept Class of VC Dimension One with a Non-PAC Consistent Learner in ZFC

新的ZFC证明表明VC维度一不能保证PAC可学习性

作者 PulseAugur 编辑部 · [1 个来源] · 2026-09-01 04:00

研究人员已经证明，具有VC维度为一的Borel集概念类在存在一致学习规则的情况下，也不能保证PAC可学习性。这一在包含选择公理的策梅洛-弗兰克尔集合论（ZFC）中取得的发现，消除了先前认为对此类证明所必需的连续统假设的必要性。研究表明，有限的VC维度和Borel可测性本身不足以确保所有适当的一致学习规则的PAC可学习性。 AI

影响挑战统计学习理论的基础性假设，可能影响AI模型训练的理论保证。

排序理由详细介绍机器学习理论理论发现的学术论文。[lever_c_demoted from research: ic=1 ai=1.0]

在 arXiv cs.LG 阅读 →

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报道来源 [1]

arXiv cs.LG TIER_1 English(EN) · Mateus Jesus de Arruda Campos, Gabriel Fernandes, Vinicius de Oliveira Rodrigues · 2026-09-01 04:00

ZFC中具有非PAC一致学习器的VC维度为一的Borel概念类

arXiv:2608.30246v1 Announce Type: cross Abstract: The fundamental theorem of statistical learning states that, under suitable measurability assumptions, finite Vapnik--Chervonenkis (VC) dimension guarantees that every proper consistent learning rule is probably approximately corr…

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ZFC中具有非PAC一致学习器的VC维度为一的Borel概念类

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