English(EN) Constructive Bounds for the Topological Expressivity of Neural Networks

新理论定义神经网络拓扑表达能力

作者 PulseAugur 编辑部 · [1 个来源] · 2026-10-12 04:00

研究人员为神经网络的拓扑表达能力开发了新的理论界限，将范围从二元分类扩展到回归和其他问题。该研究提出通过检查神经网络输出的贝蒂数来衡量拓扑表达能力，而不是仅仅关注其决策边界。研究结果为贝蒂数建立了上限，并为同胚于球体的空间提出了更紧密的界限。 AI

影响为理解神经网络在简单分类任务之外的能力提供了一个理论框架。

排序理由关于神经网络表达能力理论方面的学术论文。[lever_c_demoted from research: ic=1 ai=1.0]

AI 生成摘要 · Google Gemini · 来自 1 个来源。我们如何撰写摘要 →

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arXiv cs.LG TIER_1 English(EN) · Kosio Beshkov · 2026-10-12 04:00

神经网络拓扑表达能力的构造性界限

arXiv:2610.13931v1 Announce Type: cross Abstract: The expressivity of a neural network $\Phi$ describes the class of functions that a network can express. The term topological expressivity refers to a family of measures particularly suited to understand binary classification and …