English(EN) Persistent Homology as a Theory of Emergent Structure

新理论利用持久同调解释涌现结构

作者 PulseAugur 编辑部 · [1 个来源] · 2026-06-11 04:00

一篇新的研究论文提出将持久同调作为理解各种系统中涌现结构的数学框架。该理论认为，持久的、非平凡的同调类代表了尽管底层微观变化但仍然稳定的宏观特征。这种方法将涌现视为一个测量问题，使用收缩相似图和霍奇分解等工具来预测从流体动力学到神经网络和社会系统等现象中的鲁棒性和分层组织。 AI

排序理由该集群包含一篇发表在arXiv上的研究论文。[lever_c_demoted from research: ic=1 ai=1.0]

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arXiv cs.LG TIER_1 English(EN) · Xin Li · 2026-06-11 04:00

持久同调作为涌现结构理论

arXiv:2507.03065v2 Announce Type: replace Abstract: Why do some macroscopic structures remain identifiable even though their microscopic constituents continually change? Vortices persist while fluid parcels turn over, neural memories persist while spikes and synapses fluctuate, a…