English(EN) Formalized Hopfield Networks and Boltzmann Machines

Lean~4 中形式化的 Hopfield 网络和玻尔兹曼机

作者 PulseAugur 编辑部 · [1 个来源] · 2026-09-16 04:00

研究人员使用 Lean~4 证明助手形式化了 Hopfield 网络和玻尔兹曼机，解决了验证神经网络行为的挑战。该形式化包括证明 Hopfield 网络的收敛性和用于模式编码的赫布学习的正确性。此外，它还涵盖了玻尔兹曼机的动力学和学习，通过对 Perron--Frobenius 定理的新颖形式化证明了其遍历性，从而确保收敛到唯一的平稳分布。 AI

影响增强了循环神经网络和随机神经网络的理论理解和可验证性。

排序理由该集群包含一篇详细介绍神经网络模型形式化的学术论文。[lever_c_demoted from research: ic=1 ai=1.0]

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报道来源 [1]

arXiv cs.LG TIER_1 English(EN) · Matteo Cipollina, Michail Karatarakis, Freek Wiedijk · 2026-09-16 04:00

形式化霍普菲尔德网络和玻尔兹曼机

arXiv:2512.07766v2 Announce Type: replace Abstract: Neural networks are widely used, yet their analysis and verification remain challenging. We present a Lean~4 formalization covering both deterministic and stochastic models. We first formalize Hopfield networks -- recurrent netw…

本文如何被排名

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形式化霍普菲尔德网络和玻尔兹曼机

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