English(EN) On the Approximation Complexity of Matrix Product Operator (MPO) Born Machines

新研究详细阐述了MPO生成模型近似中的NP-hard挑战

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

一篇新发表在arXiv上的论文探讨了矩阵乘积算子（MPO）生成模型（一种用于概率建模的张量网络模型）的理论近似能力。该研究提出了一个负面结果，证明了使用多项式键MPO-BM来近似具有有界KL误差的任意连续目标是一个NP-hard问题。然而，该论文也提供了一个积极的发现：对于基于分数的变分推断，满足对数-索伯列夫不等式的目标在与损失诱导哈密顿量相关的特定条件下，可以得到具有可证明KL保证的近似。 AI

影响这项研究有助于加深对张量网络模型概率建模的理论理解，可能为未来复杂数据表示的进步提供信息。

排序理由该集群包含一篇同行评审的学术论文，详细介绍了机器学习领域的理论发现。[lever_c_demoted from research: ic=1 ai=1.0]

在 arXiv cs.LG 阅读 →

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arXiv cs.LG TIER_1 English(EN) · Chao Li, Zerui Tao, Yuchen Cong, Jian Xu, Qibin Zhao · 2026-10-12 04:00

关于矩阵乘积算子（MPO）玻尔兹曼机的近似复杂度

arXiv:2605.11471v2 Announce Type: replace Abstract: Matrix product operator Born machines (MPO-BMs) are tractable tensor-network models for probabilistic modeling, yet their approximation capabilities remain poorly understood in theory. In this paper, we characterize these capabi…

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关于矩阵乘积算子（MPO）玻尔兹曼机的近似复杂度

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