高斯普适性及其在张量网络机器学习中的破缺
Gaussian Universality and Its Breakdown in Tensor-Network Machine Learning
浏览论文内容
中文总结 AI 辅助
本文解析研究了张量网络机器学习中高斯普适性的出现与破缺条件，证明大键维下模型收敛于高斯过程，而大物理维下全局可观测量出现非高斯修正，揭示其受参数数、架构缩放、可观测量局域性和谱性质共同控制。
中文摘要 AI 辅助
高斯过程极限在描述过参数化机器学习模型时非常强大，然而它们在结构化张量网络架构中的有效性仍不清楚。这里我们解析性地提出一种基于矩的方法，该方法精确识别了张量网络学习模型中高斯普适性出现和破缺的条件，重点关注矩阵乘积态。我们证明在大键维极限下，具有局域和全局可观测量（observables）的学习模型都收敛到高斯过程，并给出了高阶矩偏差的显式有限尺寸界。而在大物理维极限下，高斯普适性不再持续：虽然具有局域可观测量的模型保持高斯过程行为，但全局情况表现出持续的非高斯修正。我们的结果表明，张量网络学习中的高斯过程行为不仅受参数数量控制，还受架构缩放、可观测量的局域性以及谱性质的影响。
英文摘要
Gaussian-process limits are powerful in describing overparameterized machine learning models, yet their validity in structured tensor-network architectures remains unclear. Here we analytically present a moment-based approach that identifies precise conditions for the emergence and breakdown of Gaussian universality in tensor-network learning models, with a focus on matrix product states. We prove that in the large bond dimension limit, the learning models with both local and global observables converge to Gaussian processes, with explicit finite-size bounds on higher-order moment deviations. Whereas in the large physical dimension limit, the Gaussian universality no longer persists: while the models with local observables retain Gaussian-process behavior, those global cases exhibit persistent non-Gaussian corrections. Our results reveal that Gaussian-process behavior in tensor-network learning is controlled not only by parameter number, but also by architectural scaling, observable locality, and the spectral properties.
发表机构
- Nankai University（南开大学）
- Max Planck Institute of Quantum Optics（马克斯·普朗克量子光学研究所）
机构由 AI 辅助整理，请以论文原文为准。
