用神经网络模拟量子场论，发现有限节点下微扰展开收敛性差
Viability of perturbative expansion for quantum field theories on neurons
- 用单层神经网络模拟量子场论，打破参数统计独立性
- 有限节点数下两点、四点关联函数修正项对紫外截断敏感，微扰级数弱收敛
- 提出改进架构并给出参数与节点数的缩放关系以提升精度
提出一种打破参数统计独立性的神经网络架构，用于模拟局域量子场论（QFT）。在神经元数量无限时，单层网络可精确重现QFT结果。本文以 $d$ 维欧氏空间中的标量 $ϕ^4$ 理论为例，研究有限神经元数 $N$ 下该架构在微扰计算中的可行性。发现重整化后的 $O(1/N)$ 修正对两点和四点关联函数产生依赖于紫外截断的微扰级数，导致弱收敛。为此提出架构改进方案，并讨论理论参数与 $N$ 的缩放关系，以确保能提取准确的场论结果。
原文摘要 · Abstract (English)
Neural Network (NN) architectures that break statistical independence of parameters have been proposed as a new approach for simulating local quantum field theories (QFTs). In the infinite neuron number limit, single-layer NNs can exactly reproduce QFT results. This paper examines the viability of this architecture for perturbative calculations of local QFTs for finite neuron number $N$ using scalar $ϕ^4$ theory in $d$ Euclidean dimensions as an example. We find that the renormalized $O(1/N)$ corrections to two- and four-point correlators yield perturbative series which are sensitive to the ultraviolet cut-off and therefore have a weak convergence. We propose a modification to the architecture to improve this convergence and discuss constraints on the parameters of the theory and the scaling of N which allow us to extract accurate field theory results.
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