标题： 量子场论在神经元上的微扰展开的可行性 显示英文标题

标题： Viability of perturbative expansion for quantum field theories on neurons

摘要： 神经网络（NN）架构打破了参数的统计独立性，被提出作为一种新的方法来模拟局部量子场论（QFT）。在无限神经元数量极限下，单层NN可以精确再现QFT结果。本文以标量$\phi^4$理论在$d$欧几里得维度为例，考察了该架构在有限神经元数量$N$下对局部QFT微扰计算的可行性。我们发现，重整化后的$O(1/N)$对两点和四点关联函数的修正产生微扰级数，对紫外截断敏感，因此收敛性较弱。我们提出了对该架构的修改以改善这种收敛性，并讨论了理论参数和N的缩放限制，使我们能够提取准确的场论结果。 显示英文摘要

摘要： 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 $\phi^4$ 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.