发表机构
Northeastern University; NSF Institute for Artificial Intelligence and Fundamental Interactions（东北大学; 美国国家科学基金会人工智能与基本相互作用研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究探讨有限宽度神经网络模型（NN-QM、NN-FT）与常规欧几里得QFT的性质差异，提出方法分析有限参数下模型可保留与无法保留的特征。
AI 中文摘要
在温和假设下，任何量子力学（QM）模型或量子场论（QFT）都可表示为具有可数多个随机参数的神经网络集合。我们研究具有有限个参数的NN-QM和NN-FT模型的特征，例如宽度N<∞的前馈网络。我们发现，这类模型通常必须违反常规欧几里得QFT的某一性质，如反射正性或簇分解。我们提出多种互补方法，以理解在有限N下，QM和QFT中哪些特征可被保留、哪些无法保留。
英文摘要
Under mild assumptions, any quantum mechanical (QM) model or quantum field theory (QFT) admits a representation in terms of an ensemble of neural networks with countably many random parameters. We investigate the features of NN-QM and NN-FT models with finitely many parameters, such as a feedforward network of width $N < \infty$. We find that, generically, such models must violate one of the properties of conventional Euclidean QFTs, such as reflection positivity or cluster decomposition. We present several complementary ways of understanding which features can and cannot be preserved at finite $N$, both in QM and in QFT.
Comments37 pages
