用神经网络构造共形缺陷，实现对称性与可解释性的结合。
Conformal Defects in Neural Network Field Theories
- 通过指定网络结构和参数先验，构建共形不变缺陷
- 在两个标量场模型中验证了缺陷相关函数的展开形式
- 为神经网络场论中的缺陷研究提供新视角，适合理论物理与机器学习交叉研究者
神经网络场论（NN-FTs）是一种通过指定网络架构和参数先验来构建任意场论（包括共形场论）的新方法。本文提出了一种在这些NN-FTs中构造共形不变缺陷的形式化框架。我们在两个神经网络标量场理论的简化模型中展示了该方法的有效性。进一步地，我们发展了类似缺陷算符乘积展开（defect OPE）的展开形式，并在两点关联函数中给出了其神经网络解释。
原文摘要 · Abstract (English)
Neural Network Field Theories (NN-FTs) represent a novel construction of arbitrary field theories, including those of conformal fields, through the specification of the network architecture and prior distribution for the network parameters. In this work, we present a formalism for the construction of conformally invariant defects in these NN-FTs. We demonstrate this new formalism in two toy models of NN scalar field theories. We develop an NN interpretation of an expansion akin to the defect OPE in two-point correlation functions in these models.
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