用神经网络构造高维共形场，实现自由玻色子与层间递推关系。
Conformal Fields from Neural Networks
- 通过限制( D+2)维神经网络到投影零锥，生成D维共形场。
- 精确计算多点关联函数，并在4维中完成共形块分解揭示谱结构。
- 适用于研究共形场论与深度神经网络的交叉应用，尤其适合理论物理与机器学习交叉研究者。
我们利用嵌入形式，通过将 (D+2) 维的洛伦兹不变齐次神经网络限制在投影零锥上，构造出 D 维的共形场。神经网络的参数空间描述可用于计算共形关联函数。在若干例子中，我们精确求解了四点关联函数，并对4维情形进行了共形块分解以揭示其谱结构。部分分析借助了近期费曼积分的新方法。通过神经网络的无限宽高斯过程极限，实现了广义自由共形场论，成功构建了自由玻色子模型。扩展至深度网络时，每一层均可构造共形场，且存在递推关系连接其共形维度与四点函数。文中也讨论了数值实现方法。
原文摘要 · Abstract (English)
We use the embedding formalism to construct conformal fields in $D$ dimensions, by restricting Lorentz-invariant ensembles of homogeneous neural networks in $(D+2)$ dimensions to the projective null cone. Conformal correlators may be computed using the parameter space description of the neural network. Exact four-point correlators are computed in a number of examples, and we perform a 4D conformal block decomposition that elucidates the spectrum. In some examples the analysis is facilitated by recent approaches to Feynman integrals. Generalized free CFTs are constructed using the infinite-width Gaussian process limit of the neural network, enabling a realization of the free boson. The extension to deep networks constructs conformal fields at each subsequent layer, with recursion relations relating their conformal dimensions and four-point functions. Numerical approaches are discussed.
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