神经网络共形场论的代数视角注记
Notes on algebraic perspective on neural network conformal theories
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中文总结 AI 辅助
本文从代数视角深入分析神经网络共形场论中关联函数结构与算符关系，并提出构造该理论代数的具体方案。
中文摘要 AI 辅助
神经网络共形场论首次在文献[Halverson:2024axc]中引入，并从无限宽神经网络的系综中计算了精确的二点、三点和四点关联函数。特别地，任何标量算符的四点关联函数满足交叉对称性，且不同通道间的共形分块分解在无需对矩施加任何约束的情况下保持一致。研究发现了一个具有相同标度维数的无限简并算符塔。在本注记中，我们更仔细地审视了关联函数的结构以及算符之间的关系。我们还提出了一种构造该理论代数的方案。
英文摘要
Neural network conformal theories were first introduced in \cite{Halverson:2024axc} and exact two-, three- and four-point correlators were computed from an ensemble of infinite-width neural networks. In particular, the four-point correlator of any scalar operator satisfied crossing-symmetry and conformal block decomposition across different channels were in agreement without any constraint on moments. An infinite tower of degenerate operators with the same scaling dimension were found. In this note, we take a closer look at the structure of correlators and relation between operators. We also layout a recipe to construct the algebra of the theory.
发表机构
- Kavli Institute for Theoretical Physics（卡弗里理论物理研究所）
- Department of Physics, Northeastern University（东北大学物理系）
- The NSF AI Institute for Artificial Intelligence and Fundamental Interactions（美国国家科学基金会人工智能基础相互作用研究所）
- Beijing Institute of Mathematical Sciences and Applications（北京数学与应用数学研究所）
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