用神经网络模拟量子场论，揭示了权重动态与物理场的深层对应。
Emergent field theories from neural networks
- 将哈密顿系统与神经网络学习过程建立对偶关系，激活与学习动态对应位置动量方程。
- 对称权重张量对应克莱因-戈尔登场，反对称因子对应狄拉克场，精确匹配物理结构。
- 适合对量子场论与深度学习交叉感兴趣的科研人员，为理论物理提供新计算范式。
我们建立了哈密顿系统与基于神经网络的学习系统之间的对偶关系。证明了位置和动量变量的哈密顿方程分别对应不可训练变量的激活动力学和可训练变量的学习动力学。该对偶关系被用于通过神经网络的激活与学习动态建模多种场论。对于克莱因-戈尔登场，对应的权重张量为对称；而对于狄拉克场，权重张量必须包含反对称张量因子。权重和偏置张量的动态分量分别对应规范场的时空分量。
原文摘要 · Abstract (English)
We establish a duality relation between Hamiltonian systems and neural network-based learning systems. We show that the Hamilton's equations for position and momentum variables correspond to the equations governing the activation dynamics of non-trainable variables and the learning dynamics of trainable variables. The duality is then applied to model various field theories using the activation and learning dynamics of neural networks. For Klein-Gordon fields, the corresponding weight tensor is symmetric, while for Dirac fields, the weight tensor must contain an anti-symmetric tensor factor. The dynamical components of the weight and bias tensors correspond, respectively, to the temporal and spatial components of the gauge field.
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