Emergent field theories from neural networks

• URL: http://arxiv.org/abs/2411.08138v1
• Date: Tue, 12 Nov 2024 19:30:18 GMT
• Title: Emergent field theories from neural networks
• Authors: Vitaly Vanchurin,
• Abstract summary: We show that the Hamilton-Jacobi equations for position and momentum variables correspond to the equations governing the activation dynamics of non-trainable variables. The duality is then applied to model various field theories using the activation and learning dynamics of neural networks.
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• Abstract: We establish a duality relation between Hamiltonian systems and neural network-based learning systems. We show that the Hamilton-Jacobi 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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