Fermions and Supersymmetry in Neural Network Field Theories

• URL: http://arxiv.org/abs/2511.16741v1
• Date: Thu, 20 Nov 2025 19:00:05 GMT
• Title: Fermions and Supersymmetry in Neural Network Field Theories
• Authors: Samuel Frank, James Halverson, Anindita Maiti, Fabian Ruehle,
• Abstract summary: We introduce fermionic neural network field theories via Grassmann-valued neural networks.<n>Free theories are obtained by a generalization of the Central Limit Theorem to Grassmann variables.
• Score: 2.904892426557913
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce fermionic neural network field theories via Grassmann-valued neural networks. Free theories are obtained by a generalization of the Central Limit Theorem to Grassmann variables. This enables the realization of the free Dirac spinor at infinite width and a four fermion interaction at finite width. Yukawa couplings are introduced by breaking the statistical independence of the output weights for the fermionic and bosonic fields. A large class of interacting supersymmetric quantum mechanics and field theory models are introduced by super-affine transformations on the input that realize a superspace formalism.

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