Title: Neural Network Field Theory: Fermions and Supersymmetry

Abstract:  Based on a duality between Neural Network (NN) architectures, the backbone of modern AI/ML, and field theory, the Neural Network Field Theory (NNFT) correspondence offers a robust, interpretable, and training-free simulation framework for scalar, fermionic, and supersymmetric field theories. By constraining NNs in a maximally physics-informed manner, this approach eliminates the need for optimization altogether and guarantees vanishing generalization error (test loss) for any out-of-distribution dataset. Building on earlier results for free scalars and interacting $\lambda \phi^4$ theories, I will present the engineering of fermionic field theories via Grassmann-valued NNFTs. As in the scalar case, free fermionic NNFTs arise from a Grassmann generalization of the Central Limit Theorem, enabling the realization of free Dirac spinors at infinite width and four-fermion interactions at finite width. Yukawa couplings naturally emerge by breaking the statistical independence of the NN output weights, associated with fermionic and bosonic fields. A broad class of interacting supersymmetric quantum-mechanics and field-theory models is further made accessible by implementing super-affine transformations on the NN input space that realizes a superspace formalism. Altogether, the NNFT correspondence provides a principled and efficient route to sampling scalar, fermionic, and supersymmetric field configurations, and is directly applicable to computing observables such as correlators on a lattice.This talk is based on: https://arxiv.org/abs/2511.16741

https://lbnl.zoom.us/j/94928022788?pwd=emVQWG1mTnhSbHVqekVuenk0VEVQZz09