[2604.02313] Topological Effects in Neural Network Field Theory

High Energy Physics - Theory arXiv:2604.02313 (hep-th) [Submitted on 2 Apr 2026] Title:Topological Effects in Neural Network Field Theory Authors:Christian Ferko, James Halverson, Vishnu Jejjala, Brandon Robinson View a PDF of the paper titled Topological Effects in Neural Network Field Theory, by Christian Ferko and 3 other authors View PDF HTML (experimental) Abstract:Neural network field theory formulates field theory as a statistical ensemble of fields defined by a network architecture and a density on its parameters. We extend the construction to topological settings via the inclusion of discrete parameters that label the topological quantum number. We recover the Berezinskii--Kosterlitz--Thouless transition, including the spin-wave critical line and the proliferation of vortices at high temperatures. We also verify the T-duality of the bosonic string, showing invariance under the exchange of momentum and winding on $S^1$, the transformation of the sigma model couplings according to the Buscher rules on constant toroidal backgrounds, the enhancement of the current algebra at self-dual radius, and non-geometric T-fold transition functions. Comments: Subjects: High Energy Physics - Theory (hep-th); Machine Learning (cs.LG) Cite as: arXiv:2604.02313 [hep-th]   (or arXiv:2604.02313v1 [hep-th] for this version)   https://doi.org/10.48550/arXiv.2604.02313 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Christian Ferko [view email] [v1] Thu, 2 Apr ...