Topological Effects in Neural Network Field Theory
2026-04-02 • Machine Learning
Machine Learning
AI summaryⓘ
The authors extend neural network field theory to include discrete parameters that track topological features, allowing them to study phase transitions involving vortices. They successfully reproduce the Berezinskii–Kosterlitz–Thouless transition, which describes how certain materials change their behavior at different temperatures due to vortex activity. They also demonstrate the T-duality symmetry of bosonic strings on a circle, confirming that swapping momentum and winding numbers leaves the physics unchanged, and show related mathematical transformations in the theory. This work connects neural network approaches with important concepts in topological and string theory.
Neural network field theoryTopological quantum numberBerezinskii–Kosterlitz–Thouless transitionVorticesSpin-wave critical lineT-dualityBosonic stringSigma modelBuscher rulesT-folds
Authors
Christian Ferko, James Halverson, Vishnu Jejjala, Brandon Robinson
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.